Tag Archives: poker stars

Social Gaming Features Gain Popularity at Online Poker Rooms

 

PokerStars November Mission Week promotion adds another mission format to the social gaming features being adopted by major poker rooms.

Social gaming features have made their way into the promotional portfolio of some of the top online poker rooms. This month, PokerStars joins the club with…

Social gaming features have made their way into the promotional portfolio of some of the top online poker rooms. This month, PokerStars joins the club with November Mission Weeks and MPN adds “Achievements.”

PokerStars

November Mission Weeks provide a promotional tool for PokerStars to encourage higher volume play. At the start of each week players select a mission appropriate to their game preferences and likely volume of play. At its simplest, players are setting themselves a VIP points (VPP) target for the week.

If they hit the target, they receive a freeroll “All In Shootout” tournament entry where the prize pools range from $10k to $250k. The “All In Shootout” format means that players that don’t turn up will be automatically put all in on every hand.

MPN

MPN has just introduced “Achievements” along similar lines. Achievements reward players with a badge that can be displayed at the table for completing a series of challenges.

Players who win three badges by the end of November will be entered into a $500 freeroll tournament.

Each achievement comes with a “Pips” rating. The more difficult the achievement, the more Pips players earn for completing it. Pips add up to a score and MPN suggests that players can challenge their friends to beat their score.

PartyPoker

Since introducing missions with its radical software upgradePartyPoker has regularly introduced new missions of varying complexity. An example from last month is the WPTMontreal Mission. Players who achieved the mission tasks were given a freeroll entry into a tournament that awarded three seats—one a full package—to the WPT Montreal.

The tasks that players had to complete to achieve the mission crossed several game formats, and each was tenuously linked to some facet of Canadian history, geography or culture.

Winamax

French regulated site Winamax has taken a different slant on the mission idea. The challenge is called “Guns and Glory” and players move up in levels as they collect experience points (XP).

Starting with a plastic sword at level one, new weapons are provided as players move up levels. Players can wear this weapons with a chosen character avatar, and with increased levels, new character avatars become available.

It is likely that missions at online poker rooms are going to become a permanent fixture. The combination of social and financial rewards make them an effective method of encouraging more play and adding entertainment value to existing players’ poker experience.

http://pokerfuse.com/features/special-feature/social-gaming-features-gain-popularity-at-online-poker-rooms-21-11/

Optimal Postflop Play in NLHE 6-max – Part 6

1. Introduction
This is Part 6 of the article series “Optimal Postflop Play in NLHE 6-max” where we’ll study optimal strategies for heads-up postflop play in NLHE 6-max.

I Part 1, Part 2, Part 3, and Part 4 we discussed postflop play heads-up in position after flatting preflop. Then in Part 5 we began working on postflop strategies for the preflop raiser out of position in this scenario.

We’ll continue this work in Part 6. Some of the things we’ll discuss are:

  • More about the consequences of choosing to bet a street
  • Show mathematically that the raiser’s optimal turn/river strategies defends her against any-two-cards floating
  • Study the effect of the raise’s opening range on her postflop strategies

We’ll warm up with a discussion of “follow through” when you have chosen to bet a street:

2. On the consequences of choosing to bet a street

The scenario we studied in Part 5 were based on the following set of assumptions:

  • Alice (100 bb) raises out of position and Bob (100 bb) flats in position
  • Alice’s standard bet sizing on the flop/turn/river (those times she chooses to bet) is 0.75 x pot/0.75 x pot/0.60 x pot
  • Alice c-bets 100% of her preflop range on the flop

Now Bob has position on Alice, and he defends postflop using the optimal strategies we built for him in Parts 1-4 of this article series. He will raise some hands, flat some hands, and fold some hands. The most interesting scenarios for us to study are the ones where Bob flats, so that Alice gets a bet/check-raise/check-call/check-fold decision to make on the next street. The reason these scenarios are the most interesting ones for us is that the rest of the hand will often be automatic when Bob raises anywhere (most of the time Alice will fold her weak hands and 3-bet her best hands for value, and there will be no real decisions to make.

So we will here focus on the postflop scenarios where Alice has the betting lead on the turn after c-betting the flop and getting called. As discussed in Part 5, it’s ow important for her to use a turn strategy adapted to her c-betting range. If she gives up too easily on the turn after c-betting the flop and getting called, Bob can exploit her by floating her c-bet with any two cards, planning to auto-bluff turns those times Alice checks.

To illustrate how this can happen, let’s warm up with some simple math. Let’s say that Alice openraises her default ~25% range from CO, and Bob flats on the button. The flop comes dry and without any possible draws:

Alice now decides to c-bet her entire range, since Bob’s preflop flatting range should mostly miss this flop. This is a reasonable assumption, since Bob’s default preflop flatting range in this case is:

IP flat list after ~25% CO openraise

JJ-22
AQs-ATs AQo-AJo
KTs+ KQo
QTs+
JTs
T9s
98s

140 combos
11%

We have the tools for checking this assumption, and we can use Pokerazor to calculate how often Bob’s flatting range has flopped a pair or better on this dry texture:

We see from the figure above that there’s only a 39.4% chance that Bob has flopped one pair or better (see the list “Cumulative frequency” to the right). Alice’s c-bet is 0.75 x pot, so if she picks up the pot more than 0.75/(1 + 0.75) =43% of the time, she profits from making a c-bet with any two cards. Therefore, if Bob only calls the c-bet with a pair or better (and there are no draws he can have), a c-bet will be automatically profitable for Alice, since Bob then folds 100 – 39.4 =60.6%.

But this does not mean that Alice’s any-two-cards c-bet is profitable against a good, thinking player that understands the situation. Bob knows that Alice knows that his range has missed the flop more than half the time. He also knows that if he folds more than 100 – 43 =57%, he is giving Alice a license to steal with any two cards. Therefore, Bob will also call the flop with some hands without a pair or a good draw, for example the overcard hands AK and AQ.

These calls that Bob makes with overcards and weak draws (when he has any), are floats. Bob bases this on a combination of several factors:

  • The chance of getting a bluffing opportunity on a later street
  • The chance of checking the hand down on the turn and river and winning a showdown unimproved
  • The chance of checking the hand down on the turn and river and winning a showdown after improving marginally (for example after making a low pair on the turn)
  • The chance of making the best hand on a later street and getting paid (in particular, having good implied odds when he floats with a good draw)

Note that may of the thin flop calls/floats Bob makes can’t be justified based on pot-odds alone, if Bob’s plan is to play strictly fit-or-fold on later streets. We’re only getting pot-odds 1.75 : 0.75 =2.33 : 1 on the flop, and we’re calling with a hand like AQ only to spike a pair, we need (47 – 6) : 6 =7 : 1 to call and draw to 6 outs on the turn (and not planning to sometimes steal the pot when we miss).

For a new NLHE player these thin flop calls might seem “incorrect”, since Bob seems to call with hands like AQ only to draw to two overcards, hoping to make a pair on the turn. But this is not the only reason why Bob calls. Keep in mind he is already beating many hands in Alice’s wide and weak c-betting range, and he will sometimes with unimproved against these hands. For example, he can win with ace high when the turn and the river goes check-check. Bob will also be able to steal some pots on the turn or river if he chooses to use AQ as a bluff when Alice checks to him.

Therefore, since Bob will often (and correctly) float the flop without a pair or a good draw on dry flops, Alice can’t check and give up on the turn every time her flop c-bet gets called. She knows that her 25% CO range is weak on the flop, and she knows that Bob knows this as well:

Alice’s Default 25% CO-range

22+
A2s+ A9o+
K9s+ KQo
Q9s+ QTo+
J8s+ JTo
T8s+
97s+
87s
76s
65s

326 combos
25%

Not only is Alice’s c-betting range (which is her entire preflop range) weak on this flop, but it’s weaker than Bob’s range!. We see from the figure above that the chance of Alice having flopped one pair or better is a measly 25.4%, compared to 39.4% for Bob’s range. The observant and optimally playing Bob can therefore easily make many light flop floats, hoping Alice will screw up on the turn or river and give him opportunities to steal profitably with any two cards.

If Alice also plays optimally postflop, Bob can’t expect to profit from any-two-cards floating (as we’ll see in a minute), but at the very least he can float enough to prevent her from c-betting any two cards profitably (and we showed that this was possible for him in Part 5).

The gist of it is that Alice knows that Bob’s range is weak, but her range is weak as well. She knows this, Bob knows this, and Alice knows that Bob knows this. Therefore Alice can expect Bob to call his optimal 57% on this flop (and as discussed in previous articles, Bob chooses to slowplay his few monster hands on thus type of flop). So Alice can’t c-bet her entire preflop range on this dry flop without having a plan for how to 2-barrel/check-call/check-raise on later streets to prevent Bob from floating her profitably with any two cards. A player that thinks he is exploiting the player in position by c-betting a lot on dry flop, expecting lots of folds, runs the risk of getting counter-exploited by the player in position if this player understands what is going on.

To illustrate what can happen without a good turn/river plan, assume that Alice gives up on 50% of turns (and she will have no pair/no draw far more often than this after c-betting her entire 25% CO range on a dry flop). Now Bob can call her 0.75 x pot c-bet on the flop and then auto-bet turns when Alice checks. If Alice never check-calls or check-raises, Bob knows that he wins when she checks. Bob’s risk when floating the flop was then only 0.75 x flop-pot, since his turn bluff has zero risk (Always check-folds).

So Bob risked 0.75 x flop pot (P) to win 1.75P (the flop pot + Alice’s c-bet). 50% of the time he loses 0.75P and 50% of the time he wins 1.75P. The EV for his any-two-cards flop float is then:

EV (float) =0.50(+1.75P) + 0.50(-0.75P) =0.5P

Bob’s EV for floating the flop with a random hand against a weakly playing Alice was 1/2 of the flop pot. Not bad! So what should Alice do? In Part 5 we designed the following defense equation for Alice’s turn play after c-betting the flop and getting called:

2-barrel% + 1.75 x check-continue% =70%

where check-continue =check-raise or check-call. And the same equation also applied to river play after 2-barreling the turn and getting called:

3-barrel% + 1.75 x check-continue% =70%

Note that the mathematics does not tell us whether or not it’s correct for Alice to c-bet her entire range on the flop. What it does tell us is that when she has chosen to do so she will be vulnerable to any-two-cards floating if she is not willing to play the next street according to these defense equations.

