Typical Situation Math Problem

[David Sklansky]

25-50 Blind. You have 1000 in front of you. You make it 200 with AK. Someone behind you makes it 500 and you are almost certain he will do this with queens or better and nothing else. If you just call and bet all in on the flop, he will always call. He will always move in if you check. If you move in preflop he will always call. What's the right play?

Assuming the above assumptions remain true, with what size original stacks, if any, is it correct to fold to his original reraise? (Assume all flop bets and preflop reraises are move ins).

[HoldenFoldem]

AK vs QQ is about even.
AK vs KK is -EV
AK vs AA is -EV

therefore you fold this hand to this raise , from this raiser, regardless of stack size.

"He will always move in if you check. If you move in preflop he will always call."

He will do this with QQ regardless to whether the flop comes with an A or K. The question is what is the mathematical answer?

DS, does opponent do this re-raise with AK as well? If so, that changes the % of the time he has AA or KK. If only AA, KK, and QQ then it's 33% each.

So if he has QQ 33% of the time and your AK hits the flop 33% of the time and you win the remaining 500 then what is your EV? Also what is your EV if he has KK 33% of the time and you hit your A on the flop ~17% of the time and win the remaining 500?

Now take into account the times you whiff the flop and check/fold. You don't lose the remaining 500.

Not sure how this all works out...would be interested to hear.

[LearnedfromTV]

He doesn't have AA/KK as often as QQ b/c you have an Ace and a King. It's AA 3 ways, KK 3 ways, QQ 6 ways.

[Scotty.]

You are calling 300 into a 775 pot with a hand that is a 30:70 underdog.

[LearnedfromTV]

Your options:

1. Fold. Expected Stack Size = 800.

2. Call and push any A/K flop that doesn't have a queen, check fold otherwise. This is clearly better than/indifferent to calling and doing anything else, because betting the last 500 on a missed flop is -EV and you know he's calling your bet and betting if you check, so check-calling is the same as betting.

If he has AA, an ace or king will flop 1 - (44*43*42)/(48*47*46) = 23.4% of the time. The board wil include a Q ~12.5% of those times, so you will push ~ 20.5% and lose your stack nearly every time (KKx the very unlikely exception).

If he has KK, an ace will flop 18% of the time, the case king will flop 6.25% of the time. Again, 12.5% of those time you'll get away b/c of a Q on board (even though specifically when he has KK, this is a mistake). You'll push and be ahead 16% of the time, push and be behind 5.5%. To balance the KKx board v AA, let's assume he never catches the case K on Axx board when he holds KK. It should be close to even.

If he has QQ, you'll flop an Ace or King 33.7% of the time. He'll flop a set 8.5% of those times, and you'll fold b/c of the Q on board, so you will push ~ 30.8% of the time. This assumes, again, that you fold AQx boards (KQx is automatic, AQx is correct b/c you only beat 3/18 combinations). He'll turn or river a set ~ 8.5% of the time, so you will win 28.1%, lose 2.7%.

He has AA 1/4, KK 1/4, QQ 1/2. If you call and push an A/K flop, your expected ending stack size is

.25*.205*0 + .25*.795*500 (AA)

+ .25*.16*2150+.25*.055*0+.25*785*500 (KK)

+ .50*.281*2150 + .50*.027*0 + .50*.792*500 (QQ)

= $784

3. Push allin preflop. He has AA 1/4 and you are a 93/7 dog. KK 1/4 and you are a 70/30 dog. QQ 1/2 and you are a 57/43 dog.

Average stack size = (.25*.07+.25*.30+.50*.43)*2150 = $661.

Conclusion: FOlding is best, calling and pushing is slightly behind, going allin is worst.

I ignored flopping a straight, but that is too rare to make up $16.

My guess is that calling is profitable with AKs, because putting 500 in to win 2150 is +EV with a flush draw and occasionally a flush/straight draw whether you have clean overcards or not, and that increased EV is likely to be > $16. I doubt that flopping draws with Ako (monotone flops) is significant enough to sway AKo to a call.

So, fold AKo. Call and push favorable flop w/ AKs.

[LearnedfromTV]

[ QUOTE ]

Assuming the above assumptions remain true, with what size original stacks, if any, is it correct to fold to his original reraise? (Assume all flop bets and preflop reraises are move ins).

[/ QUOTE ]

You are actually right at the borderline w/ a stack of 1000. Slightly more and your opponent's mistake of calling allin w/ QQ on an A/K board is large enough to make calling preflop correct.

The main reason the strategy of pushing an A/K flop can become profitable somewhat quickly is that

a) He's relatively more likely to have QQ because you have AK.

b) you are more likely to get an A/K flop the times he holds QQ than when he has you dominated.

This is somewhat counterintuitive in comparison to the idea that AK would prefer to see all five cards versus an underpair. Ideally, you would see all five cards here and then put your money in if you had a pair and there wasn't a queen on board. You can't do this because the pair won't let you, but you are wrong to push to see all five, because this eliminates the main advantage of your strategy to push when you flop a pair, which is that you are much less likely to flop a pair you don't want (vs. AA/KK) than one you do (vs. QQ).

Of course, this guy can crush you if he folds QQ on an A/K high flop, which he would have to start doing as the stacks get deeper.

[JMa]

how is this typical? do you often play 25/50 w/ 20BB?

[catlover]

David -- here is the problem I have with the line of reasoning that seems to be developing here.

It looks like we are heading towards folding AK here. Similar reasoning will definitely lead us to fold all pairs except AA and KK. But if we are folding this often, isn't our opponent correct to make this preflop reraise with any two cards? The only exception would be, if there are a lot of people still to act behind him, the risk that one of them might have AA could swing this reraise to incorrect.

Also worthy of note for those doing the math -- David said "almost certain". The "almost" in there could make a lot of difference and needs to be quantified.

I guess what I am getting at is -- it can't possibly be correct play to only reraise with monsters. If you play this way, your opponent can now correctly fold everything but *his* monsters. But for the reraiser, it is much better if a fold by the original raiser is an iffy play for the majority of his hands.

[AJFenix]

[ QUOTE ]
how is this typical? do you often play 25/50 w/ 20BB?

[/ QUOTE ]

The book is gonna be loaded with goodies like this one isn't it [img]/images/graemlins/crazy.gif[/img]