TOP: Fundamental Theorem discussion.
 

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.

Re: TOP: Fundamental Theorem discussion.
 

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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.

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

Re: TOP: Fundamental Theorem discussion.
 

"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.

Re: TOP: Fundamental Theorem discussion.
 

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).

Re: TOP: Fundamental Theorem discussion.
 

"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.

Re: TOP: Fundamental Theorem discussion.
 

[ 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.

[ QUOTE ]
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.

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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?

[ 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.

[/ 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.

Re: TOP: Fundamental Theorem discussion.
 

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]

Re: TOP: Fundamental Theorem discussion.
 

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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Re: TOP: Fundamental Theorem discussion.
 

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.

Re: TOP: Fundamental Theorem discussion.
 

[ 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.

[/ QUOTE ]

[/ 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.

Re: TOP: Fundamental Theorem discussion.
 

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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).


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Just like to mention that ESPN's odds are a lot truer than what a player could calculate. They know the dead cards that the players mucked, while the Englishman has to assume they are still live.

Re: TOP: Fundamental Theorem discussion.
 

good post - i like what was just said by above poster about hand ranges. i feel that is more important in holdem than this 'fundamental theorem' because we NEVER know EXACTLY what villian is holding.

Re: TOP: Fundamental Theorem discussion.
 

True (but a little besides the point). Here are the odds from poker stove. They aren't too far off. And I couldn't swear ESPN had it as 57:43.

Board: Ah Kc Qh
Dead:

equity (%) win (%) tie (%)
Hand 1: 41.4141 % 36.26% 05.15% { Jh9h }
Hand 2: 58.5859 % 53.43% 05.15% { AcJs }

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
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.

[/ QUOTE ]
<font color="blue"> PLEASE everyone, argue the theory, not the assumptions, it's way more productive. Don't play semantics. </font>

[ QUOTE ]

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.

[/ QUOTE ]

This is applying the fundamental theorem of poker to play. Good. First part of fulfilling the FTOP is to put him on a good range of hands, that's the best you can do to seeing his cards. Your own skill and experience, and the opponent's plays/ability will cause this to vary.

From there you decide your play.


I said we need to discuss as it applies to us, part of that means that the majority of the time we won't have to induce a player to make a mistake. You must decide how closely the opponent can play as if your cards were shown given a certain action. That's the other part of it.

The Fundamental Theorem is indeed fundamental, it is not simple. It is not the introductory theorem. It's incredibly complex and far reaching.

Re: TOP: Fundamental Theorem discussion.
 

mikechops[ QUOTE ]
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).

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Sklansky makes the distinction between a FTP "mistake" and the kind of mistake you are talking about, where someone makes a correct call by the numbers but considering what the other could have been holding the call is pretty stupid.

So you can have a mistake according the the FTP but good play according to the educated poker player.

mikechops[ QUOTE ]
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.

[/ QUOTE ]
grimstarr[ QUOTE ]
good post - i like what was just said by above poster about hand ranges. i feel that is more important in holdem than this 'fundamental theorem' because we NEVER know EXACTLY what villian is holding.

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Assigning hand ranges and playing accordingly is a fundamental skill that a player uses to play good poker. But its not a fundamental way of describing what the ideal course of action is.

Guess Sklansky was trying to be all sciency by trying to set out principles of poker. So it doesn't feel to poker players that this is what they are doing when they play poker. But I think that it is a reasonable way of describing what optimal play is.

Re: TOP: Fundamental Theorem discussion.
 

I think there's another facet to it. You can make the maximum value play only if you know your opponents cards *and how he would play them given all future boards cards*. If you play idealy corresponding to his cards, but incorrectly based on how he will play them, then you are making a mistake in an EV sense, which is all that matters.

Re: TOP: Fundamental Theorem discussion.
 

Ok if you know his cards and your cards how can you play incorrectly? What mistake could you make? If you know he has AA it doesn't matter how he bets, you will be able to calculate the correct play.