There’s a subtle point buried here:

If you bet a street, and the thought of barreling 70% (or an equivalent combination of barreling, check-calling and check-raising) on the next street will make you feel sick, almost regardless of which card falls, you are probably betting too much on the current street

An obvious example would be if Alice elected to c-bet her entire 25% CO range on a coordinated flop like this one:

This range hits Bob’s solid preflop flatting range hard, as shown below:

Bob’s flatting rage is full of pocket pairs and suited/coordinated medium/high cards, and this is a very good flop for him. There a whopping 63.9% chance he has one pair or better, and he also has lots of gutshots, open-enders and flush draws in his range. Alice’s range has also connected often with this flop, but rarely hard (wide ranges hits lots of flops in various ways, but often in weak ways), and she is out of position to boot.

Therefore, c-betting this coordinated flop, planning to 2-barrel/check-call/check-raise optimally on the flop seems like a very bad and unprofitable idea for Alice. She ha to respect the fact that Bob’s preflop range has hit this flop harder than her range, and that he also has advantage of position. So Alice should check some of her weak hands (hands like 22, A2s, etc) instead of c-betting her entire range.

By removing weak hands from her flop c-betting range, Alice is setting herself up for reaching the turn with a stronger range those times she chooses to c-bet and she gets called. When her turn range is stronger, it will be easier and much more comfortable for her to play the turn optimally, according to the defense equations, since a larger fraction of her turn range now will be strong enough to 2-barrel, check-calling, or check-raising without feeling sick about having to do so.

The main point is that if you often find yourself on the turn, out of position after having c-bet the flop and gotten called, and without a hand you feel comfortable 2-barreling, check-calling or check-raising, you have a problem. You might try to fix this problem by check-folding a lot of turns so that you don’t spew more chips, but you will probably (and correctly) feel that the player in position is bluffing you a lot.

And then you might conclude “Playing the turn out of position is hard, I need to get better at it” without realizing that the root of your problem is located in your flop c-betting strategy. You should fix the problem by starting with your flop c-bet decisions on textures that are bad for you and good for your opponent. Check and give up with more weak hands on these flops, and I can guarantee that your turn decisions will become easier and more pleasurable those times you do c-bet and get called.

The next step for us is to verify that the raiser’s optimal turn/river barreling/check-calling/check-raising strategies that we designed in Part 5 in fact do defend her sufficiently against any-two-cards floating.

3. Verifying mathematically that the preflop raiser’s turn/river strategies defend her against any-two-cards floating
We’ll now show that Alice’s turn/river strategies according to the defense equation protects her from getting exploited by a player who floats her with random weak hands in position.

In Part 5 we verified that Bob’s optimal calling with a bluffcatcher in position defended him correctly against any-two-cards barreling from Alice. She could not make money by c-betting a random worthless hand on the flop and then continuing to bet the turn or river when called.

Here we’ll use the same method to show that Alice’s optimal turn/river strategies defends her against Bob’s floating with random worthless hands. We calculate the probabilities associated with all possible outcomes, find Bob’s EV for each of them, and then write out the total EV equation for his float.

We’re assuming that Bob is floating with a worthless hand on a dry flop (where Bob is calling with all hands he defends with). To keep the math simple, we’ll assume that Bob’s only chance to win is when Alice checks and gives up on a later street (he has 0% pot equity, and will never win a showdown). Bob’s plan is to call the c-bet on the flop, and then auto-bluff the turn when Alice checks. Those times Alice 2-barrels the turn, Bob always folds.

Alice’s strategy is to play the turn and river in such a way that random floating is not automatically profitable for Bob. She does this by building barreling/check-calling/check-raising ranges that satisfy the defense equations defined previously.

Alice’s strategy on the flop
Let the pot size be P on the flop. We begin by assuming Alice c-bets 0.75P with 100% of her opening range on a dry flop. Bob calls with his worthless float, planning to bluff the turn if checked to. The pot grows to P + 2 x 0.75P =2.5 P, and both players have put 0.75P into the pot postflop.

Alice’s strategy on the turn
We’ll show that Alice can make Bob’s flop floats break even by playing the turn according to the defense equation:

2-barrel% + 1.75 x check-continue% =70%

First, assume that Alice defends by only 2-barreling, so that check-continue% =0 and 2-barrel% =70.

– Alice 2-barrels: 70%:
– Alice check-raises/check-calls: 0%
– Alice check-folds: 30%

Bob then folds his float to Alice’s 2-barrel 70% of the time and loses his 0.75P flop call. 30% of the time he gets the opportunity to bluff the turn. Alice always check-folds, and Bob makes +1.75P (the flop pot + Alice’s c-bet).

The EV equation for Bob’s flop float is:

EV (float)
=0.70(-0.75P) + 0.30(+1.75P)
=-0.525P + 0.525P
=0

So Alice’s 2-barrel strategy makes it impossible for Bob to profit from floating the flop with any two cards. Now we look at the more general form of the equation where Alice also check-calls and check-raises. For example, assume Alice 2-barrels 35% (Bob folds), check-raises 10% (Bob bets and folds to the check-raise), and check-calls 10% (Bob bets and gives up when called). Bob then folds to Alice’s 2-barrels, auto-bets the turn when checked to, and gives up with his worthless hand when check-called or check-raised.

– Alice 2-barrels: 35%:
– Alice check-raises: 10%
– Alice check-calls: 10%
– Alice check-folds: 45%

Note that this strategy satisfies the defense equation since:

35% + 1.75(10% + 10%) =70%

35% of the time Bob folds his float to Alice’s 2-barrel and loses his 0.75P flop-call. 10% + 10% =20% of the time he bluffs the turn with a 0.75 x turn-pot bet, gets check-raised or check-called and gives up. Hen then bets 0.75 x turn-pot =0.75 x 2.5P =1.875P, and loses this amount in addition to his 0.75P flop-call for a total loss of -0.75P – 1.875P =-2.625P. The remaining 100 – 35 – 20 =45% of the time he bluffs the turn successfully and picks up the 2.5P pot, where 1.75P is profit (the flop pot + Alice’s 0.75P flop c-bet).

The EV equation for Bob’s float now becomes:

EV (float)
=0.35(-0.75P) + 0.20(-2.625P) + 0.45(+1.75P)
=-0.2625P -0.525P + 0.7875P
=0

And we see that Alice can also defend optimally and make Bob’s random floats break even by going from a 2-barrel/check-fold strategy to a 2-barrel/check-raise/check-call/check-fold strategy. She builds her 2-barreling, check-calling, and check-raising ranges so that they satisfy the defense equation, and Bob’s random flop floats can not make money.

4. The effect of the raiser’s preflop range on her postflop strategies
We end this article with a new set of flop/turn/river strategies for the flop example we worked through in Part 5. In that example, Alice started out with her 15% EP range:

~15% UTG range

22+
A9s+ AJo+
KTs+ KQo
QTs+
J9s+
T9s
98s
87s
76s
65s

194 combos
15%

Bob called with his standard “IP flat list” against an UTG raiser:

IP flat list after ~15% EP openraise

QQ-22
AKs-ATs AKo-AJo
KTs+ KQo
QTs+
JTs
T9s
98s

162 combos

Flop/turn/river came

4.1 Alice’s postflop strategy after 15% UTG-raise
Alice began by c-betting 100% of her preflop range on the flop, and Bob called (we know that he will defend on this type of dry flop by only calling). Then Alice used turn/river strategies designed to prevent Bob from floating her profitably with any two cards on the flop or turn. Alice’s flop7turn/river bet sizing was 0.75 x pot/0.75 x pot/0.60 x pot, and Bob called flop and turn. We found the following turn/river strategies for Alice, based on this bet sizing and the defense equation we derived previously:

  • Check-raise:
    {JJ} =3 combos
    Value bet:
    {99,66,33,J9s,AA-QQ,AJ} =41 combos
  • Check-call
    {KJs,QJs,JTs,TT,A9s} =18 combos
    Bluff:
    {QTs,AK,AQ,KQs} =40 combos

 

  • Check-raise:
    {99} =3 combos
    Value bet:
    {66,33,J9s,AA-QQ} =26 combos
  • Check-call:
    {AJ} =12 combos
    Bluff:
    {10 AK-combos} =10 combos

We’ll now estimate Alice’s turn/river strategies after starting out with a 25% openraise in CO. Bob flats the same preflop range as before, except for 3-betting QQ/AK for value instead of flatting them.

4.2 Alice’s postflop strategy after a 25% CO-raise
Alice openraises:

Alice’s default 25% CO-range

22+
A2s+ A9o+
K9s+ KQo
Q9s+ QTo+
J8s+ JTo
T8s+
97s+
87s
76s
65s

326 combos
25%

And the flop comes as before:

As before, Alice begins postflop play by c-betting 100% of her preflop range, and Bob calls. We have to estimate her new turn/river strategies, based on her opening range, card removal effects and the requirement that the defense equation should be satisfied.

On the turn Alice’s range is reduced from 326 to 282 combos:

She must now play the turn so that:

2-barrel% + 1.75 x check-continue% =70%

If she only 2-barrels, this corresponds to barreling 70% of 282 combos, which is 0.70 x 282 =197 combos. We can rewrite the defense equation as:

2-barrel-combos + 1.75 x check-continue-combos =197

Below is a suggestion for a turn strategy for Alice that satisfies the defense equation. The corresponding turn strategy after a 15% UTG openraise is listed for comparison:

Turn strategy after 25% CO-raise

  • Check-raise:
    {JJ} =3 combos
    Value bet:
    {99,66,33,J9s,AA-QQ,AJ,KJ,QJ,JT} =77 combos
  • Check-call
    {J8s,TT,A9s,T9s,98s,97s} =21 combos
    Bluff:
    {QTs,T8s,AK,AQ,KQ,KT,87s} =76 combos

Test of defense equation:

(77 + 76) + 1.75(3 + 21) =195 (optimal =197)

Turn strategy after 15% UTG-raise

  • Check-raise:
    {JJ} =3 combos
    Value bet:
    {99,66,33,J9s,AA-QQ,AJ} =41 combos
  • Check-call
    {KJs,QJs,JTs,TT,A9s} =18 combos
    Bluff:
    {QTs,AK,AQ,KQs} =40 combos

Test of defense equation:

(41 + 40) + 1.75(3 + 18) =118 (optimal =118)

Compared to play after an UTG raise Alice is now forced to barrel and check-call much thinner in order to protect herself against Bob’s floats. We will not discuss whether or not these ranges are too loose, but keep in mind what we discussed previously about setting ourselves up for weak turn ranges by c-betting too wide a range on the flop. The defense equation does not mention the quality of our turn ranges, only that they should defend against random floating. The looser we c-bet the flop, the looser we have to barrel/check-call/check-raise the turn in order to avoid getting exploited by floating. If we’re not careful, we might take this too far.

