Poker problem

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RCC
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Poker problem

Post by RCC »

Oldie but a classic:

You are playing limit 7 card stud against a few slightly weak but not stupid players. After 5 cards the pot is quite large...

Your hand after 5 cards is (AA)QQQ

[cards in "()" are the pocket cards]

Your opponent shows 7cKhTc

You bet, and to your suprise your opponent calls.

6th street gives you (AA)QQQQ for exposed quads

Your opponent has 7c Kh Tc Ah showing.

You bet out again, and are called!

Last card you get the 2s. It is your turn to act. What do you do and why?
varwoche
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Re: Poker problem

Post by varwoche »

Well, he could have 4 kings or a straight flush clubs. I suspect the latter because it could have been realized (in full or potentially) sooner and thus explain the betting behavoir.

As to what to do and why, I have no clue and hold little hope that a clue is on my horizon. Right now I say I'd fold, but looking at 4 Qs I doubt I really would.

edit to add: This post didn't postulate a royal flush possibility. It wasn't edited. Honest. All in.
Last edited by varwoche on Wed Aug 25, 2004 9:14 pm, edited 1 time in total.
Beleth
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Post by Beleth »

You've got four of a kind showing and your opponent still calls?

Well, what's better than QQQQ? KKKK, AAAA, and a straight flush.

He doesn't have AAAA because you have two pocket A's.

He doesn't have the heart royal flush because one of the Q's you have is Qh.

He might have a club straight flush or KKKK, but at the end of the 6th card, the best he could have is an open SF or 3 kings, while you're sitting there with four queens in his face. He has two possible outs on the 7th card, but that's no reason to justify him calling on the 6th.

I'd bet.
RCC
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Re: Poker problem

Post by RCC »

varwoche wrote:Well, he could have 4 kings or a straight flush clubs. I suspect the latter because it could have been realized (in full or potentially) sooner and thus explain the betting behavoir.

As to what to do and why, I have no clue and hold little hope that a clue is on my horizon. Right now I say I'd fold, but looking at 4 Qs I doubt I really would.

edit to add: This post didn't postulate a royal flush possibility. It wasn't edited. Honest. All in.


It is your turn to act. I'll hint that folding is not a realistic option with 4 queens, in part because the pot is big as is your hand, but mostly because your opponent has not bet yet.
Last edited by RCC on Thu Aug 26, 2004 3:07 am, edited 1 time in total.
RCC
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Post by RCC »

The answer:


The rational play is to check your four queens. This is an exaggerated version of a very important poker concept.

He will only call if he can beat you, and at that he is going to raise.

You have zero chance of being called and winning, assuming your opponent is not a complete idiot.


This illustrates a basic idea about betting on the end with one opponent. The most important thing to consider is not how often you have the best hand, rather how often you will be called with a hand you can beat rather than called or raised by a hand that beats you, combined with how often an opponent will fold a better hand.

In this case you will never be called by a worse hand as your strength is exposed. A better hand will never fold. You will either force a worse hand to fold or cause a better one to raise.

(Bluffs complicate the picture but do not change it, unless the opponent bluffs into 4 of a kind with alarming frequency, a less than realistic condition)
Beleth
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Post by Beleth »

Ah ha. I didn't know you could check in 7 card stud.
<- noob

I see why checking is the right move, but it still astounds me that an intelligent opponent would call on 6th street when you have four queens showing and the best he could possibly have at that point is 3 kings or an outside straight flush draw.

So what's the next move? You check, he raises. Do you call or fold? Would the answer change if your 7th card was a K or one of 689Jc?
RCC
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Post by RCC »

Beleth wrote:Ah ha. I didn't know you could check in 7 card stud.
<- noob

I see why checking is the right move, but it still astounds me that an intelligent opponent would call on 6th street when you have four queens showing and the best he could possibly have at that point is 3 kings or an outside straight flush draw.

So what's the next move? You check, he raises. Do you call or fold? Would the answer change if your 7th card was a K or one of 689Jc?

I wouldn't call the opponent intelligent, just not crazy. More people than you think would have a problem throwing away an open-ended straight flush draw no matter the situation. In fact, if we posit a pot of more than 20 bets, his call on 6th street is actually correct with an open ended straight flush draw. He would need closer to 40 bets to call with 3 kings.

Consider he knows what 10 of the cards out are, at least. More if there were other players in the game at the begining, so lets just say he has seen 14 cards of the 52, none of which are what he needs. That leaves 38 cards, 2 of which make his hand. Thus he makes his hand one of nineteen times, or 18 to 1 against. If he gets better than 18:1 from the pot, which he does if the pot has 19 bets in it, he has positive expectation. In other words, if you played the scenerio over and over where he is drawing to 2 cards with 20 bets in the pot, he will in the long run make money.

Weird, but true...


With a large pot I will always call. Very rare exceptions. Beyond the math I get into below there are longer term reasons. In short, a fold here may encourage more people to take shots at me.

Say if the pot had 39 bets in it, I check and he bets. I am getting 40 to 1 for my call. I lose one if he has it, win 40 if he doesnt. If I fold I save one where he has a better hand, lose forty if he folds.

So he needs to only be sucessful once out of 40 bluffs to turn a profit.

Likewise, as long as he bluffs more often than one out of 40 times he bets, I am better off calling every time. But if I never fold he should never bluff. If he never bluffs I could pick up a bet by folding now and then. This means he should bluff now and then.


It would be possible to compute from this an optimal calling frequency that does the best in the long run, a frequency that maximizes all possible outcomes...