Deception and the Fundamental Theorem of Poker

[Toonces]

Something that has always bugged or confused me about the Fundamental Theorem of Poker is that I've never seen it address the cost of deception. It seems that bluffing, semi-bluffing, slowplaying and sometimes raising with the second-best hand are all things that you would not do if the cards were public and therefore all would cost you money according to the FToP.

Is it a correct conclusion to make that deception is only correct if the sum of the EV of mistakes you cost your opponents to make through deception outweigh the sum of the EV of mistakes you purposely make by deception? In addition, since you are theoretically making a "mistake" 100% of the time, if you cause your opponent to make a mistake 50% of the time, their mistake would need to be twice as costly as yours to turn a profit?

I would like some feedback from others as I don't know if I am looking at this properly, but I've never seen the cost of deception as it relates to the FToP in the same way I have seen the value of deception discussed.

[Eclypse]

Your understanding of FToP is flawed. It states

“…if you could see all your opponents cards”

OR

“…if they could see all your cards.”

NOT “…if you could see all your opponents cards AND they could see all your cards.”

[Toonces]

I see the difference, but I thing the FToP makes more sense my way. In a game of complete public information, two reasonably intelligent players would play the hands identically playing either set of cards. Playing off the obvious line of play costs you, whether or not your opponent knows what you have. The good news is that if your opponent doesn't know what you have, your "mistake" is more likely to induce a "mistake" by your opponent.

There must be a definite cost to deception, or the betting decisions would be random and meaningless. Deception on a given decision is no less costly because "I meant to do that with full understanding" rather than simply betting "incorrectly".

[Eclypse]

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Something that has always bugged or confused me about the Fundamental Theorem of Poker is that I've never seen it address the cost of deception.

[/ QUOTE ]

Chapter 8 of TOP: "The Value of Deception"

I believe this will be exactly what you are looking for.

[pzhon]

[ QUOTE ]

Is it a correct conclusion to make that deception is only correct if the sum of the EV of mistakes you cost your opponents to make through deception outweigh the sum of the EV of mistakes you purposely make by deception? In addition, since you are theoretically making a "mistake" 100% of the time, if you cause your opponent to make a mistake 50% of the time, their mistake would need to be twice as costly as yours to turn a profit?


[/ QUOTE ]

No, you should consider playing deceptively if it is better than the alternative of not playing deceptively. If you are not deceptive, it may be that the net FTOP error is not 0. If you expect to cause FTOP errors by playing in a straightforward fashion, this is an extra argument against playing deceptively. If you expect to make FTOP errors after you play naturally, this argues for playing deceptively.

For example, suppose you have the nuts on the river HU, acting first. The natural thing to do is to bet. This might provoke a bad call or raise. The deceptive play is to try to check-raise. You need to weigh the chips your opponent would put into the pot if you check against the chips your opponent would put in if you bet. That checking may provoke FTOP errors from your opponent is not enough to conclude that checking is right.

[parachute]

[ QUOTE ]
Is it a correct conclusion to make that deception is only correct if the sum of the EV of mistakes you cause your opponents to make through deception outweigh the sum of the EV of mistakes you purposely make by deception? In addition, since you are theoretically making a "mistake" 100% of the time, if you cause your opponent to make a mistake 50% of the time, their mistake would need to be twice as costly as yours to turn a profit?

[/ QUOTE ]

You are exactly correct. This is something that a lot of players don't get. I keep meaning to write an essay about this but I haven't gotten around to it yet.

[parachute]

In the "heads-up nuts on the river" case, note that the "face-up EV" for you is the same whether you check or bet; if all the cards were face up, your opponent would check if you check and fold if you bet, and you wouldn't get any extra money over what's already in the pot in either case.

So the check-raise question here is whether the money you earn through the possibility of your opponent making the "mistake" of betting after you check is greater than the money you earn through the possibility of your opponent making the "mistake" of calling or raising the standard play of a bet. Both checking and betting are "face-up-optimal" plays, so it's not a question of whether his mistake outweighs your mistake (since neither of your plays is a mistake in that sense), it's just a question of how to induce the biggest mistake on his part.

("Mistake" above always refers to a FTOP mistake, that is, playing your cards differently than you would if they were all face-up.)

[pzhon]

The original poster asked whether it was right to estimate the errors you make versus the errors your opponent makes if you play deceptively. This asks whether the net error of playing deceptively is greater than 0. The right question is whether the net error if you play deceptively is greater than the net error if you don't play deceptively.

[Monty Cantsin]

[ QUOTE ]
In a game of complete public information, two reasonably intelligent players would play the hands identically playing either set of cards.

[/ QUOTE ]

It's interesting to note that in the face up game between two identical rational players the EV of every play is 0. With a total understanding of the odds, no hand that was behind would ever call a bet.

Of course, in reality, two actual players of the face up game might disagree about the odds or might be willing to take the worst of it in certain situations for the fun of gambling, and the game might proceed that way.

This is what happens in, like, Chess or Go or any 2-player game of perfect information. The players are essentially in disagreement about the optimal play. If the argument was ever finally settled for good no rational players with a total understanding of the game would ever make any move.

So, real poker deviates from the face up game in a more profound sense than implied by your argument.

Anyway, I think you've got it right. Every deceptive play in poker is a gambit, and the effects need to sum +EV for it to be g00t.