The solution to this problem (if in fact it becomes a real problem for us) is to check more weak hands on the flop so that we get to the turn with a stronger range after c-betting and getting called. As discussed previously, this is very important on draw-heavy flops that hit the preflop flatters range hard.

Here we’ll simply assume that Alice has chosen to c-bet her entire range on the flop, and that she is willing to take the consequences of her flop actions on the turn. She 2-barrels the turn with the value/bluff ranges above, and Bob calls again. Alice now has the following range on the river:

99,66,33,J9s,AA-QQ,AJ,KJ,QJ,JT} + {QTs,T8s,AK,AQ,KQ,KT,87s} =77 + 76 =153 combos

The river card doesn’t touch these ranges, and Alice still has 153 combos in her range after accounting for card removal effects:

If Alice defends her turn betting range only by 3-barreling, she needs to defend 70% of 153 combos which is 0.70 x 153 =107 combos. Using the defense equation we get:

2-barrel% + 1.75 x check-continue% =70%

 

2-barrel-combos + 1.75 x check-continue-combos =107

With the bet sizing 0.60 x pot on the river, Bob is getting 1.60 : 0.60 on a call, so Alice uses 0.60/(1.60 + 0.60) =27% bluffs in her 3-barreling range to make it break even for Bob to call with a bluffcatcher. So she uses 27/73 =0.37 bluff combos per value combo.

Below is a suggestion for a river strategy for Alice that satisfies the defense equation. The strategy corresponding to a 15% UTG openraise is listed for comparison:

River strategy after 25% CO-raise:

  • Check-raise:
    {99} =3 combos
    Value bet:
    {66,33,J9s,AA-QQ,AJ} =38 combos
  • Check-call:
    {KJ,QJ,JTs} =28 combos
    Bluff:
    {AK} =16 combos

Test of defense equation:

(38 + 16) + 1.75(3 + 28) =108 (optimal =107)

River strategy after 15% UTG-raise:

  • Check-raise:
    {99} =3 combos
    Value bet:
    {66,33,J9s,AA-QQ} =26 combos
  • Check-call:
    {AJ} =12 combos
    Bluff:
    {10 AK-combos} =10 combos

Test of defense equation:

(26 + 10) + 1.75(3 + 12) =62 (optimal =57)

The widening of our postflop ranges that we observed on the turn is carried over to the river, and Alice is forced to value bet and check-call thinner on the river in order to prevent Bob from floating her turn bet profitably with random weak hands. But note that there should also be an adjustment for Bob.

We have let Bob flat the same preflop range in both cases (except that he 3-bets QQ/AK against the CO raise but flats them against the UTG raise). But an observant and optimally playing Bob should adjust his preflop flatting range to Alice’s position. When Alice moves from UTG to CO her opening range widens and more difficult to play out of position. This means more preflop flatting hands should become profitable for Bob.

And since Bob also needs to defend his preflop range enough against Alice’s postflop barreling, he will be forced to widen his postflop ranges as well, if he starts by widening his preflop range when Alice widens hers. So a certain symmetry should develop in this scenario where both players loosen up preflop, and as a result are forced to loosen up postflop as well. When both players are forced to play wider and weaker ranges postflop, Alice can value bet and check-call thinner.

So even if Alice’s two postflop strategies for the 15% UTG range and the 25% CO range seem very different, it’s not necessarily a big problem for Alice in practice. If Bob has started out with a wider preflop range as well, he will have to call and value bet weaker hands himself.

5. Summary
We have gone one step further with our study of optimal postflop strategies as the preflop raiser out of position. We started with a discussion of what it means to follow up a bet made on the current street. Simply put, we’re committing ourselves to a certain amount of betting, check-calling and check-raising on the next street. If we’re not willing to do this, we’re opening ourselves up for getting exploited by loose floating by a player with position on us.

Then we used mathematics to show that the turn/river strategies we designed for the raiser defended her optimally against random floating (by making them break even).

Finally, we studied the effect of the raiser’s opening range by building a new set of turn/river strategies for Alice, corresponding to her opening a 25% CO range instead of the 15% UTG range used in the previous example from Part 5. This resulted in significantly looser postflop strategies. We noted that starting postflop play by c-betting 100% of our preflop range on the flop leads to looser turn/river ranges, and that c-betting 100% of a wide preflop opening range perhaps isn’t optimal, even if the flop is dry and without draws.

In Part 7 we’ll talk about:

  • Optimal bet sizing for the raiser out of position on a dry flop, when he knows that the flatter in position has a weak range (he can use bigger bets to maximize value)
  • The effect of the player in position slowplaying his monster hands on dry flops (the raiser now must be a bit cautious when value betting big on the turn and river)
  • Some simulations of EV where we let the raiser’s and the flatter’s postflop strategies meet, and use Pokerazor to calculate EV for the raiser’s barreling line

Good luck!
Bugs – See more at: http://en.donkr.com/Articles/optimal-postflop-play-in-nlhe-6-max—part-6-823#sthash.cVW6OWN8.dpuf

Optimal Postflop Play in NLHE 6-max – Part 5

1. Introduction
This is Part 5 of the article series “Optimal Postflop Play in NLHE 6-max” where we’ll study optimal strategies for heads-up postflop play in NLHE 6-max.

In Part 1, Part 2, Part 3 and Part 4 we discussed postflop play heads-up in position after flatting preflop. This is an important postflop scenario for us, since our preflop strategies include lots of flatting in position.

When we have position on the raiser it’s important that we defend enough postflop to prevent her from c-betting any two cards profitably on the flop. When we flat on the flop, we have to defend enough against her turn bets to prevent her from 2-barreling any two cards as a bluff, and the same goes for river play after we flat the turn. How often we defend on each street depends on the raiser’s bet sizing. The smaller she bets, the more hands we defend. This makes sens intuitively, since smaller bets means the raiser is getting a better prize on her bluffs (we should defend more), while we’re getting better pot-odds to continue (so more of our weak hands are getting the right prize to see the next street).

We have used the following standard bet sizes in the postflop articles:

– 0.75 x pot on the flop
– 0.75 x pot on the turn
– 0.60 x pot on the river.

If Alice raises preflop and Bob flats in position, Alice is getting pot-odds 1 : 0.75 on her flop and turn bets. She then automatically makes a profit if Bob folds more than 0.75/(1 + 0.75) =43% , so Bob has to defend at least 100 – 43 =57% against Alice’s c-bets and turn bets. On the river Alice’s pot-odds on a 0.6 x pot river bet are 1 : 0.60. She automatically makes a profit if Bob folds more than 0.6/(1 + 0.6) =38%, so Bob should defend the river at least 100 – 38 =62% to prevent this.

Bob’s total postflop strategy in position after flatting preflop is made up of of value raising, bluff raising and flatting on each street. But as we discussed in previous articles, it will be better for him to only defend by flatting on the driest flops (like 2 6 6 ) to prevent his flatting range from being weak and easy for Alice to read and play against on later streets.

Bob did not have this problem when flatting on coordinated flops (like J 9 3 ), since these flops hit his preflop flatting range much harder and gives him many strong hands/strong draws that he can raise for value. Furthermore, his flatting hands on this type of flop will often improve to strong hands on the turn. So Alice can’t assume Bob’s turn range is weak on a coordinated board, just because he flatted the flop. Therefore, it is on the dry flops that we often have scenarios where the raiser c-bets the flop, 2-barrels the turn, and 3-barrels the river, while the raiser is calling down in position with a weak range.

In these scenarios both players rarely have anything better than one pair. Forcing the other player to fold his weak one pair hands and good overcards is therefor an important value component in both players’ postflop strategies. For example, if the raiser c-bets A A on a Q 8 4 flop and the flatter folds 2 2 , the raiser has gained a lot.

The raiser out of position tries to achieve this by c-betting a lot as a bluff, and then sometimes bluffing again on the turn when called, and again on the river when called on the turn. And the player in position tries to win pots by calling down a lot with his one pair hands, but also sometimes floating with very weak hands, planning to bluff with these hands if the raiser checks and gives up on a later street.

We define a float as a call done either with a weak hand that can’t win a showdown unimproved (so we plan to often bluff on later streets if we get the chance) or a hand with mediocre showdown value that we are hoping to take cheaply to showdown (but we are too weak to call down if the raiser bets all 3 streets). Using this definition, calling with both T 9 and 2:heart: 2:spade: on a Q 8 4 flop would be floats.

In previous articles we have studies Bob’s strategies in position. In this article we’ll turn the tables and study Alice’s strategies out of position. We’ll start with the following model:

– Both players begin with 100 bb stacks
– Alice openraises preflop and Bob flats in position
– Alice c-bets her entire preflop range on the flop

This creates a turn/river dynamic between the two players those times Bob calls the flop. In this article we’ll only look at dry flops, since this lets us use two simplifying assumptions:

1. Alice begins by c-betting her entire preflop range (reasonable, since Bob’s preflop flatting range will be weak on dry flops)
2. Bob never raises the flop (reasonable, since it makes sense for him to slowplay his best hands on dry flops for reasons previously discussed)

Whether or non Alice should c-bet her entire range on dry flops is not something we’ll discuss here, but it is reasonable on dry flops. We’ll use this as an assumption in our model, since it can never be a big mistakes when we are heads-up against a preflop flatter that will often have missed a dry flop. Furthermore, we’ll limit our discussion to scenarios where Bob never has a hand strong enough to raise for value on any street. This puts him in a situation where he is either calling or folding on each street. This creates a postflop dynamic where:

– Bob needs to defend enough against Alice’s barreling on all 3 streets
– Alice needs to defend enough against Bob’s floats on the flop and turn

Bob’s task is to prevent Alice from having an automatically profitable bet/bet/bet strategy (3-barreling) with any two cards. Alice’s task is to prevent Bob from having an automatically profitable float with weak hands on the flop and turn.

