Fundamental Theorem and Imperfect Information?

[DocOfDan]

Hi

I've been thinking about Sklanskys Fundamental Theorem of Poker recently. The assumption is that you can see your opponents cards and this knowledge therefore informs the optimal choice of fold/call/bet.
Extrapolating from this would seem to that the 'correct' play in any given situation is the one that would have the maximum EV, given our 'perfect information' scenario.

In reality of course we have 'imperfect information' in that we can't (usually!) see our opponents cards until the hand is over. Is it possible to judge our play retrospectively. That is, armed with the 'perfect information' AFTER the game, is it possible for us to go back and determine individual decisions to be 'correct' (as in optimal) in any sense. If it is possible how do we make that decision?

Furthermore, given that our opponent(s) has no knowledge of our pocket cards, how do we account for deception? It isn't simply a case of which hand is most likely to win a showdown and pot odds. Do we have to estimate the probability of the person folding, calling or raising to our action? If so, how?

[TStoneMBD]

just because a guy has his hand face up and doesnt realize you know what his cards are doesnt mean that you can play the hand perfectly. you have to understand fundamental poker first. then, you have to understand what course of action your opponent will take. if for instance you see he has bottom pair no kicker, you may plan to bet him out of the pot. how do you know he wont call you down? it takes more than just knowing your opponents hole cards to play perfect poker. also, if you were to find out what your opponents hole cards were, and analyze your play according to it, your analysis will be biased and you wont be able to come to a fundamental judgment. that is why players withhold results on these forums when posting a hand because he wants unbiased advice. just because a player had a particular hand in a situation does not mean he will always have that particular hand. yes, we can look at the hand afterwards and realize that he had a flush draw and therefore try to discover how to make him pay the most for that. however, that is not to disregard the possiblity that he in fact had a set. if you have AA and the board is Jc5c6d, and your opponent rivers a flush, and you forgot to 4bet him on the flop, you allowed him to draw to his flush for less than he had to. however, next time you have AA on a board of Jc5c6d vs the same opponent, it may be silly to 4bet the flop because this time he may in fact have trip 5s. therefore its silly to analyze your play soley based on results as it doesnt help you in future situations. that is not to say that results shouldnt be considered during future hands. experience plays an important role in knowing when your opponent may or may not be on a flush draw, and experience is grown predominantely by the history of results we have encountered.

[dana33]

The FTOP is just a starting point. It tells you what your goal is, but by itself does not tell you how to get there. It tells you that, over the long term, your profit comes from your opponents' mistakes. This means that your goal is to seek out opponents who make many mistakes, and when at the table, behave in a way that causes them to make more mistakes than you do.

This is where the skills of reading players, reading hands, computing pot odds, deception, and all the rest come in. You ask how we make our FTOP-based decisions given that we can't see our opponents' cards. The answer is by developing and applying these skills.

[Beavis68]

I think you are taking it a little too literally. What it is really saying is that when you play your hand "as if" you could see your opponents hole cards, you win. This is because you are making correct decisions, and that is +EV for you. When you play differently than you would if you could see your opponents hole cards, your oppenent wins and vice-versa.

This comes from the theory that we make money from mistakes and lose money when our oppenents play correctly (which is not always true in multi-way pots).

The only really good way to judge your play on specific hands is by judging the range of hands your oppenents would play and how your hand stacks up to that.

[DocOfDan]

Thanks for all the replies guys - I don't think I made myself clear enough - I am talking here in conceptual terms about what the Fundamental theorem tells us (or doesn't!)

Just to clarify (and not picking on Beavis' reply!)
[ QUOTE ]
What it is really saying is that when you play your hand "as if" you could see your opponents hole cards, you win.

[/ QUOTE ]
Agreed, the question is how should that be? Even if we can see our opponents hand we don't know how they will respond to our play - e.g. if we bet they may call, while a check-raise may be possible.

[ QUOTE ]
This is because you are making correct decisions, and that is +EV for you.

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Is it possible to know what a correct decision is? For example consider the following situation. I have an inferior hand with $50 in the pot after the river card is dealt, but somehow (remember we are hypothesising here /images/graemlins/wink.gif) know that my opponent will fold 30% of the time to my $10 bet, then I know that it is a +EV situation for me to bet (30% of the time I take in $60 and 70% of the time I lose $10 - so my EV is +$11 for my $10 bet).
Armed with my perfect knowledge I just select the check/bet option that has the higher EV. That is the 'correct' move.
But some instances of the above scenario will see me lose money even though it is the 'correct' play.
In reality we don't have perfect information, so we can only estimate the EV of each particular action and our 'correct' (in the imperfect information, i.e. real, game) is the move which we estimate to have the highest EV. The more accurate our estimation, the better the player we are.