Re: TOP: Fundamental Theorem discussion.
 

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Ok if you know his cards and your cards how can you play incorrectly? What mistake could you make? If you know he has AA it doesn't matter how he bets, you will be able to calculate the correct play.

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If you have him beat, and you want to maximize value, will he raise if you bet? will he bet if you check? will he call a check raise? if you check multiple streets will he bet his whole stack?

If you're beat, but want to draw a cheap card, will he just call if you bet small? will he bet small if you check? could he fold his AA if you make a big bluff? If the flush card hits will he be scared of it and fold?

Clearly you can't play for maximum value unless you know how he'll play his cards in every situation. (you can play optimally in a game-theory sense, assuming that he also plays optimally).

Re: TOP: Fundamental Theorem discussion.
 

yes of course I'm an idiot

Re: TOP: Fundamental Theorem discussion.
 

Edited for stupidity

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]


mikechops[ QUOTE ]
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.

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...

Assigning hand ranges and playing accordingly is a fundamental skill that a player uses to play good poker. But its not a fundamental way of describing what the ideal course of action is.

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Well I wouldn't want to argue semantics with anyone, but I would say that IS a fundamental way of describing the correct decision process for arriving at the ideal action. I think that paragraph says more clearly what we should be trying to do than the FTOP. The ideal action is the one that wins you most in the long run, not the one that happens to be right because you opponent happened to have a particular hand.

Another example. Heads up. AA vs KK. KK raises, AA calls trying to set trap. Flop comes AKx rainbow. Both players end up all-in. Did KK make a mistake? Of course not. If you posted this hand and said you folded KK, people would rightly call you an idiot. You had no way of knowing you were up against AA.

That is the whole point of poker. It is a game of imperfect information. So-called fundamental theorms that don't take this into account aren't fundamental in my book.


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Guess Sklansky was trying to be all sciency by trying to set out principles of poker. So it doesn't feel to poker players that this is what they are doing when they play poker. But I think that it is a reasonable way of describing what optimal play is.

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I disagree. Optimal play is making the best decisions we can with the information available to us. It isn't what we could have done, had we known for sure what the opponents cards were. If we start trying to do that, we may as well try to play as if we know what the turn and river cards are going to be ahead of time too.

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]
<font color="blue"> PLEASE everyone, argue the theory, not the assumptions, it's way more productive. Don't play semantics. </font>



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Poker is a fundamentally a game of imperfect information. I would respectfully suggest that pointing this out is not playing semantics.

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The Fundamental Theorem is indeed fundamental, it is not simple. It is not the introductory theorem. It's incredibly complex and far reaching.

[/ QUOTE ]

[ QUOTE ]

Dictionary.com
Fundamental - Of or relating to the foundation or base; elementary


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Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
The Fundamental Theorem is indeed fundamental, it is not simple. It is not the introductory theorem. It's incredibly complex and far reaching.

[/ QUOTE ]
Hmm...well maybe I don't understand it fully then, but to me it seems true by definition. It says(or "should" say) that there is an optimal way for your opponent to play his hand if he could see your cards. If he doesn't play that optimal way, then he loses AND you gain.

That doesn't appear to be earth shattering news, and it makes intuitive sense: opponent bungles his hand, he loses, you win. Imo, the only reason the ftop is at all interesting is because of what Morton showed. He showed that in multiway pots, there are times when an opponent can play sub-optimally, i.e. he chooses an action that has -EV, yet you don't gain from his mistake. In fact, not only do you not gain from his mistake, you are hurt by his mistake i.e. your EV decreases. What happens is that a 3rd opponent is acquiring EV from the both of you when your opponent makes a mistake.

Re: TOP: Fundamental Theorem discussion.
 

The Fundamental Theorem of Poker (TFTOP) is incomplete I think. It doesn't take into account that bluffs are profitable when you do them at the right interval. At least according to a later chapter in TOP.

