TOP: Fundamental Theorem discussion.

[Pokey]

OK, chapters 1-4 had one critically important concept that we really SHOULD discuss in detail: the Fundamental Theorem of Poker. To recap: on page 17 Sklansky says:[ QUOTE ]
Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. COnversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.

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This theorem holds true if we may one critically important extra assumption: given all information revealed, people would play in mathematically optimal ways. I'm sure that at Sklansky's tables that's true; at MY tables, I'd be highly surprised if it turned out to be correct.

Look at a blackjack table some time. See the dealer showing a king. Watch the guy with 15 stay because "I know I'll bust if I take a card." Watch the folks split tens, take insurance or even-money blackjacks when dealer is showing an ace, hit (not double) when they have 11 and dealer shows a 6, etc., and you'll quickly realize that common folks simply do NOT always make the mathematically correct choices.

The pot is built up to $50 with two players left. The last one pushes all in for his last $5 and flips up AA unimproved. I'll bet that many nits would fold their T9o on a board of K92r because "he's got me beaten."

The pot is $15. One player pushes all-in on the flop for his last $60 and flips up JJ for a set. I'll bet that many maniacs would call with an OESD because "I won't let him muscle me off my draw."

Encouraging mistakes is definitely a good thing, but to say that any time our opponents know our cards AUTOMATICALLY makes their moves optimal seems erroneous at the small-stakes tables.

[Isura]

[ QUOTE ]

Encouraging mistakes is definitely a good thing, but to say that any time our opponents know our cards AUTOMATICALLY makes their moves optimal seems erroneous at the small-stakes tables.

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They may not play optimally. But any player will make less mistakes if he knows what you have.

[bitter&twisted]

"Encouraging mistakes is definitely a good thing, but to say that any time our opponents know our cards AUTOMATICALLY makes their moves optimal seems erroneous at the small-stakes tables."

I don't think Sklansky is saying this Pokey.
All he is saying is that if you can see all the cards then there is a mathematically optimal way to play.
Not that if you can see all the cards then your play will be optimal. Which seems to be what you are suggesting he says.

[cbloom]

I think the phrasing of the fundamental theorem is really strange. If they're a bad player there could be cases where if they knew your cards they'd actually play *worse* because they make bad decisions (eg. if you have a good hand, they might fold even though they have pot odds to call, etc.). I think it's better to think just in terms of your own play, and thinking of their exact cards is silly too.

Any time you make a play which is not optimal against their correct Bayesian card range (the best knowable card range given their action), you lose (compared to optimal).

If you play such that your cards are obvious, it allows them to play optimally against you (if they're capable of that).

[bitter&twisted]

"If you play such that your cards are obvious, it allows them to play optimally against you (if they're capable of that). "

Sklansky talks about this in the ""Mistakes" according to the Fundamental theorem of poker" section.

General idea "I think" is that the closer you play to optimally the more you gain/they lose, and the further they play from optimally the more they lose/you gain.

So yes when you play optimally you become obvious therefore it is easy for your oponent to play close to optimally.

So you use deception to try and get your opponent to play as far from optimal as possible, while at the same time trying to keep your play as close to optimal as possible.

[7stud]

[ QUOTE ]
Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain

[/ QUOTE ][ QUOTE ]
This theorem holds true if we may one critically important extra assumption: given all information revealed, people would play in mathematically optimal ways.


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Most of the time, I think that's incorrect. Morton's theorem shows there are some exceptions to the Fundamental Theorem in multiway pots, but the Fundamental Theorem holds true in heads up play.

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I don't think Sklansky is saying this Pokey.
All he is saying is that if you can see all the cards then there is a mathematically optimal way to play.
Not that if you can see all the cards then your play will be optimal. Which seems to be what you are suggesting he says.

[/ QUOTE ]
As bitter&twisted said, if you can see the cards, then you can determine the mathematically optimal play. However, if a person can see the cards, but he can't determine the mathematically optimal play, or he can't bring himself to make the mathematically correct play, then he loses and you gain. By definition, if you don't make the mathematically optimal play, you lose. I believe all the fundamental theorem of poker is saying is that there is a mathematically optimal play when all the cards are known, and anytime you deviate from that optimal play, you lose.