/mc

[parachute]

[ QUOTE ]
It's interesting to note that in the face up game between two identical rational players the EV of every play is 0.

[/ QUOTE ]

Well, if you have AA and your opponent has 72o then the EV of your bet is positive, since your opponent will certainly fold and you'll pick up the blinds.

But the difference in EV between your play and the optimal play is 0, by definition. So all non-face-up-optimal plays are "mistakes" and require a reciprocal "mistake" by your opponent to make more money than the face-up-optimal play.

(Of course, in a real face-down situation, players are going to be making "mistakes" all the time, without any deception even being involved. So this is more an explanation of the game theory behind poker than a discussion of deceptive play. But note that the FTOP as written doesn't say anything about deception either; "deception is a valuable tactic" simply follows from it.)

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With a total understanding of the odds, no hand that was behind would ever call a bet.

[/ QUOTE ]

This isn't true, because of the difference between pot odds and "round odds" (what do you call the odds you're getting on this round's betting only?). If I have a 2/3 chance of winning the hand to your 1/3 and there are 2 bets already in the pot, I should bet (because I am getting back most of the money going into the pot this round) and you should call (because you are betting one bet to win three but the odds are only 2:1 against you).

[parachute]

[ QUOTE ]
The original poster asked whether it was right to estimate the errors you make versus the errors your opponent makes if you play deceptively. This asks whether the net error of playing deceptively is greater than 0. The right question is whether the net error if you play deceptively is greater than the net error if you don't play deceptively.

[/ QUOTE ]

OK, I think I see what you mean (that playing non-deceptively is not guaranteed to be playing face-up-optimally, so that in practice you're not really comparing deception against "perfect play"), and I agree. You are actually comparing the deceptive play against the non-deceptive play, even if both of them have a reference point of perfect play.

I think we agree on all the math and that what we're disagreeing on (if anything) is how relevant it is to the original question. Here's the Theory Of Poker quote that got me started down this road:

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Suppose your hand is not as good as your opponent's when you bet. Your oponent calls your bet, and you lose. But in fact you have not lost; you have gained!

[/ QUOTE ]

This really confused me for a while, until I realized that I gained EV when he called instead of raising, but I lost EV when I checked instead of betting., and you have to compare these two costs to compute whether it's a good play or not. I think a lot of people overvalue deception because they don't think about the second cost.

So when I said the original poster was exactly correct, I meant that he is correct that this second cost exists, which I think everyone posting here is agreeing with.

[Toonces]

[ QUOTE ]

It's interesting to note that in the face up game between two identical rational players the EV of every play is 0. With a total understanding of the odds, no hand that was behind would ever call a bet.

[/ QUOTE ]

Like other have said, in the face-up game, until the river card, it is often correct for one person to bet and the other to call. In a many-handed pot, it may even be correct for someone to bet and someone else to raise, even face-up.

[ QUOTE ]

Of course, in reality, two actual players of the face up game might disagree about the odds or might be willing to take the worst of it in certain situations for the fun of gambling, and the game might proceed that way..

So, real poker deviates from the face up game in a more profound sense than implied by your argument.


[/ QUOTE ]

True, in a real face-up game, people still make probability mistakes or would be willing to make a -EV gamble. But those are still mistakes.

My contention is that for every hand of poker, there is an optimum face-up line of play. To determine how much a player can expect to win in the future, you can add up the EV he earns from all the times his opponents veer from the optimal line, and subtract all the EV he costs himself from veering from the optimal line. The river is an exception case, since checking and betting on the river with the best hand are equivalent EV on the river in the face-up game.

[Monty Cantsin]

[ QUOTE ]

Like other have said, in the face-up game, until the river card, it is often correct for one person to bet and the other to call.


[/ QUOTE ]

I was thinking of the 2-player face-up game. But I didn't make that clear.

Of course, even in a heads-up face-up game you can manipulate the size of the blinds to make calling correct. (And even with normal blinds you will sometimes be getting the necessary overlay to call with a slight dog) So I'm still wrong!! I was thinking of the river, where it's pointless to bet, and working backwards, but I didn't go back far enough (to the blinds).

[ QUOTE ]

My contention is that for every hand of poker, there is an optimum face-up line of play.


[/ QUOTE ]

Ok (I have a caveat that for this to be the case you also need your opponents' overall strategy to be "face-up" but I'm not going to mention it because it's nitty and possibly wrong).

[ QUOTE ]
To determine how much a player can expect to win in the future, you can add up the EV he earns from all the times his opponents veer from the optimal line, and subtract all the EV he costs himself from veering from the optimal line.

[/ QUOTE ]

Shouldn't you start with the base-line EV of the hand as played optimally by all parties and then add in the sum of the deviation EV? Maybe this is what you mean.

/mc

[Toonces]

[ QUOTE ]
Shouldn't you start with the base-line EV of the hand as played optimally by all parties and then add in the sum of the deviation EV? Maybe this is what you mean.

/mc

[/ QUOTE ]

In a look-back sense, yes. But I am thinking of in a look-ahead sense. Take a heads-up game. After 1000 hands, player A wins $500 from player B. But player A makes $2000 in mistakes deviating from the optimum line while player B makes $1900 in mistakes deviating from the optimum line. If they played another 1000 hands, you would expect player B to win $100 from player A (with obviously a lot of variance).