Bob starts by calling Alice’s c-bet with many medium/weak hands that are not strong enough to call down. Alice’s job on the turn and river is then to play these streets in such a way that Bob can’t call the flop or turn with any two cards and make a profit. For example, if Alice c-bets 100% of her range on the flop, but then check-folds 2/3 of her range on the turn without ever check-calling or check-raising, Bob can call her c-bet with any two cards, planning to auto-bet the turn as a pure bluff those times Alice checks and gives up.

If Bob can call a flop c-bet with automatic profit with a hand as weak as 2 2 on a J T 4 flop, Alice is probably doing something wrong on the turn and river. Note that when Alice checks the turn and gives up after getting floated on the flop, she has in reality lost the hand. If Bob has floated with a worthless hand, he will now bet and Alice will fold. If he has a hand with weak showdown value, as in the 2 2 hand above, he can choose between betting it as a bluff or checking it to showdown (we’re assuming Alice isn’t planning to bluff the river when the turn goes check-check). If the hand get checked down, Bob will usually win, since Alice on average will have few outs those times she checks and gives up on the turn.

At any rate, Alice can not allow Bob to sit behind her and call c-bet and turn bets profitably with any two cards, so she has to make sure she defends her betting range on the current street by not giving up too easily on the next street after getting called. In this article we’ll show how Alice can build turn and river strategies, based on pot-odds and simple theory, that prevents a player in position from floating her with any two cards on the turn or river.

Alice does this by betting, check-calling and check-raising enough on the next street after betting the current street and getting called. This prevents the player in position from getting enough profitable bluffing opportunities, or opportunities to get cheaply to showdown with weak hands that have some showdown value. Precisely how often Alice needs to continue on the next street after betting the current street and getting called is something we can estimate using mathematics and simple assumptions.

We’ll use theory borrowed from Matthew Janda’s excellent game theory videos at /Cardrunners.com. Then we adapt this theory to the “model game” we have designed throughout the NLHE preflop article series and this NLHE postflop article series. We’ll use our default preflop “core ranges” as a starting point for out postflop ranges.

Before we begin building Alice’s postflop strategy, we’ll warm up by verifying that Bob’s calling strategy in position (discussed in Parts 1-4 in this article series) does what it was designed to do, namely prevent Alice from c-betting/2-barreling/3-barreling profitably with any two cards those times Bob doesn’t have a hand strong enough to raise for value on any street.

2. How Bob’s calldown strategies makes Alice’s any-two-cards bluffs break even
Let’s quickly repeat an example from Part 4 where Alice c-bets the flop, 2-barrels the turn, and 3-barrels the river. We’re only looking at the region of possible outcomes where Bob only has a calling hand on each street.

Alice (100 bb) raises her default ~25% range from CO, Bob (100 bb) flats on the button with his standard flatting range in position (“IP flat list”):

IP flat list after a ~25% CO openraise

JJ-22
AQs-ATs AQo-AJo
KTs+ KQo
QTs+
JTs
T9s
98s

140 combos

The flop comes:

Bob’s preflop flatting range of 140 combos was reduced to 130 combos on this flop (card removal effects):

Bob then had to defend 57% against Alice’s c-bets on the flop, which is 0.57 x 130 =74 combos. We estimated Bob’s optimal flop strategy as:

  • Raise for value
    None
  • Flat
    {88,55,33,JJ,TT,99,77,66,44,AQ,AJ} =77 combos
  • Bluffraise
    None

Bob slowplayed all his strong hands on this very dry flop, and the reasons for this choice were discussed previously. Then the turn came:

The flop flatting range of 77 combos was reduced to 73 combos, given this turn card:

Again, Bob has to defend 57% of his range, which is 0.57 x 73 =42 combos. On the turn he will use a raising range of strong hands (some slowplayed monsters from the flop) and he balances this with bluffs in a 1 : 1 value/bluff ratio. The rest of the defense is done by flatting. We estimated his optimal turn strategy to be:

  • Raise for value
    {88,55,33} =9 combos
  • Flat
    {AQ,JJ,TT} =24 combos
  • Bluffraise
    {AJs,9 9 ,9 9 ,9 9 ,9 9 ,9 9 } =9 combos

we then moved on to playing the river after Bob had flatted the turn:

The river card had no effect on Bob’s range, and his 24 turn flatting combos were intact on the river:

Bob then had 24 combos in his river range, and he had to defend them optimally against Alice’s 0.60 x pot river bet. As calculated previously, Bob then has to defend 62% of his range to prevent Alice from bluffing profitably with any two cards. He has no hands strong enough to raise for value (he only has one pair hands to use as bluffcatchers), so he needs to defend 0.62 x 24 =15 combos by flatting them. We estimated Bob’s optimal river strategy to be:

  • Raise for value
    None
  • Flat
    {AQ,J J , J J , J J } =15 combos
  • Bluffraise
    None

What generally happens from street to street those times Bob finds himself inn a call-down process (those times he has medium/weak hands) on a dry flop texture is that he begins by flatting the flop with a wide range of almost any pair plus his best overcard hands. The overcard hands are floats that he doesn’t plan to call down with, but he has to call the flop with them in order to defend enough. Then he typically drops his overcards and lowest pairs to a turn bet when Alice bets again. And finally, he calls a 3rd bet with his best pairs on the river and folds his lowest pairs.

This makes sense intuitively, since Bob needs to balance two factors:

– He has to prevent Alice from often bluffing him out of the pot with any two cards
– But he has to avoid paying off her better hands too often

The optimal call-down strategy outlined above makes sure Bob isn’t giving Alice a big opening for bluffing profitably with any two cards on any street. He calls down enough to prevent this, but he also folds enough to prevent Alice’s strong hands from extracting a lot of value from his bluffcatchers.

We’ll now use mathematics to show that Bob’s optimal call-down strategy prevents Alice from running a profitable any-two-cards bluff against him. We’ll assume that:

– Bob has a bluffcatcher that always beats Alice’s bluffs
– Alice has a pure bluff that never draws out on Bob’s hand
– Alice decides to run a 3-barrel bluff with her worthless hand
– Bob calls down optimally

Bob’s defense on the flop
Let the pot size on the flop be P. Alice now c-bets 0.75P with her worthless hand. Bob calls 57% of the time with his bluffcatcher (he can use a randomizer to determine when he calls and when he folds) and folds 43% of the time. Those times he calls, the pot grows from P to P + 0.75P + 0.75P =2.5P. Both players have now put 0.75P into the pot postflop.

– % Bob folds the flop: 43%
– Alice’s profit when Bob folds the flop: P

Alice wins the flop pot when Bob folds.

Bob’s defense on the turn
The pot is 2.5P on the turn. Alice now 2-barrels 0.75x pot with her worthless hand. Bob calls 57% and folds 43% to this turn bet. When he calls, the pot again grows with a factor 2.5 and becomes 2.5 x 2.5 x P =6.25P. Both players have now put (6.25P – P)/2 =2.625P into the pot postflop.

– % Bob calls the flop and folds the turn: 0.57×0.43 =25%
– Alice’s profit when Bob folds the turn: P + 0.75P =1.75P

Alice wins the flop pot + Bob’s flop call when Bob calls the flop and folds the turn.

Bob’s defense on the river
The pot is 6.25P on the river. Alice now 3-barrels 0.60 x pot with her worthless hand. Bob calls (and wins against Alice’s bluff) 62% and folds 38%. When he calls, the pot grows from 6.25P to 6.25P + 2 x 0.6 x 6.25P =13.75P. Both players have now put (13.75P – P)/2 =6.375P into the pot postflop.

– % Bob calls flop and turn, and the folds river: 0.57×0.57×0.38 =12%
– Alice’s profit when Bob folds the river: P + 2.625P =3.625P

Alice wins the flop pot + Bob’s flop call + Bob’s turn call when Bob calls the flop + turn, and then folds the river.

– % Bob calls the flop + turn, and then folds river: 0.57×0.57×0.62 =20%
– Alice’s loss when Bob calls down: -6.375P

Alice loses her flop c-bet + turn bet + river bet when Bob calls down.

Total EV for Alice’s 3-barrel bluff
Below is a summary of all the possible outcomes, with Alice’s profit/loss for each of then in parentheses:

  • Bob folds flop: 43% (P)
  • Bob calls flop/folds turn: 25% (1.75P)
  • Bob calls flop/calls turn/folds river: 12% (3.625P)
  • Bob calls flop/calls turn/calls river: 20% (-6.375P)
  • Total: 100%

 

EV (3-barrel bluff)
=0.43(P) + 0.25(1.75P) + 0.12(3.625P) + 0.20(-6.375P)
=0

Bingo! Alice’s 3-barrel bluff project is exactly break even when Bob sits behind her with a bluffcatcher and calls down optimally. His call/fold percentages on each street are functions of Alice’s bet sizes on each street. If Alice had changed her bet sizes, Bob would have adjusted his call/fold percentages correspondingly (smaller bets =Bob calls more, bigger bets =Bob folds more). For example if Alice had bet the pot on each street, Bob would have called 50% and folded 50% on each street (since Alice’s pot-odds on a bluff are now 1 : 1 on each street). You can easily verify that Alice’s 3-barrel bluff EV would have been zero with this bet sizing scheme as well.

This verifies that when Bob is inn a call/fold scenario that stretches over multiple streets, his optimal postflop strategies will prevent Alice from running a profitable any-two-cards 3-barrel bluff against him. So Alice can’t exploit Bob by bluffing aggressively, but note that Bob isn’t doing anything to exploit Alice’s bluffing either.

To exploit Alice’s any-two-cards bluffing strategy (if she is in fact using such a strategy) Bob needs to call down more than optimally to exploit the opening Alice is offering him. For example, he can choose to call down 100% with his bluffcatcher if he believes that Alice is betting 100% of her range on every street in an attempt to bluff him off his weak hands.

This should be profitable for him, since there should be many more bluffs than value hands in Alice’s range on a dry flop. However, by doing so he is offering Alice an opening for exploiting him back by stopping to bluff and only betting her value hands. But Bob can always return to the optimal call-down strategy if he isn’t sure whether or not Alice is bluffing way too much, or if he suspects she will quickly adjust to his attempts to exploit her bluffing.