If we look at a hand after it has been played (assuming a showdown) we know what our opponent had - is there any way we can judge the 'correctness' of our actions during this hand?
Do we have to know the probability of all possible opponent responses to our actions to pass judgement? Even if we do know all opponent responses and their probabilities, what about the idea of creating a table image etc. i.e. we may play sub-optimally in one hand for deceptive purposes to increase our overall income.

[ QUOTE ]
This comes from the theory that we make money from mistakes and lose money when our oppenents play correctly (which is not always true in multi-way pots).

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I am aware of the exceptions to the FTOP for multi-way pots.

Bottom line - elegant conceptualisation though the FTOP is, how much does it help us to learn to play good, even optimal, poker?

[Beavis68]

No, it is not possible to know, but this is theory.

Whenever you make +EV moves you make money, when you make -EV moves you lose money, regardless of the outcome of the hand (this is theory too, but based on the fact that profitablility is over the long run not the short term).

It is really not a good way to judge your play after the fact, it is just a fact of poker.... at least that is my 2c.

[DocOfDan]

isn't judging your play after the fact - learning from experience?

/images/graemlins/wink.gif

[the alex]

[ QUOTE ]
isn't judging your play after the fact - learning from experience?

/images/graemlins/wink.gif

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The heart of the theory itself to not solely use the outcome of a hand to evaluate your play. Your play is a compilation of bets, raises, call, checks, and folds, within hands, sessions, weeks, months, and years.

When evalauating your play on a couple of similar situations, you always look at all of the streets. The FTOP is the foundation for incorporating your instincts with the math (EV). The math is based on a constant of a 52 card deck that if you had no need for instinct, in the long term, you play the math and you win.

You make your calculations based also on your instincts (implied odds). Experience improves your instincts which strengthens your math with heightens your EV.

I think this is what you were asking. If not, maybe you could be clearer. Remember that when you say that Player X will fold 30%, you're guessing with information from your instincts. Maybe your math was wrong, but most of the time it's instinctual flaws that contribute to -EV moves.

[DocOfDan]

Thanks Alex

I view the FTOP as a conceptual device to guide us towards playing better poker - I suspect in the same way as all of the posters in this thread do.

What I am discussing, is the limits of that conceptualisation.

Lets look at it like this (taking limit hold'em as our example)
The 'perfect' (and of course impossible) situation would be something like this:
1) We could 'see' all of our opponents cards
2) We would know what cards will fall on the flop, turn and river
3) We would know how our opponent(s) will respond to any action we take.

The correct play is then deterministic - it is the one with the highest EV.
Of course, in reality none of (1-3) above are true. The FTOP theorem of poker works by using the conceptualisation that (1) is in fact true - i.e. we can see our opponents cards
(2) is not in fact that difficult to deal with - it is a matter of probability
(3) is in practice dealt with by our ability to 'read' other players and infer their likely actions based on our belief as to their likely holdings

If we now turn to post-game evaluation - we now have perfect information for (1) and (2), but not for (3) - all we know is our opponents response that time to that particular action.

We can all take views on (3) to inform our belief in the correctness of a hand, e.g. someone bets on the turn with an underpair against another player who has shown strength. It is possible that we might scare out the other player, we might make trips on the river, catch the other player bluffing etc. However most of us would say, unless there was very good reason to suspect a bluff, or a very strong draw there, that betting here was a bad play.

But is there any way we can really say this (was a bad play) in isolation. Our hero might have had very good reason to believe the bluff, he might be looking to create a table image etc.

Is there any way we can look at a play and pass judgement on its correctness? The FTOP doesn't go this far - it just says that if we play differently to how we would with knowledge of our opponents cards we lose. But is there any way of saying how we should play, even with this knowledge? What other knowledge would we need? How much of this extra knowledge do we have after a game to learn from our past play? Is there any way we can infer something with regard to any missing knowledge?

[parachute]

When I think about the FTOP I actually envision the scenario in which both players can see each other's cards and both know how to play perfectly from a mathematical optimizing-your-EV point of view.

In reality there are two ways to make mistakes: 1) making a math mistake (calculating your pot odds badly, or counting your outs wrong, or not realizing you can bet for value) even given that you know (or have guessed correctly) your opponent's cards, thus making the wrong EV-optimal play, and 2) misguessing what your opponent's cards are, thus causing a non-EV-optimal play because your understanding of the situation was insufficient.

In games of perfect information like chess, the only kinds of mistakes are of type 1. In games like poker, you can make type 2 mistakes too, which is what the FTOP is all about. But the fact that type 2 mistakes exist doesn't mean that type 1 mistakes don't exist. (I was just harping on this point in another thread too.)

As far as determining optimal play given that your opponent can't actually see your cards, that's what poker is all about, and it's pretty impossible to quantify except by assigning more or less arbitrary probabilities to your opponent's actions, which is how Sklansky analyzes situations in TOP.