When I make a stone cold bluff, I'm definitely making a mistake according to TFTOP since I'm putting more money in the pot while I'm behind. If my opponent played correctly according to TFTOP he'd always raise my bluffs and I'd pay for my mistake. But I'm making a mistake willingly in the hope that I can get him to make an even bigger mistake by laying down the better hand.

Re: TOP: Fundamental Theorem discussion.
 

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But I'm making a mistake willingly in the hope that I can get him to make an even bigger mistake by laying down the better hand.

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Bingo!

The FTOP makes complete sense in a vacuum, but sometimes you make incorrect plays intentionally that increase your EV on later hands. You make a stupid play, and now your opponenet thinks your a donk, not realizing it was a set-up.
Also, the FTOP does not account for all aspects of poker. If it were only a mathmatical game, the FTOP would stand on every paly. I think it has to be used as a guideline, and a concept, not as a rigid way of play. In the long run whoever makes the least mistakes wins. Sometimes you have to make your opponents make mistakes, ie the bluff, and sometimes they'll make them on their own. The only way you win this war is by hand reading and player reading, and trying to make the most optimal play after deductive reasoning.

Re: TOP: Fundamental Theorem discussion.
 

One other aspect of bluffing that I haven't seen mentioned is that if you never bluffed then you will make it easier for opponents to play correctly (i.e. you will always bet when you have a hand and always fold when you do not). Bluffing the correct % of time is perfectly aligned with the FTOP.

Re: TOP: Fundamental Theorem discussion.
 

I don't get how you can call a bluff a mistake if you know he would lay his cards down. You know his cards, and how he would play them. We are behind and we know the only way to win is to bluff. Bluffing in this case is obviously the optimal play.

Yes someties we bluff to increase our EV in later hands, but do you bluff if you know hes going to call? The optimal play would be to bluff when he might lay it down so that if he does call not all is lost.

Re: TOP: Fundamental Theorem discussion.
 

The FTOP absolutely applies to the bluffing scenario. You induced your opponent to play differently than he wouldve had he known what you were holding. You cant get a more direct correlation than that.

Re: TOP: Fundamental Theorem discussion.
 

Maybe my interpretation of TFTOP is too narrow. I think bluffing - if done correctly - is +EV. But the TFTOP says you should play as if you could see your opponents cards. Putting money in the pot when you're behind is not the way to win if you read TFTOP literally. That's why I think it's incomplete.

I had a hand yesterday when someone tried an all-in bluff against me when I had the nuts. That was a definite mistake by him according to TFTOP - and in practice.

My interpretation of TFTOP - which I'll be the first to admit is on the narrow side - leads to strict ABC poker. Bet when you're ahead. Fold when you're behind. No bluffing. No slow-playing. No table image considerations.

I think TFTOP lacks something about your opponent as a poker player. A wider formulation might be "Play as if you know your opponents cards and what he thinks you have". As it stands, TFTOP only relies on the cards. It doesn't include the players at all.

Re: TOP: Fundamental Theorem discussion.
 

Think about the meaning of the word fundamental, which someone has actually posted. This is the axiom of correct poker play, from which everything else proceeds. Now the issue of optimal play arises. Take the bluffing scenario. Clearly, if he knows your cards, he calls, you lose, he wins. Very straighforward. Now, you know his cards. Now you know that the only way you win is to bluff. Now we have to calculate how often we make him fold by bluffing. If we know he folds enough time to make this profitable than we bluff. We cause him to make a bigger mistake than our bet theoretically was. Yes you didnt play optimally, but you moved your opponent further away from the optimal play.

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
Maybe my interpretation of TFTOP is too narrow. I think bluffing - if done correctly - is +EV. But the TFTOP says you should play as if you could see your opponents cards. Putting money in the pot when you're behind is not the way to win if you read TFTOP literally. That's why I think it's incomplete.


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You are not understanding it correctly. If your opponent has a hand they will fold which is better than yours, clearly bluffing is correct under the FTOP. Knowing exactly what hands they'll fold and what size of bets is part of knowing your opponent's psychology. Obviously if you bluff into the nuts, you are making a "mistake" according to FTOP because you would never do that if you could see their cards.

