[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."

[/ QUOTE ]

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