Now we have warmed up, and we move on to the main topic for this article:

3. Optimal 2- and 3-barreling heads-up and out of position
We’ll now look at the scenario where:

– Both players start with 100 bb stacks
– Alice raises preflop and Bob flats in position
– Alice c-bets her entire preflop range on a dry flop, and Bob flats
– Alice then uses a turn/river barreling strategy designed to prevent Bob from floating profitably with any two cards on the turn or river

We’ll do this in to steps:

1. Study a simple mathematical model
2. Implement the theory working through an example

3.1 Modeling barreling out of position
First, let’s define barreling. This is simply to keep betting on the next street after you have bet the current street and gotten called (and it doesn’t matter whether you’re weak or strong). So if Alice raises preflop, c-bets the flop, and then bets the turn, she has done a 2-barrel. If she also bets the river after getting called on the turn, she has done a 3-barrel.

When Alice is out of position versus Bob, c-bets the flop and gets called, it’s important for her to have a balanced strategy for turn play in order to prevent Bob from exploiting her by floating with any two cards on the flop (planning to steal the pot on later streets). If Alice checks and gives up on too many turns, it will be profitable for Bob to call her c-bet regardless of what he has, planning to auto-bluff the turn when checked to (for example if he floated the flop with a gutshot straight or overcards), or planning to check down a hand with marginal showdown value (for example, if he floated the flop with a low pair).

Alice can counter Bob’s floating strategy with random weak hands by 2-barreling enough on the turn and we’ll see how often she needs to do that in a minute). But Alice can’t only defend her flop betting range by 2-barreling, since this makes her turn checking range transparent and easy to exploit (since Bob then knows that Alice is always weak when she checks). So Alice needs to mix in some check-calling and check-raising on the turn as well.

The same logic applies to river play after Bob flats Alice’s turn bet. She has to 3-barrel/check-call/check-raise enough to prevent Bob from floating the turn with any two cards, planning to steal the pot on the river, or win a showdown with a weak hand that has showdown value (but not strong enough to call both the turn and the river.

We’ll use a simple model and a bit of math to estimate how often Alice needs to defend on the next street after betting the current street and getting called. We use our standard postflop bet sizing scheme:

– 0.75 x pot on the flop
– 0.75 x pot on the turn
– 0.60 x pot on the river.

When Alice c-bets 0.75 x pot on the flop, Bob is getting pot-odds (1 + 0.75) : 0.75 =1.75 : 0.75 on a call. If Alice never check-raises or check-calls the turn, Bob can float a random weak hand with automatic profit if Alice checks and gives up more than 0.75/(1.75 + 0.75) =30% on the turn. Therefore, if Alice defends against Bob’s flop floats by only 2-barreling, she needs to 2-barrel 100 – 30 =70% of her flop betting range on the turn. We can express this as:

2-barrel%=70%

This is a mathematically acceptable defense strategy against flop floats, but Alice can make things easier for herself by also check-calling and check-raising some on the turn. This makes it more expensive on average for Bob to steal the pot (which means Alice can get away with less 2-barreling). It also makes Alice’s turn checking range much harder to read, since she isn’t always ready to give up the pot when she checks.

Those times Alice 2-barrels the turn and Bob folds his random flop float, his loss is limited to his flop call of 0.75 x flop-pot. Now, assume Bob always bets his floats as a turn bluff when Alice checks to him. His plan is to fold to a turn checkraise, and give up his steal attempt if Alice check-calls Bob is then prepared to check down the hand and lose a showdown). Bob’s turn bet is 0.75 x turn-pot, and the turn-pot is 1 + 0.75 + 0.75 =2.5 x flop-pot. Bob then invests 0.75 x 2.5 =1.875 x flop-pot with his turn bluff.

Then his total risk for trying to steal the pot with a flop float + turn bluff is (0.75 + 1.875) =2.625 x flop-pot. When Alice check-calls or check-raises the turn, Bob’s expense is then 2.625/0.75 =3.5 x higher than when Alice 3-bets (so that Bob only loses his flop call of 0.75 x flop-pot).

To make Bob’s steal attempt break even, the following equation needs to be satisfied:

2-barrel%(-0.75P) + check-continue%(-2.625P)
+ (100 - 2-barrel% - check-continue%)(+1.75P) =0

In words:

The amount Bob loses by floating the flop and getting 2-barreled (-0.75P each time), plus the amount he loses by floating the flop and getting his turn bluff check-called or check-raised, plus the amount he makes when his turn bluff succeeds, should sum to zero. That makes his float flop + bluff turn strategy break even, which is what Alice’s wants her turn strategy to do for her.

We simplify this equation to get:

2-barrel%(-0.75P) + check-continue%(-2.625P)
+ 175P - 2-barrel%(1.75P) - check-continue(1.75P) =0
2-barrel%(-0.75P - 1.75P)
+ check-continue%(-2.625P - 1.75P) + 175P =0
-2.5P x 2-barrel% - 4.375P x check-continue% + 175P =0
2.5P x 2-barrel% + 4.375P x check-continue% =175P
P x 2-barrel% + 1.75P x check-continue% =70P

And the above equation for Alice’s turn defense strategy against flop floats can be generalized to:

2-barrel% + 1.75 x check-continue% =70%

The term check-continue is the label we use for all of Alice’s check-calling and check-raising. We have here assumed that Bob always loses the hand when he bets the turn and Alice doesn’t fold. Note that we are ignoring the equity of Bob’s hand, and we assume that he never wins a showdown after Alice check-calls the turn. Bob is always behind when this happens, he never improves to the best hand on the river, and he never bluffs the river. These are simplifying assumptions, but this is fine when we’re modeling a situation. Also, keep in mind that sometimes Alice bets or check-calls the worst hand, and then she draws out on the river. So as a first approximation we can assume that these two effects cancel out.

We’ll now put the above equation to work by studying an example scenario heads-up with the raiser out of position on a dry flop. On these flops we’ll often get a call-down scenario where the raiser c-bets any two cards on the flop, and then the preflop flatter sits in position with a medium/weak range of mostly one pair hands and overcards. usually the caller is not strong enough to raise anywhere along the way, so he will often be faced with a call/fold decision on every street those times the raiser fires multiple barrels.

What typically happens when two good, thinking players clash in this type of scenario is that both will be playing wide ranges on the flop (the raiser c-bets a lot and the player in position flats a lot). Then both players drop many (but not all) of their bluffs, floats and weak one pair hands on the turn, and then again on the river. And both players are trying to prevent the other player from bluff-barreling/floating profitably with any two cards on any street.

3.2 Example of optimal c-betting/2-barreling/3-barreling heads-up and out of position on a dry flop
Alice raises her default ~15% opening range from UTG:

~15% UTG-range

22+
A9s+ AJo+
KTs+ KQo
QTs+
J9s+
T9s
98s
87s
76s
65s

194 combos
15%

Bob flats on the button. At this moment we’re not particularly concerned with Bob’s flatting range or postflop strategy, but we can assume he uses his standard flatting range outside of the blinds (“IP flat list”):

IP flat list after ~15% EP openraise

QQ-22
AKs-ATs AKo-AJo
KTs+ KQo
QTs+
JTs
T9s
98s

162 combos

The flop comes:

We’ll now focus on Alice’s postflop strategy from street to street. She begins by c-betting her entire preflop range on this dry, low flop, since it mostly misses Bob’s preflop flatting range, and she expects him to fold a lot. We don’t know what Bob has, but we can assume his range is weak. Alice must now have a strategy ready for the turn, so that Bob can’t exploit her by floating the c-bet with any two cards.

We saw previously that Alice can achieve this by 2-barreling, check-calling and check-raising the turn so that the following equation is satisfied:

2-barrel% + 1.75 x check-continue% =70%

The turn comes

Before Alice builds a turn strategy, we take card removal effects into consideration and count the number of combos in her turn range, given the cards on the board. Since she c-bet her entire preflop range on the flop, her turn range equals her preflop range minus the combos that are eliminated due to card removal effects:

There are 168 combos remaining in Alice’s range. If she only 2-barrels and never check-calls or check-folds, she needs to bet 70% of these combos, which is 0.70 x 168 =118 combos. If she also check-calls and check-raises, we can rewrite the defense equation as:

2-barrel-combos + 1.75 x check-continue-combos =118

Alice now uses a turn strategy where she:

– Check-raises a few of her best hands
– Bets the rest of her best hands for value
– Check-calls with some medium strong hands
– Balances her value bets with some bluffs in a 1 : 1 ratio
– Check-folds the rest of her hands

Here we’ll not go into detail about which hands are good enough to check-raise, value bet or check-call, and we’ll use good poker sense when putting hands into different categories. Furthermore, we haven’t shown mathematically that 1 : 1 is the best value/bluff ratio to use for Alice’s 2-barrels, but we’ll assume this is reasonable (and it’s easy to remember).

Let’s estimate a reasonable total turn strategy for Alice and check whether or not this gives her enough protection against floats according to the defense equation:

  • Check-raise:
    {JJ} =3 combos
    Value bet:
    {99,66,33,J9s,AA-QQ,AJ} =41 combos
  • Check-call
    {KJs,QJs,JTs,TT,A9s} =18 combos
    Bluff:
    {QTs,AK,AQ,KQs} =40 combos

So Alice 2-barrels 41 + 40 =81 combos using an approximate 1 : 1 value/bluff ration, and she check-calls/check-raises 3 + 18 =21 combos. She makes things simple and choose top pair/top kicker or better as her value hands, check-calls with the remaining top pair hands + the best of the lower pairs, and bluffs with an open-ended straight draw and the best overcard hands.

The defense equation gives:

2-barrel-combos + 1.75 x check-continue-combos
=81 + 1.75 x 21
=118 (optimal =118)

Our estimate of Alice’s turn strategy satisfies the defense equation exactly. Now we can go back to our ranges and do some polish if we want to, particularly for the hands in between the obvious check-calling hands and the “air hands” (our 2-barrel bluffs). For example, we chose to check-fold T9s since we had enough better one pair hands to use for check-calling, and we preferred to bluff with draws and overcards, since these on average have more outs than marginal one pair hand.

Here it’s important to note that T9s will win some showdowns, since Bob will sometimes check the turn and give up. So check-folding these marginal one pair hands does not automatically mean they lose, since the player in position will sometimes be willing to check down weaker hands. And of the turn and river goes check-check we’d rather have T9s than two overcards. So it makes more sense to check turns with our weakest one pair hands, instead of turning them into bluffs. And then we pick our bluffs from hands that can’t win showdowns unimproved.

At any rate, when we’re building a mathematically sound total turn strategy this type of marginal decision making is not very important. For the moment we’re only concerned with building a reasonable turn strategy for Alice, and then we can polish it later.