This also provides an example of what I've been trying to talk about Re: opponent psychology in the FTOP. Say they hold a very weak hand which they should fold if you bluff, and you know that's what they have. You (correctly) bluff and they (incorrectly) call, and you lose the hand. This is a -EV move, but did you make a mistake? According to the strict or game-theory version of FTOP you did not, but if you including opponent's actions in the FTOP this is a mistake.

Now, the idea of intentionally making a mistake in one hand to set up future hands is a whole other topic which is outside the scope of the FTOP. It would still be a "mistake" in the original hand because it was not the maximum +EV play for that hand, though it may be beneficial in the long run.

Re: TOP: Fundamental Theorem discussion.
 

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It would still be a "mistake" in the original hand because it was not the maximum +EV play for that hand, though it may be beneficial in the long run.

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That makes no sense. The EV of folding is 0. If you bluff correctly, then you make money over the long, and thus is the maximum EV play.

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
[ QUOTE ]
Now, the idea of intentionally making a mistake in one hand to set up future hands is a whole other topic which is outside the scope of the FTOP. It would still be a "mistake" in the original hand because it was not the maximum +EV play for that hand, though it may be beneficial in the long run.


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That makes no sense. The EV of folding is 0. If you bluff correctly, then you make money over the long, and thus is the maximum EV play.

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I'm not talking about the simple bluffing situation in the last paragraph, that's why I said it's a whole other topic. A previous poster brought up the idea of making a play which is -EV in one hand but is a long term +EV move because of the set up value. That might be something like pushing a semibluff when you know it's slightly -EV (in that hand), but you know will set you up for increased value in the future. It's open to intepretation what the FTOP thinks of a play like that.

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
Ok if you know his cards and your cards how can you play incorrectly? What mistake could you make? If you know he has AA it doesn't matter how he bets, you will be able to calculate the correct play.

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contrary to this statement. In my home game we decided to do a tournament of blind mans bluff. Of course me being the best player in our game thought for sure I could do well. One particular hand player to my right has JJ and everyone else has rags. I can see by the players reaction that I too had a decent hand. I thought "ok I either play really aggresive or fold" I chose to fold because I know players at my home game sometimes think that AJ being the 4th person in the action against all ins big bet is good. I had 44. Anyways to sum this up Ppl clearly see the JJ and start raising against it. So just because they can see your cards there is some ppl out there who and this is a quote from an argument that came up at my home game, I wasn't even part of it, but the quote is this "I will win more money with luck than your so called odds and skill" It all started when he caught his flush against a big raise and chase with Q-4 suited. Just goes to show at the low levels you never know what someone can be on because top pair makes ppl push their whole stack not even thinking they can be beat.

Re: TOP: Fundamental Theorem discussion.
 

Listen, I think you are thinking of FTOP and applying it in a vacuum. I think the conditions and caveats are made clear. FTOP although it sounds simple, is in fact very complex and far reaching, and that applying a specific hand, with specific consideration, including meta-game issues simply to point out a "paradox" or "flaw" is misapplication.
I think FTOP encompasses all of the above factors.

Re: TOP: Fundamental Theorem discussion.
 

Ok my fault. My opinion is that to some degree, this discussion is more over semantics. Some one said David was trying to be "sciency". The definition of theorem is "an idea that has been proven to be true or assumed to be demonstrable". Mathematics has a slightly different defintion but essentially the same. The FTOP is the rock on which all the rest of good poker play is built. All other things are derived from it. If I know your hand, the FTOP says if I played it differently when not knowing your hand, then I lose money. But the question is, what is the optimal play when I know your hand? If I know you are a LAG who will bet into me street after street with marginal hands but will usually fold if I raise, when I know your cards, is my optimal play to raise when I am ahead or is it to call down? Of course it is to call down. So my mistake if I didnt know your cards would be if I raised you! But against a different player with the exact same cards, it could be completely reversed. The FTOP says nothing about how you should play cards, only that you lose money when you play differently than you would if you knew their cards.

