Fundamental Theorem of Poker vs. Pot Odds

[LouisCyphre]

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What am I missing or not understanding?

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The Fundamental Theorem assumes you can see all the cards.
It's not very practical in that sense. In reality you don't see the cards and you can only make educated guesses.
For example, on the river you get 9:1(not uncommon in limit) on your call. You are pretty sure you are beaten but you you need to be more 90% certain you are right. So if you think there's a 11% chance your opponent is bluffing or missed a draw you have to call.

Often enough I think I can't beat any legitimate hand but call with a weak hand because of pot odds. Again and again I am amazed what kind of crap your average opponent will keep betting.

[Kmon]

good points, I like to work them both in, combine them to put them together gives u some wiggle room on the next move.

[AKQJ10]

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You have exactly enough outs to the nut hand to call a pot sized bet. The problem is that both you and your opponent have $200 left. If you call this bet on the flop, then the pot will be $300. If the board blanks, then your opponent surely is going to be $100 all in and you will be forced to call $100 into a $500 pot and will surely have to do this.

If there isn't enough money left for a full PSB on the next street (turn), where you will be pot committed, how can you just call on the flop? It seems that you don't have enough pot equity to push all in on the flop, but folding would be a "mistake".

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First of all, to understand your example I need to resolve the ambiguity in the bolded sentence. Are you saying that 2:1 is sufficient with one card to come, or with two cards to come? If the latter, then you really need to figure whether it's either worth it to call $100 to see one card or worth it to call $200 to see two cards. I'm not sure if you could construct a big-bet scenario where only the latter rationale would make a call worthwhile. In other words, I don't think you could construct a draw where 2:1 is insufficient to see one card but 3:2 is sufficient to see two cards, and so on regardless of how big the stacks get.

This is handled in TOP, I believe, but it's from more of a fixed-limit perspective. It's called something like effective odds.

I'm sleepy so my numbers may be screwed up.

[El_Hombre_Grande]

The Fundamental Theorem refers to what action is best to take IF you knew all cards, not just your own. Thus it has very little to add to the decision of a crying call, which is based on calculating the small % chance you are actually winning as compared to the size of the pot. The two principles can never be in conflict. If you could see your opponents hole cards, and perfectly understood his reactions to each of your possible actions other than folding, you would know what to do. The FTOP might have something to say about a bluff raise, though.

[Troll_Inc]

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You have exactly enough outs to the nut hand to call a pot sized bet. The problem is that both you and your opponent have $200 left. If you call this bet on the flop, then the pot will be $300. If the board blanks, then your opponent surely is going to be $100 all in and you will be forced to call $100 into a $500 pot and will surely have to do this.

If there isn't enough money left for a full PSB on the next street (turn), where you will be pot committed, how can you just call on the flop? It seems that you don't have enough pot equity to push all in on the flop, but folding would be a "mistake".

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First of all, to understand your example I need to resolve the ambiguity in the bolded sentence. Are you saying that 2:1 is sufficient with one card to come, or with two cards to come?

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I am saying that after the flop, you have can call exactly a PSB to make your hand on the TURN, so in your parlance your 2:1 odds are with one card to come. This is just thinking street to street, not the hand as a whole. (I know this is wrong, I just want to know the literature that deals with it..and the effective odds section doesn't seem to really cover this example explicitly. I'm pretty sure I read about this somewhere before.)

[AKQJ10]

OK, so you have a draw that's 2:1 to come in on the turn card. You call, miss, and now the pot lays you 4:1 for your draw to come in on the river. Wouldn't that be an easy call?

[mvdgaag]

I haven't got HOH here atm, but I think I can answer your question anyways.

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Answer: It costs you $5,000 to see a pot of almost $20,000. Those are excellent odds. Of course, Player F knows that and he gave you those odds anyway, so you're probably beaten. But just in case, I would call anyway."

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You don't see your opponents hand, but for example, if the flop came rainbow and with no pair and you're drawing to the nut straight, than your opponent can't have that straight beat and is not likely to have it beat on a later street. Therefore if he has you beat at the moment and he bets to little so you get sufficient odds it's his fundamental mistake and you make advantage by calling. So the fact that he bets too little does not mean you have to fold according to the fundamental theorem. This is where you are mistaken. If he bets too little but if you call the hand you're drawing to might very well be beat (your drawing to a straight but he is likely to hold a flush), than you have to fold (also according to the fundamental theorem if it was really beat).

Fundamental theorem poker is poker where you and your opponent both see everyone's cards, so there is no deception at all. There are odds to calculate though. For example:

He has two pair and I'm drawing to a flush. I catch my flush this many times to win and sometimes he gets his full house and my flush is worthless. What are the odds I need to be able to call profitably? That is fundamental theorem poker.

This is the real poker equivalent: I don't know what he's got, but he probably has me beat at the moment and I very likely have him beat if I catch my draw. Now how many times do I win when I catch my draw, what are the odds I get to catch my draw and what am I going to pay compared to what I'm going to earn?

As you can see in both fundamental theorem poker and real poker you use odds to decide on an action. The only difference is that you have to think what your opponent might hold in real poker and his actions could be purposely mistaken to deceive you. In your example you assume that you are beat and the draw you are drawing to is beat, because your opponent choses to bet so small. If you could see each others cards you would either see he made a mistake or he really has the hand that's got the hand you're drawing to beat already. But you can't see his cards and you have to quess what he's holding. Is he stupid and giving me the odds or smart and sucking me in? It is a matter of judgement and some knowledge of probabilities.

As a note: Some bad players use the odds to draw from flop to river all the time. You can exploit this by giving them the odds on the flop and if they have likely missed you screw their odds on the turn by betting too big for them to call. This is why some players (at low stakes) purposely give you the odds to call.

Hope this helps,
GL

[PantsOnFire]

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It seems that you don't have enough pot equity to push all in on the flop, but folding would be a "mistake".

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If you have 2:1 odds on a draw for one card, then you have to ahead in the hand. A 33% draw indicates 15 outs for one card. With two cards to come, your draw jumps to about 66% for a full board. So that is really your pot equity. So push all-in with the best hand here.

Also, if you just call with exactly the right odds and miss, you will still have 33% equity for the river card and 4:1 pot odds to call.

If you are thinking of playing a line to call twice, which would be correct by pot odds, there are other lines and percentages you need to think about. If you call the flop and hit your draw, villain may fold your $100 turn bet and you will miss an extra bet. If you push on the flop and hit your draw, you will have that extra bet. If you push on the flop and villain folds, you miss two bets but you might not have hit your draw.

Not sure if this makes sense so somebody straighten me out if need be.

[LouisCyphre]

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A 33% draw indicates 15 outs for one card. With two cards to come, your draw jumps to about 66% for a full board.

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Your math is wrong.
Two 33% chances do not result in a 66% chance. Just as two 50% chances do not mean you have 100% chance and win every time.

[AKQJ10]

No, you're correct. It's an estimate that people apply for lower constituent probabilities, when 1/10 + 9/10 * 1/10 is almost = 1/10 + 1/10 . It's really not appropriate here unless the difference between 55% and 66% is negligible. To make the point that you're still a favorite, I guess that could be considered negligible.

And yes, as a 55-45 favorite you should be happy to get your money in on the flop.