[ QUOTE ]
you'll quickly realize that common folks simply do NOT always make the mathematically correct choices.

[/ QUOTE ]

All the examples you gave are of people making bad plays. How does that prevent them from losing and the house or their opponent from winning?

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Encouraging mistakes is definitely a good thing, but to say that any time our opponents know our cards AUTOMATICALLY makes their moves optimal seems erroneous at the small-stakes tables.

[/ QUOTE ]
The Fundamental Theorem does imply that your opponent's will pay optimally if they can see your cards. However, that doesn't mean they will win if they deviate from the mathematically optimal play. For instance, if someone will fold pocket Kings to your raise preflop because they don't want to risk that much of their bankroll on one hand, it doesn't mean they don't lose if they make the same play when you show them your pocket Queens before you raise. Yet, they played the same way when they didn't know your cards as when you showed them your cards.

So, I guess a strict literal reading of the fundamental theorm could lead you to conclude that your opponent isn't losing by folding his pocket Kings because he played the same way when he could see your cards, but hopefully you can see why that's not true.

[mikechops]

I think the whole theorm is a over-rated. It certainly isn't what I'd call fundamental. Talking about inducing a 'mistake' from an opponent, when he doesn't know your cards and you don't know his, is a bit silly.

Poker comes down to putting people on a range of hands and playing optimally from there. You need to make correct estimates of the relative probability of your opponents' holding(s) and their likely reactions to your possible actions. Then you select the action that gives you the highest EV. That's fundamental.

I'll give an example that might clarify the difference. I was watching a re-run of the 2004 WSOP ME last night. Down to 3 tables and the last 19. 1 more player had to go before they could finish the session. Josh Arieh raised J[img]/images/graemlins/heart.gif[/img]9[img]/images/graemlins/heart.gif[/img] UTG pre-flop and got a couple of callers. Flop is A[img]/images/graemlins/heart.gif[/img]K[img]/images/graemlins/club.gif[/img]Q[img]/images/graemlins/heart.gif[/img]. Josh pushes for an over bet of about 200% of the pot. An English guy on the BB calls all-in with AJo. Josh had him just covered.

Josh is openly disgusted with the call. "You called with Ace-Jack?!? What you look down and see Ace-Jack and think 'Wheeeeee let's go'?". Manners aside, I think he had a right to disgusted. Now maybe Josh had a tell and the dude put him on a draw. Maybe he had been psuhing people around all session and the dude decided to take a stand, but for the sake of argument suppose Josh had just sat down at the table.

If you look at the range of hands you could put an UTG raiser who pushes that flop, it is to say the least a very gutsy call to make. I would argue it was huge mistake. However according to the FTOP, the call was correct because the guy was ahead 57:43 (according to ESPN).

If you want to analyze and improve your game, it isn't helpful to think of a decision as a 'mistake' because the actual holdings were what they were. We must accept we can only make estimates of the relative probability that somebody is drawing or has TPTK. The correct decision is the one that makes you the most money in the long run.

Go ahead flame away [img]/images/graemlins/smile.gif[/img]

[7stud]

I just read the other thread, and I think Mercman572 says it best:

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[The fundamental theorem] says that if the opponent plays his cards as he WOULD if he could see your cards he gains and you lose. ...we should consider that word to mean SHOULD.

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[man]

Pokey,

I don't have much to contribute right now because it's bedtime. but I'd like to ask you to never move up in limits, because if you do, I fear that you might leave this forum and never write awesome posts again. that is all.

[Mercman572]

[ QUOTE ]
I just read the other thread, and I think Mercman572 says it best:

[ QUOTE ]

[The fundamental theorem] says that if the opponent plays his cards as he WOULD if he could see your cards he gains and you lose. ...we should consider that word to mean SHOULD.

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[/ QUOTE ]

[img]/images/graemlins/smile.gif[/img] Awww gee thanks! I have alot I want to contribute to this that I feel most players here overlook or don't properly apply but my workload has been obscene. Hopefully tomorrow I will be able to type something up that is logically sound, understandable, and able stand up to all the semantics that will be hurled at it.