Re: TOP: Fundamental Theorem discussion.
 

I've been reading a lot of discussion in this thread talking about how Slansky's FTOP is "overrated", "incomplete", etc.

I really think people are missing how important this theorem is at any level of play. I think in the long run (not just one hand), this theorem doesn not say that bluffing is incorrect, and in fact it provides a key justification for bluffing, semi-bluffing, etc.

I think people who don't understand the primary purpose of bluffing should especially study this theorem. The primary purpose of bluffing is not to be +EV in that particular had (although it is possible to be +EV overall). In fact if you never get picked off while bluffing you are doing at an improper frequency, because the primary purpose of bluffing is to make your opponents play incorrectly on future hands. The secondary purpose is to pad your win rate a little bit. I would argue, that if bluffing is a major source of our income, then you are not bluffing enough to make your optimal win rate (unless you never want to move past 25NL).

At low limits, it describes why against a weak player, it is worth it to call with almost any two cards if you are sure they have a big pocket pair and the stacks are deep enough. You know what they have, but they have no idea what you have, and the implied odds are such (because they are bad SS players) that you can profitably call.

I also find it funny that the first time I've seen this part of TOP dismissed so easily is on the SSNL board.

Re: TOP: Fundamental Theorem discussion.
 

[ QUOTE ]
I also find it funny that the first time I've seen this part of TOP dismissed so easily is on the SSNL board.

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I didnt want to be the first to say it, but, yeah.

Re: TOP: Fundamental Theorem discussion.
 

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Ok my fault. My opinion is that to some degree, this discussion is more over semantics. Some one said David was trying to be "sciency". The definition of theorem is "an idea that has been proven to be true or assumed to be demonstrable". Mathematics has a slightly different defintion but essentially the same. The FTOP is the rock on which all the rest of good poker play is built. All other things are derived from it. If I know your hand, the FTOP says if I played it differently when not knowing your hand, then I lose money. But the question is, what is the optimal play when I know your hand? If I know you are a LAG who will bet into me street after street with marginal hands but will usually fold if I raise, when I know your cards, is my optimal play to raise when I am ahead or is it to call down? Of course it is to call down. So my mistake if I didnt know your cards would be if I raised you! But against a different player with the exact same cards, it could be completely reversed. The FTOP says nothing about how you should play cards, only that you lose money when you play differently than you would if you knew their cards

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I can understand what your saying. I think a lot of the trouble comes in the different ways people define the term "win" and "lose" and "mistake" as it applies to the theorem. For instance, a "mistake" may occur when someone plays a hand correctly based on his read, re the KK v AA scenario. The "mistake" is not a description of an "incorrect" play neccessarily, just that If you would have been able see the AA in the opponents hand, you would have played it differntly.

Also take in mind the caliber of player involved. For instance if an experienced pro, by a certain tell can put someone on an exact hand, or to take it even further, suppose he has x-ray vision and can see the opponents cards. He would be able incorporate past play in similar circumstances, the present situation at table (loose, tight) any other variables in which a knowledgable player would apply to their reasoning, and make his play based on that information. If he would play that hand differently, with the same given variables stipulated if he couldn't see the cards then he loses according to the theorom, even thought that play might be "correct" simply in terms of +/- EV.

If a novice player can see those same cards, and applys whatever misconceptions or errors he is prone to make. It is possible for him to make an eggregious error in judgement, which normally would be considered a "mistake" and still accidentally make the optimal play, making this play "correct" in a theoretical sense.

In effect people are strictly applying their own definition of a "mistake" as opposed to understanding that it has different meanings in it's particular appliction.

Re: TOP: Fundamental Theorem discussion.
 

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also find it funny that the first time I've seen this part of TOP dismissed so easily is on the SSNL board.


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I was shocked as well..