Now we let Alice bet her turn 2-barrel range, which is a 1 : 1 mix of value hands and bluffs (note that top set JJ is not a part of our range, since we put it in our turn check-raising range):

  • Value bet:
    {99,66,33,J9s,AA-QQ,AJ} =41 combos
  • Bluff:
    {QTs,AK,AQ,KQs} =40 combos

Bob calls turn turn bet, and the river comes:

Alice’s 2-barrel-range of 40 + 41 =81 combos is unaffected by this river card, and she still has 81 combos on the river:

We remember that Alice’s bet sizing is 0.60 x pot on the river. Now there aren’t any more cards to come that can change hand strength, and only one round of betting remains. we can now calculate the exact optimal value/bluff ratio for Alice’s 3-barrels. When she bets 0.6 x pot, Bob is getting pot-odds (1 + 0.60) : 0.60 =1.60 : 0.6. Alice now wants to bluff exactly so often than Bob becomes indifferent to calling or folding with his bluffcatchers (those of his hands that can only win if Alice is bluffing, for example a marginal one pair hand).

The logic behind this is that if Alice bluffs less, Bob can exploit her by always folding his bluffcatcher and save money (since he isn’t getting the right pot-odds to call). But if she bluffs more than optimally, relative to her bet sizing, Bob can exploit her by calling with even more bluff catchers (since he is getting better pot odds than he needs), and Alice now loses money.

Therefore, Alice wants to bluff just enough to make Bob’s EV zero when he calls with a bluffcatcher. Then she has a guaranteed minimum profit from betting the river. If Bob tries to save chips by not paying off with his bluffcatchers, Alice will steal some pots with her bluffs. If he tries to snap off a possible bluff by calling with all his bluffcatchers, he will mostly be paying off Alice’s value hands.

Alice now makes her value/bluff ratio for the 3-barrel equal to the pot-odds Bob is getting, namely 1.60 : 0.60. Alice then bluffs 0.60/(1.60 + 0.60) =27% of the time and value bets 100 – 27 =73% of the time. She then needs 27/73 =0.37 bluff combos per value combo.

In addition to the requirement of optimal value betting/bluffing on the river, Alice needs to 3-barrel/check-raise/check-call the river so that:

3-barrel% + 1.75 x check-continue% =70%

This follows from her 0.75 x pot turn bet, which gives us the same mathematics as her 0.75 x pot flop bet, and the same defense equation (she has to play the river in such a way that Bob can’t flop her turn bet with any two cards). Alice’s 2-barrel-range on the turn had 81 combos and she still has 81 combos on the river. 70% of this is 0.70 x 81 =57 combos. The defense equation can be written as:

3-barrel-combos + 1.75 x check-continue-combos =57

The range Alice brought with her from the turn to the river after c-betting and 2-barreling is {99,66,33,J9s,AA-QQ,AJ} + {QTs,AK,AQ,KQs} =40 + 41 =81 combos. Below is a suggestion for a total river strategy that satisfies the defense equation and also has the optimal value/bluff ratio for her river 3-barreling range:

  • Check-raise:
    {99} =3 combos
    Value bet:
    {66,33,J9s,AA-QQ} =26 combos
  • Check-call:
    {AJ} =12 combos
    Bluff:
    {10 AK-combos} =10 combos

Alice check-raises one of her sets and value bets all other sets, two pair and overpairs. She check-calls top pair/top kicker, and bluffs with 10 of the 16 AK combos (for example all AKs and the 6 remaining A Kx and A Kx). She 3-barrels a total of 26 + 10 =36 combos with a bluff% of 10/(26 + 10) =28% (close to the optimal 27%), and she check-calls/check-raises 3 + 12 =15 combos.

We plug these numbers into the defense equation and get:

3-barrel-combos + 1.75 x check-continue-combos
=36 + 1.75 x 15
=62 (optimal =57)

We see that it’s easy for Alice to defend enough on this river when she starts out with a strong UTG range preflop and then gets called on the flop and turn on a dry board. She has enough sets and overpairs in her barreling range to comfortably get to showdown with only top pair or better, without giving Bob any opportunities to float her profitably with any two cards anywhere along the way. Note that Alice does not need to make crying check-calls on the river to defend optimally. But as we shall see in the next article, Alice’s opening range is an important factor. The tighter her opening range, the more of our range will be made up of top pair or better postflop, and the easier it becomes to defend optimally out of position.

For example, had we opened our default 25% range from CO and gotten the same flop, we would have had a much larger percentage of worthless hands in our postflop range after c-betting our entire range on the flop. Compared to a 15% UTG open range we would now be forced to defend with a much weaker range on the turn to satisfy the defense requirement of 70% 2-barreling (or the equivalent amount of 2-barreling, check-calling and check-raising, according to the defense equation). We would have carried this problem with us to the river, and we would have to defend a weaker range there as well. We’ll talk more about this in Part 6.

So what can we learn from the work done in this article? For example, we see that out one pair hands drop steadily in value from flop –> turn –> river. At the river top pair/top kicker became a check-calling hand in this example. Further more, all worse one pair hands (if we had had any) would have been put in the check-folding range, since we don’t need to check-call these hands to satisfy the defense equation.

Does all this make sense intuitively? Yes, since we can’t expect to win many pots by betting or check-calling a mediocre one pair hand after we have bet for value on the flop and turn and gotten called twice on a dry board. Villain will often have a better hand, and we will pay off a lot if we insist on taking all our mediocre one pair hands to showdown.

So the ranges we build based on pot-odds, mathematics and principles from game theory correlate well with our intuitive understanding of the situation. But of course, if you’re at the river in such a scenario and you expect Villain to bluff enough to make check-calling profitable with a mediocre one pair hand, by all means go ahead and check-call. The main point of the optimal strategy is that it gives us a good starting point for playing correctly.

If we follow the optimal strategy, Villain can’t exploit us by loose floating, that’s the big picture idea here. If we have additional information that tells us he is likely to bluff way too much if we check the river, we can exploit him by check-calling more than optimally.

Therefore, if the strategies above seem to loose or too tight to use as a default at the limits you are playing, you can view this as a sign that you usually have additional information that allows you to build exploitative strategies that are better than the optimal default strategy. But you will still benefit from training a good understanding of what the optimal strategies look like, so that you know where to start when you adjust to individual opponents’ mistakes. You will also have a solid default strategy to use against unknown players.

4. Summary
In this article we moved from postflop play heads-up in position after flatting preflop to postflop play out of position as the preflop raiser. We used simple mathematics and modeling to estimate an optimal c-bet/2-barrel/3-barrel strategy for the raiser.

We assumed that the raiser began postflop play by c-betting her entire preflop raising range on a dry flop texture, and the player in position called. On the turn and river the raiser used strategies that prevented the player in position from floating the flop or the turn profitably with any two cards- The raiser did this by barreling/check-calling/check-raising enough to make it mathematically impossible for the player in position to make a profit from floating a street with a weak hand, planning to bluff or sneak cheaply to showdown when the raiser checks the next street. We worked thoroughly through an example to illustrate how the theory can be implemented at the table.

In the next article we’ll continue with this topic. Some of the things we’ll talk about are:

  • More about the consequences of choosing to bet a street
  • Show mathematically that the raiser’s optimal turn/river strategies defends her against any-two-cards floating
  • Study the effect of the raise’s opening range on her postflop strategies

The plan for the rest of the article series is to move on from heads-up play in singly raised pots to heads-up play in 3-bet pots (which new players tend to find difficult). But before we move on to 3-bet pots we will gain a lot of insight from studying play in singly raised pots both as the raiser out of position and the flatter in position. The mathematics and models we use will come in handy when we learn about play in 3-bet pots later.

Good luck!
Bugs – See more at: http://en.donkr.com/Articles/optimal-postflop-play-in-nlhe-6-max—part-5-821#sthash.0OkTQEBC.dpuf

As Bitcoin Price Soars, SealswithClubs Reaches New Traffic High

The BTC-only poker room is benefiting from recent virtual currency enthusiasm, with cash game traffic doubling since early September.

Image

Bitcoin-only site SealswithClubs (SwC) has seen its cash game traffic more than double since its seasonal low in early September. The individualistic site offers an online poker room to US players that exclusively uses the Bitcoin virtual currency rather than legal tender.

Bitcoin has had a volatile ride recently. From an exchange rate low of $65 in June, the price of a Bitcoin rocketed to a high of $900 before falling back to a little over $600 today. Players who kept their bankroll in Bitcoin accounts at SwC have enjoyed the ride.

SWC cash game traffic graph (see below) mirrors the Bitcoin price graph, suggesting that the site benefited from sentiment about the currency. The latest boom has come as the US Senate has been holding hearings on potential Bitcoin regulation.

While regulation may be against the initial philosophy of early proponents of the currency, it would legitimize it and potentially create a much greater demand—sending the price up.

The SwC founders prefer to remain anonymous, but Bryan “The Icon” Micon provides a public face as the “Seals Team Pro Chairman.” A desktop client and an Android app are available, and rake at no limit tables is set at a relatively low 2.5% with a cap of the lesser of 3 big blinds or 0.005BTC.

Optimal 3-bet/4-bet/5-bet strategies in NLHE 6-max – Part 1

1.1 Presenting the problem

Against weak low limit opposition, we can get away with playing an almost completely value-based game. We 3-bet/4-bet/5-bet mainly for value, and it’s not a big mistake to assume our opponents are doing the same. If we reraise as a bluff, we usually limit ourselves to the occasional 3-bet bluff. A value-based style with little bluffing works well at small stakes because our opponents use more or less the same strategy, and many of them execute it poorly. Of course, every now and then we run into aggressive players who are capable of reraising as a bluff, but there are plenty of fish that will pay off our straightforward game, even if we bluff much less than is game theoretically optimal.

But let’s say our Hero has built a bankroll by patiently grinding the low limits, and now he wants to take a stab at $200NL. He will now experience a lot more 3-betting, especially if he’s out of position.

For example:

Example 1.1.1: We get 3-bet out of position

$200NL
6-handed

Hero ($200) raises to $7 with J T from UTG, it’s folded to the button ($200) who 3-bets to $24, the blinds fold, and Hero folds.

Straightforward, and although Hero expects to get bluffed some of the time, he really doesn’t have any choice but to fold. It’s correct that his hand can no longer be played for value, but as we shall see later, it’s possible to turn it into a 4-bet bluff.

