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#111
10-12-2004, 10:27 AM
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Re: My Implicit Assumption
[ QUOTE ]
I don't have to prove the obvious fact that in any normal game you will win a checked down showdown hand often enough to more than compensate for the split pots when your bluff fails. [/ QUOTE ] Yes you do to say decisively that the bluff must work > 20% of the time. Unless I made a error in my calculations and assumptions in my earlier post, you need to be able to show the hand down for free about 40% of the time for checking to be correct. If you can’t show the hand down for free 40% of the time betting is correct. [ QUOTE ] It is obvious to everyone else that the original reason for my post was not because people wouln't know how to weigh these two factors but rather because most would totally MISS the more important factor. Your comment that I am like a physicist that ignores friction but takes wind resistance into account would be OK unless I was teaching a chapter on wind resistence. Everybody else realizes that that was what I was doing here. [/ QUOTE ] I think David’s point is that everyone missed that checking has a positive EV. (I agree that nearly everyone missed check folding is positive EV on the first glance) While Bama’s and my point is that both checking and betting have positive EV, we need further information to determine which is greater. The fact is the original question is flawed. There is not enough information to determine if the correct answer is above or below 20%. 
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#112
10-12-2004, 10:32 AM
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Re: My Implicit Assumption
Assume that a bluff will work exactly 20% of the time. Then we need to compare $20*p and $40*q, where
p = prob that you split the pot, given your opponent has a better hand q = prob that it gets checked to the river and you outdraw your opponent $40*q > $20*p => 2q > p You are claiming that q > 1/2 * p is clearly true in any typical game, right? According to Expunge p ~ 4.5% (assuming when called that the prob. of each hand 44 or better is uniformly distributed). This means q must be > 2.25%. What is the Pr[q > 2.25%]? Is it so large that you can give a problem and expect everyone to assume that it's true? Don't forget 80% of the time your opponent holds 44-AA or Jx. If I offered you two bets: (1)I’ll give you 23o against a hand that has an 80% chance of being 44-AA or Jx. I’m going to deal a flop JJJ. For you to win this bet, the other hand has to check it to the river and you have to out-draw him. If this happens you get $40. (2)I’m going to put 450 blue marbles and 9525 red marbles in an urn. If I draw a blue marble, you win $20. Is (1) clearly a better bet than (2)?
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#113
10-12-2004, 11:29 AM
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Re: My Implicit Assumption
Now that I see you are actually doing the math, I realize that the wierd paramaters I put on the problem and the precise cards involved could make you right. I hadn't realized that you had looked at this precise problem in such detail.
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#114
10-12-2004, 11:39 AM
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Re: My Implicit Assumption
Let me fix the problem for you.
[ QUOTE ] The following highly contrived example illustrates an important principle. The situation is that there is $40 in the pot in a 10-20 game. You have 32 offsuit. The flop is JJJ. You know for sure that if you bet you will be called only by pocket pairs, fours or higher. If you bet and are called you will immediately throw your hand into the muck, slap the dealer, and head to the ATM machine. You then say to yourself the following. "It is correct for me to bet $10 all in, if there is a greater than 20% chance I will steal the pot and incorrect if the chances are smaller than 20%." The above quote is wrong. The correct number is not 20%. It is a bit higher or lower. Which is it and why? [/ QUOTE ]
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#115
10-12-2004, 11:46 AM
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Re: My Implicit Assumption
David we come from the same background (just got my ASA). I analyze everything in great detail - it's my job.
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#117
10-13-2004, 11:24 AM
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Re: What\'s Wrong With This Statement?
One thing I don't understand: if you're including the slight possibility that you will win an uncontested pot after it checks around twice, why do you NOT include the possibility that someone who you might have bluffed out will then bet you out of the pot after you check? Depending on the game, the probability of being bet off the hand by somene elses bluff might outweigh the possibility that you draw to the best hand.
You make a good point about not simply making a play because it has positive EV, but there seem to be too many factors to this problem to make the answer completely straightforward.
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#118
10-13-2004, 10:13 PM
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Re: My Implicit Assumption
NitPick: you need to multiply "p" by $25 not $20, since this scenario features a possible win of $50; $40 in the pot and the $10 opponent's call. Anyway...
Yes. The original argument discounted EV for getting called and splitting. Shame on those of us that did that. No. Your "q" doesn't apply given then opponent has an overpair 80% of the time; it applies for whatever hand the opponent has 100% of the time. The discepency is that your "p" is when you bet and get called (by a pair), but "q" is when you check. Its 17:1 against a random (opponent's) hand having a pair. I suppose I guess its close to 4:1 against a playable hand having a pair. Yes, if you check heads-up there is a greater than 2.25% that 23 will get free cards and pair up and win. If that's not the case (villian bets too much) then Hero has a very profitable check-raise-bluff strategy. - Louie
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#119
10-13-2004, 10:15 PM
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Re: What\'s Wrong With This Statement?
The chances you get bet out of the pot should be calculated into the chances that it gets checked around and you get to show down a pair. Its hard to calculate. But against someone who you KNOW will not call $10 all-in unless they have a pair isn't the sort of player to bet no-pair.
- Louie
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