Anothe "Infinite Pot" Question

[David Sklansky]

This time Player A has a 30% chance to improve to the nuts and player B has a 10% to improve to a winner if Player A doesn't improve. What is the proper last round strategy for both players? (Remember B won't call A's bet if he doesn't improve). Also recall that when they both have a 50% chance of improving, a hundred dollar river bet helps A's EV by 12.50. What about in this scenario?

[Ed Miller]

Seems like A is in damage control mode now. One thing to note is that B's percentage chance to improve shouldn't affect A's strategy at all, as every time B doesn't improve, he's not going to put in any more money no matter what. It seems like A needs to check every time now, improve or not. B should then bet every time he improves, and he will get paid off 70% of the time and checkraised 30% of the time showing a profit on his bet.

90% of the time, EV is zero.
7% of the time, B gets paid off 1 bet
3% of the time, A gets the checkraise in and makes 2 bets.

A's EV per round is then 0.03*200 - 0.07*100 = -$1 per round.

[BB King's]

Your solution is wright - and a very good explaination. Good post !

[BB King's]

In your first problem you are implying that B should check behind - that is wrong !!!

[David Sklansky]

B Should check behind as long as A checks infintesimally more of his made hands than he bets. He is indifferent at exactly fifty fifty. When he is indifferent you should assume whatever action makes the problem easier to solve. I am surprised you need this spelled out for you. (This post concerns the previous problem. Not this one. And is directed only at BB.)

[pudley4]

</font><blockquote><font class="small">In reply to:</font><hr />
B should then bet every time he improves, and he will get paid off 70% of the time...

[/ QUOTE ]

No he won't because if A knows B only bets when improved, then A won't call unless he himself improved.

[pudley4]

Ok, I guess A has to call any bet by B, so the answer majorkong gave is correct.

(With this betting structure, A has to improve at least 1/3 of the time in order for him to have a strategy other than checking to B.)

[Ed Miller]

A has to call because the pot is infinite in size. If A stopped calling when B bet, then B could possibly bluff. If A were to fold to a bluff, then his mistake would be of infinite magnitude.

[rigoletto]

Hi David

I like these puzzles (even when I'm loosing sleep), but I wonder about the poker-value? The infinite pot makes the scenario slightly unrealistic /forums/images/icons/wink.gif and you can't figure pot odds. I'm strictly a LL player and only a moderate winner, but I would guess that in real life almost anybody would call a riverbet if the odds are 1:30 or more. I've read TOP (good book - I need to play more and reread though) and I can see the point in basing your descissions on statistical analysis (In TOP the examples are fortunately more realistic), but it seems to me that it's often based on assumptions of:

1) knowledge of your opponent!
2) your ability to implement different strategies for different situations and opponents over time!

I guess my questions are: What do we learn pokerwise from these questions and how do we implement the things we learn?

[David Sklansky]

The correct answer for infinite pot questions is close to the correct answer if the pot is merely big. In other words if your strategy was the infinite pot strategy you are giving up very little.

[rigoletto]

Thanks!

I guess I should go calculate some examples myself and reread TOP (but it's so much easier to ask others /forums/images/icons/wink.gif ).

[CFunk]

It seems agreed that a bluff is never correct in this situation. So why can't A fold to a bet? I recall something I read saying that when a player bets or raises on the river when he knows that a player will call his bet, he is likely not bluffing so you can fold to his bet. With the infinite pot size player B is betting for value because he has to assume that A will call. Thus A can fold to his bet. Of coarse, the infinite pot size would make a mistake infinitely costly and $100 isn't much savings for someone that can afford to put an infinite amount of money in a pot. Maybe what I read is more for limit holden anyway. Just wanted to see what you think about that.

CT

[Ed Miller]

An infinite sized pot would make it correct to call any finite bet if there were any less than absolute 100% certainty that you were beaten. In fact, the whole reason Sklansky made the pot infinite in size was so that people wouldn't argue about whether it was correct to pay off... it is always correct.

[Zoe's Echo]

By my calculation - the changes of Player A dragging the pot is 93% (30% + (70%-7%)) while Player B has a 7% chance of winning (70%*10%). Therefore, if Player A has a positive EV of 12.5 if the winning probabilities are only 50%/50% then his EV is exceptionally higher at 93%/7%.

Based on this I think Player A should always bet and reraise without improvement. If he is again reraised without improvement - then call.

Player B should raise with improvement - as when improved the probablity is 70% that he/she is winning.

That being said if Player A is likely to fold his/her unimproved hand to a raise since he/she presumes that Player B cannot raise without improvement (can't even call without improvement) then it is a positive EV play for B to raise with any hand.

Not a math whiz but my twos cents.

Good Luck!