At any rate, Hero plays on. The players behind him keep 3-betting him frequently when he is out of position, and Hero keeps folding weak hands to 3-bets. After a while, this hand occurs:

Example 1.1.2: We get 3-bet out of position (again)

$200NL
6-handed

Hero ($200) raises to $7 with A J in MP, it’s folded to button ($200) who 3-bets to $24, the blinds fold, and Hero folds.

This is getting frustrating. Hero has a decent hand, but it’s not strong enough to defend against a 3-bet from out of position, so Hero folds. But he is starting to feel exploited. If only he could get dealt a good hand and punish these bastards!

What an inexperienced player now might do (as his frustration builds up more and more), is to make up his mind to fight back against the loose 3-bettors. But he doesn’t quite know what to do, and therefore he will often use poor strategies, and the wrong types of hands!.

Let’s look at two common (and sub-optimal) ways to defend against 3-betting, out of position with 100 BB stacks:

Example 1.1.3: We get 3-bet out of position (again) and we call

$200NL
6-handed

Hero ($200) raises til $7 with K Q in MP, button ($200) 3-bets to $24. Hero thinks for a bit, decides that this hand is too good to fold, but too weak to 4-bet, so he calls.

Flop: 944 ($51)
Hero ($176) checks, button ($176) bets $30, Hero folds.

Hero is frustrated, but he doesn’t see what else he could have done out of position with a hand of this type. Too strong to fold (at least in Hero’s mind) against a loose 3-bettor, but not strong enough to 4-bet. Or? Hmmmmm …. Hero contemplates his next move, and soon another 3-bet pot occurs:

Example 1.1.4: We get 3-bet out of position (again) and we 4-bet for value (or at least that’s what we think we are doing)

$200NL
6-handed

Hero ($200) raises to $7 with A J from UTG, MP ($200) 3-bets to $24. Hero decides to fight fire with fire, and he 4-bets pot to $75. Button 5-bets all-in, Hero calls. MP has K K . Hero screams in agony.

Flop: Q T 7 ($403)

Turn: Q T 7 Q ($403)

River: Q T 7 Q 4 ($403)

Hero tears his clothing and sprinkles ashes over his head. Damn!!

What happened throughout this sequence of hands?
OK, I made up this story, but it illustrates several of the problems an ABC low limit player faces when he moves up to tougher games. He will get 3-bet left and right, so he will have to fold a lot out of position (which is correct). He realizes he has to fight back to avoid getting run over (also correct), but he’s not quite sure how to do it. So his attempts to counter the aggression are often poorly executed, frustrating and tilt-inducing.

For example, Hero might start calling 3-bets out of position with hands he feels are too good to fold, but not strong enough to 4-bet for value. This leads to many miserable experiences like Example 1.3. Or he might start 4-betting medium/weak hands without a clear understanding of whether he is doing it for value (planning to call a 5-bet), or if he is bluffing (planning to fold to a 5-bet).

What our inexperienced Hero might not realize, is that his opponents’ loose 3-betting doesn’t necessarily mean they are willing to splash around with lots of weak hands in 4-bet and 5-bet pots. When two good and aggressive NLHE-players engage in 3-bet/4-bet/5-bet warfare preflop, this is what usually happens:

Both players operate with wide ranges, and all ranges have a significant percentage of bluffs in them, especially at the early stage (raising and 3-betting)
Both players are willing to fold most of their bluffs (but not all of them), when their opponent reraises them back

This results in ranges that start loose, but get more and more (but never completely) weighted towards value. And it’s usually plain wrong to assume you can 4-bet a medium hand like AJs for value against a loose 3-bettor, and expect to be a favorite when he 5-bets all-in. Yes, AJs is a decent hand against the range that 3-bet you, but it’s crushed by the range that 5-bets you, and it’s your opponent who decides when the 5th bet goes in (and that rarely happens unless he has the goods).

Therefore, if you decide on a frustrated whim to “take a stand” against an aggressive and competent 3-bettor with a hand like AJs, you will discover that in some mysterious way he almost always manages to come up with a better hand when you get all-in preflop.

This has lead many an inexperienced NLHE player to lose his stack, since these players:

Don’t understand the roles different types of hands have in different types of ranges. First and foremost: Do I have a value hand that wants to get all-in, or do I have a bluff hand that I will fold to further aggression?
Aren’t willing to fold hands that are strong at the early stages, but turn into weak hands when Villain keeps reraising

Let’s look at Example 1.4 again. Hero open-raised AJs (correctly), and he got 3-bet. He then decided that his AJs was a good hand against Villain’s 3-bet range (debatable, but not a big mistake), so he 4-bet for value (wrong!), planning to call a 5-bet all-in. Playing AJs for value after a 3-bet and going all-in with it was a big mistake. The 4-bet in itself was not a big mistake, since Villain has a lot of bluffs in his 3-betting range, and he will fold most of them to a 4-bet. So it’s not a problem to 4-bet AJs as a bluff against a range full of 3-bet bluffs. But when Villain comes over the top with an all-in 5-bet, our AJs crumbles to dust (if Villain knows what he is doing).

But our inexperienced Hero did not realize what had just happened when he got 5-bet, and he stuck with his plan of playing AJs for value against what he perceived to be a wide and weak range. The problem is that the range he faces after a 5-bet from a competent player isn’t wide and weak, it’s very narrow and very strong.

Note what the real mistake was in this hand. 4-betting AJs against a wide range was not a big mistake in isolation, and neither was calling a 5-bet getting 2: 1. But the combination of 4-betting AJs + planning to always call a 5-bet, now that was a big mistake against a competent opponent. It caused Hero to invest his remaining 96.5bb stack as a huge underdog. The problem was, as mentioned previously, that his opponent controlled when the 5th bet went in, and Villain made sure he had a hand.

Our goal for this article is to give Hero a set of tools he can use to comfortably counter preflop aggression when he is sitting as the raiser out of position. We’ll base our work on Hero’s opening ranges, and based on these, we can deduce defensive strategies against positional 3-bets. And we will use game theory to design these strategies in such a way that the 3-bettor can not exploit Hero in these scenarios. Our work on Hero’s game theory optimal defensive strategies also gives us a set of optimal 3-betting strategies for his opponent, so we kill two birds with one stone.

We have here talked mostly about the ills of getting 3-bet when sitting out of position, and this is what I feel inexperienced players find hardest to deal with. But the mirror image of this scenario, with us being the 3-bettor in position, is also worth discussing. These are easier scenarios to play, but we will benefit a lot from understanding optimal 3-bet/4-bet/5-bet dynamics also from this perspective. We’ll learn how to construct optimal 3-betting ranges, based on the raiser’s opening range, and we’ll learn how to play against a 4-bet.

Regardless of whether we’re the raiser or the 3-bettor, we want to understand which hands we can (re)raise for value, and which hands we (re)raise as bluffs. And above all else, we want it to be 100% clear which of these two things we are doing before we engage in a 3-bet/4-bet/5-bet war preflop.

1.2 Our model and overall philosophy

In this article we’ll design so-called optimal strategy pairs for the raiser and the 3-bettor in the following scenario:

– The raiser opens some range
– A player behind him 3-bets
– The raiser 4-bets or folds
– The 3-bettor 5-bets, or folds to a 4-bet Continue reading Optimal 3-bet/4-bet/5-bet strategies in NLHE 6-max – Part 1

High Stakes Railbird: Disaster for Benefield, Hansen Continues to Rise, & Urindanger Wins Big

The action at the Full Tilt Poker high-stakes tables was in full swing this weekend, beginning with the continuation of the “durrrr Challenge”between Daniel “jungleman12” Cates and Tom “durrrr” Dwan.

In other action, Di “Urindanger” Dang emerged as the weekend’s big winner with $655,122 in the black over the course of 27 sessions and 2,993 hands. “IHateJuice” also had a good weekend playing only three sessions and 641 hands but taking down $345,850 in profit. At the other end of the spectrum, David Benefield took a beating and became the weekend’s biggest loser, dropping $716,970.

Bad Saturday for Benefield

David Benefield had a terrible day on Saturday; he just couldn’t gain traction and lost $386,000 playing $500/$1000 pot-limit Omaha againstPatrik Antonius. To make matters worse, he went on to lose almost $240,000 in the $200/$400 PLO cap game against numerous other players.

In one of Benefield’s worst hands, he was sitting with $158,393 when Antonius ($241,525) raised to $3,000 on the button. Benefield reraised to $9,000 and Antonius made the call as the flop came down {8-Clubs}{6-Diamonds}{3-Diamonds}. Benefield, first to act, led out for $12,000, which Antonius called.

The turn was the {5-Diamonds} and once again Benefield led out, this time to the tune of $32,000. Antonius called and the {3-Clubs} appeared on the river. Benefield moved all-in for a little over $105,000, and Antonius quickly called. Benefield turned over {Q-Clubs}{Q-Diamonds}{9-Clubs}{J-Hearts} for two pair while Antonius showed {6-Hearts}{3-Hearts}{K-Spades}{A-Diamonds} for a full house. With that, Antonius took down the $317k pot and added to Benefield’s weekend woes.

Hansen Headed for the Black

Gus Hansen has been back to his winning ways in recent months and is looking to rectify his disastrous start to 2010. On Sunday, he made some progress by winning $281,000 in the $200/$400 and $500/$1,000 PLO cap games. It was in the $500/$1,000 game that Hansen played 231 hands against “DrugsOrMe,” winning $183,000 in the process.

In one particular hand against Di “Urindanger” Dang ($96,097.50), Hansen ($43,897.50) was on the button and raised to $3,000. Dang pushed back with a reraise to $9,000, and Hansen opted to make it $27,000 to go. Dang called and the pair created a pot worth $54,000 before the flop, which came down {Q-Clubs}{6-Diamonds}{J-Hearts}. Dang led out for a bet of $16,000 and Hansen called, capping the pot in the process.

Hansen: {A-Hearts}{K-Hearts}{5-Spades}{K-Spades}
Dang: {6-Clubs}{9-Spades}{7-Clubs}{A-Clubs}

Both players agreed to run it twice and the {7-Spades} on the first run gave Dang two pair and the lead; however, the {Q-Spades} on the river counterfeited his two pair and gave Hansen the first half of the pot. On the second run, the turn was the {2-Spades} and the river the {Q-Hearts}, giving Hansen the same two pair. He managed to win both runs and scoop the $80,000 pot.

Urindanger Gets His Revenge

Although he lost the aforementioned hand to Gus Hansen, not everything went wrong for Di “Urindanger” Dang; he did end up the biggest winner over the weekend. In the following hand he not only managed to notch a win, but he also got some revenge against Hansen.

Hansen ($40,867) was on the button and raised to $3,000. Dang ($209,112.50) then reraised to $9,000, Hansen called, and the flop fell {4-Hearts}{J-Spades}{9-Spades}. Dang led out for $18,000, Hansen raised to $31,000, and Dang called to cap the pot.

Dang: {5-Hearts}{10-Clubs}{J-Clubs}{7-Hearts}
Hansen: {K-Spades}{7-Spades}{8-Hearts}{5-Spades}

Dang was ahead with his pair of jacks, but Hansen had picked up a flush draw. The pair agreed to run it twice and the first run came {J-Hearts},{J-Diamonds} to give Dang the first half of the pot with quads. On the second run, the turn was the {6-Diamonds}, giving both players straight draws, but the {Q-Diamonds} helped neither and Dang won again to scoop the $80,000 pot.

Who’s up? Who’s down?

This week’s biggest winners (11/26-11/29): Di “Urindanger” Dang (+$655,112), “IHateJuice” (+$345,850), Rami “Arbianight” Boukai(+$277,764), “DrugsOrMe” (+$231,035), “rumprammer” (+$216,326)

In the red: David Benefield (-$716,970), “davin77” (-$274,106), “GooGie MonA” (-$174,544), Ilari “Ziigmund” Sahamies (-$170,612)

Year to Date Winners: Daniel “jungleman12” Cates (+$4.63 million), Tom “durrrr” Dwan (+$4.02 million), Phil Ivey (+$3.02 million)

Year to Date Losers: Brian Townsend (-$2.53 million), Ilari “Ziigmund” Sahamies (-1.91 million), “Matatuk” (-1.53 million)

source: pokernews.com

 

Full Tilt Poker Announces Rush Poker Mobile

Full Tilt Poker has announced the open beta release of Rush Poker* Mobile.

Full Tilt’s revolutionary poker format is now available to all players on the go using mobile devices running Flash v10.1 or higher. The mobile version features both real money and play money tables, and Android users will also be able to download the application on Android Market.

Players can now access the Rush Poker* Mobile application by going to http://mobile.fulltiltpoker.com on their mobile device’s web browser or on their computer.

Ipad owners hating Steve Jobs in 1, 2, 3…

LAPT de Poker Stars en Playa del Carmen, Mexico?

4ª TEMPORADA DEL LAPT

El Latin American Poker Tour es el tour más importante de Latinoamerica y existe la posibilidad de que una fecha del LAPT se lleve a cabo en Playa del Carmen, Quintana Roo, Mexico, crucemos los dedos xD

Canadian Jonahtan Duhamel wins WSOP 2010 Main Event

JONATHAN DUHAMEL WINS 2010 WSOP MAIN EVENT CHAMPIONSHIP

Jonathan Duhamel is the winner of the 2010 World Series of Poker Main Event Championship.

Duhamel, from Boucherville, Quebec became the first Canadian citizen in history to win poker’s world championship.  Two Canadians had previously finished in the runner-up spot in the 41-year-history of poker’s undisputed world championship.  Tuan Lam took second place in 2007, to Jerry Yang.  Fellow Canadian Howard Goldfarb did the same in 1995, losing to Dan Harrington.
Duhamel, a 23-year-old poker pro, collected a whopping $8,944,310 in prize money.  He was also presented with the widely-cherished and universally-revered gold and diamond-encrusted gold bracelet, representing the game’s sterling achievement.

The triumph was not easy.  Duhamel overcame a huge field of 7,319 entrants who entered what was the second-largest WSOP Main Event in history.  The tournament began on July 5th, and took more than four months to complete, including the customary recess prior to the November Nine.

Duhamel’s route to victory was a determined one, albeit peppered with a few unwanted detours.  He arrived at the final table — which began on Saturday, November 6th — with the chip lead.  He held about one-third of the total chips in play.  Duhamel lost some of his momentum during stage one of the finale, which included the elimination of seven players playing down to the final two.  Michael “the Grinder” Mizrachi seized the chip lead at one point during play, but ultimately finished fifth.  Joseph Cheong also proved to be a formidable foe during the long battle, but ended up as the third-place finisher.

Stage two of the November Nine’s grand finale was played on the main stage inside the Penn and Teller Theater at the Rio in Las Vegas.  The final duel was played to a packed house of nearly 2,000 spectators and a worldwide audience following the action over the Internet.  Millions more will watch the final crescendo of the WSOP Main Event on Tuesday night, when the championship premiers on ESPN television.  The two-hour program will debut at 7:00 pm PST.
The runner up was John Racener, from Port Richie, FL.  Despite the disappointment of defeat, he could take great pride in a noble effort that resulted in overcoming all but one of the more than 7,000 players who began the pursuit of ever poker player’s greatest dream.  Racener collected poker’s supreme consolation prize — $5,545,955 in prize money.

As the Canadian champion, Duhamel was only the sixth non-American to ever win the WSOP Main Event.  He followed in the hallowed footsteps of Mansour Matloubi (UK — 1990), Noel Furlong (Ireland — 1999), Carlos Mortensen (Spain — 2001), Joe Hachem (Australia (2005), and Peter Eastgate (Denmark — 2008).

 

WSOP Main Event Final Table 2010 Wrap-Up

Wow.

As we sit here on the stage absorbing what we’ve just seen, it’s hard to find words to close this day out properly. But we’ll try.

It was just after high noon when our November Nine filed onto the stage and into their seats under the bright lights of the made-for-TV set. They were soon engulfed by a crowd of close to 2,000 spectators all decked out in matching shirts, patched up like your grandfather’s trousers, and screaming multi-lingual cheers in unison at full throat. Bruce Buffer soon took the stage to utter the most famous words in poker, and suddenly a poker game broke out amidst all the madness and pomp.

It took 28 hands to find our first casualty of the day, and it was the amateur to fall first. Soi Nguyen was content to flip his {Q-Diamonds} {Q-Spades} against Jason Senti’s {A-Diamonds} {K-Clubs}, but a third queen on the flop was all she wrote for Nguyen.

The second victim was also sent packing on a coin flip, albeit an exciting coin flip. Michael Mizrachi’s {A-Diamonds} {Q-Diamonds} loved the {Q-Spades} {8-Diamonds} {Q-Diamonds} flop, but Matthew Jarvis’ {9-Clubs} {9-Hearts} liked the {9-Spades} turn a little bit better. It looked like he’d just saved his tournament life, but the {A-Spades} river gave the pot back to The Grinder and sent Jarvis off in eighth place.

Seven-handed play dragged on for an eternity, and Michael Mizrachi took advantage of the table to build himself a fairly sizable chip lead with more than 60 million. There were still seven when they broke for dinner just before 7pm. When they returned, yet another exciting (and similar) coin flip broke out. Jason Senti’s {A-Diamonds} {K-Spades} out-flopped Joseph Cheong’s {10-Clubs} {10-Spades} in a big way as the dealer rolled out {K-Diamonds} {K-Hearts} {Q-Clubs}. The turn {J-Diamonds} was a little sweat for Senti, and the river {9-Diamonds} was a total disaster. Cheong’s straight pushed his opponent straight out the door, and Senti collected seventh-place money on his way to the bar.

John Dolan fell next in sixth place, his {Q-Diamonds} {5-Diamonds} unable to win a race (imagine that, a race) against Jonathan Duhamel’s {4-Diamonds} {4-Clubs} despite turning 16 outs to survive.

The demise of Michael Mizrachi began when his {A-Diamonds} {8-Diamonds} doubled up John Racener’s {A-Spades} {K-Diamonds} to knock him out of the chip lead. A few minutes later, he doubled up Jonathan Duhamel on a big coin flip, and it all came crashing down a few minutes later. Jonathan Duhamel played his {A-Diamonds} {A-Clubs} slow, and he lured Mizrachi into a shove when his {Q-Diamonds} {8-Hearts} flopped top pair on the {5-Diamonds} {4-Spades} {Q-Clubs}. The chips went in, and there was no further help for Mizrachi, ending his near-legendary run in fifth place. That officially gives Frank Kassela the title of 2010 WSOP Player of the Year, incidentally.

Three hands later, the volatile Italian (who was surprisingly un-volatile today) fell in fourth place. Filippo Candio got his chips in with {K-Diamonds} {Q-Diamonds}, but he could not get there against Joseph Cheong’s {A-Clubs} {3-Clubs}. Cheong flopped an ace and made a wheel by the time it was all said and done, and Candio took just over $3 million for his efforts.

When they began three-handed play, Cheong and Duhamel were running away with the show. They were each approaching 100 million while John Racener sat patiently by with his 20-ish million. Cheong, however, was in no mood to sit patiently. He went to work quickly and was the first player to crest that magical 100-million-chip mark. He and Duhamel proceeded to wage all-out war hand after dramatic hand while Racener folded his buttons, sat on his hands, and waited for the fireworks.

And the fireworks, they came. In Hand #213, 25 hands into the three-way, a battle of the big-stacked blinds broke out. It started with Cheong opening the pot, and the betting action ended with him six-bet shoving all in with {A-Spades} {7-Hearts}. Duhamel probably didn’t like the idea of playing a 180-million-chip pot, but he didn’t waste any time calling with {Q-Clubs} {Q-Diamonds}, putting himself at risk in the process. There was no ace for Cheong, and he was crushed from 95 million all the way down to just ten. It was, as far as we can tell, the largest pot in the history of the WSOP!

Cheong doubled up once in the meanwhile, but six hands after the blowup, he was gone in third place. That’s good for more than $4 million, but it doesn’t come with a ticket to Monday’s finale.

There are only two of those, and they belong to Jonathan Duhamel and John Racener. For handicapping purposes, it’s Duhamel with the big chip lead, but don’t sleep on the short stack. Racener has been playing some fine poker of late, and his short-stack abilities were certainly on display here today.

There are 13 minutes, 52 seconds left in the current level, and the button was awarded to the big stack; Jonathan Duhamel will begin with position on Monday. We’re scheduled for an 8pm start here in Las Vegas.

It’s Duhamel. It’s Racener. It’s $8.9 million and the 2010 WSOP Main Event gold bracelet. Who ya got? Find out how the final chapter plays out right back here on Monday night.