Is The FTOP Correct?

[Andrew Prock]

I sat down and wrote up a rather long winded elaboration . I probably need to be clearer about a couple of things, but I hope it's intelligible.

- Andrew

[MathEconomist]

Actually Andrew, while this may be a good explanation of why the FTOP isn't a useful concept for analyzing poker decisions, it doesn't say that it's not correct. The FTOP is results based and is correct. It's just not a good tool for analyzing decisions.

Standard game theory analysis is also not particularly useful either since if you're actually playing in a game with rational players you need to work on your game selection. Good poker analysis focuses on figuring out what strategy your opponents are playing and then exploiting it rather than looking for the NE solution.

[_TKO_]

Andrew,

Good article. FTOP is still relevant, though. Consider that in statistics, every practical example is merely an approximation to the "true value" that is being examined. That is, many experiments are conducted with a result that is accurate with 95% confidence. In poker, your level of confidence will be much lower, but the same idea applies: if you act assuming that your read is 100% accurate, then you will be acting correctly if your opponent actually has those cards, and incorrectly if your opponent does not actually have those cards.

[RagnarPirate]

well...as you recognize you are talking about two different things. The FTOP says that you gain EV by making your opponent play differently than he would if he saw all of the cards. It is so obviously true that it almost seems unimportant.
You are talking about ideal game theory play based on the available information. Game theory is more applicable to the play of poker BUT both are completely true.

[Andrew Prock]

You're right about the FTOP, but wrong about game theory.

- Andrew

[Andrew Prock]

No, the FTOP has nothing to do with EV. In particular, the FTOP is not about expectation, rather it's a metric that you might use to measure the size of mistakes that were made. And as a metric, it is a rather poor one as it gets the answers wrong quite often. In particular, good players who are playing the best game that they possibly can will be making FTOP "mistakes" very frequently. And they will be correct to do so.

- Andrew

[PokrLikeItsProse]

Via Guiness and Poker

[ QUOTE ]


This was kind of a cool post I found from David Sklansky, talking about his seminal poker book, The Theory of Poker, and his Fundamental Theory of poker.

Subject: Re: Sklansky's fundamental theorem in error

The FTOP doesn't really apply to the last round of betting.

The FTOP was written when most readers did not realize that they gained when a player folded a worse hand than their's when that player was less of an underdog than the pot odds they were getting. Other's didn't realize that making someone fold, gains less than enticing a call with bad odds (with certain multiway exceptions). Those same players were often unaware how pot odds affected their own calling strategy. Nowadays these concepts are of course much more widely known.

There were three reasons to mention this concept and give it a name (and by the way I did not use my name in front of it. Furthermore the fact that it is self evident to many people doesn't preclude using the term. The FTO arithmetic is that every number can be factored only one way. The FTO Algebra is that every equation has a root.) One reason was to illustrate the importance of reading hands so that you would know not only whether you were beat but also whether if you were beat, you were getting the right odds to play.

The second reason was to illustrate the importance of disguising your hand, not only to make your opponent think wrongly about whether you had him beat, but also to make him think wrongly about whether if you had him beat HE was getting the right odds to continue. Finally it was to show how a deceptive bet or check early on, especially in stud games, could be used as a weapon since subsequent cards that you caught on board, along with your earlier deceptive play, could induce a bad read from your opponent, who might therefore fold a hand where he was getting the right odds to call with, or call with a hand that he wasn't.

Those who think the FTOP was written for reasons other than the above are wrong. Those who think the FTOP did not accomplish the above aims are also wrong.


[/ QUOTE ]

Of course, noted math-y poker player Andy Bloch has his own opinion about the FTOP

[ QUOTE ]
Sklansky's "Theory of Poker" has a huge flaw -- the rule he calls the "Fundamental Theorem of Poker" (while I'll abreviate as "FTOP"). If you're intelligent and already understand probability and expected value ("EV"), you'll be confused at first by FTOP, because you won't see what's so fundamental about it and at first it appears to be something different than EV. In reality, in heads-up situations, it's just a poorly worded rule equivalent to the fairly obvious concept of playing to maximize EV. In multi-opponent situations, it's just plain wrong. You don't necessarily gain when your opponents make mistakes when you have more than one opponent. Sklansky himself has apparently realized the errors and quietly abandoned using his FTOP in his tournament poker book, using the concept of mazimizing EV instead.

That's why I can't recommend Sklansky's Theory of Poker. Sometime within the year hopefully there will be some new books on poker theory by real mathematicians that I'll be able to heartily recommend.

[/ QUOTE ]

I should note that the index for Small Stakes Hold Em by Miller/Sklansky/Malmuth has no references to the FTOP. If Sklansky has really "quietly abandoned" the FTOP, a similar phenomenon will be observed in the forthcoming NLHE book that he is co-authoring.

Given Sklansky's reasons for mentioning the FTOP, I think the idea still has merit. I notice that too many players are obsessed about avoiding the suckouts that are inevitable with the number of loose players that abound that they try to price out draws and longshot hands to make them fold rather than trying to make them call with incorrect odds.

The FTOP of poker is not a rule for playing correctly. You're expected to make FTOP errors in the course of a normal session. If you actually read Theory of Poker, Sklansky says outright:

[ QUOTE ]
It's very important to understand that when we talk about making a mistake according to the Fundamental Theorem of Poker, we're not necessarily talking about playing badly.

[/ QUOTE ]

I've never viewed the FTOP as a metric for evaluating single decisions (although Sklansky suggests that you win by making your opponent make signficantly more FTOP mistakes). It just takes calling a pre-flop all-in in a NLHE tournament with KK and running into AA to see how bad it is for that purpose. But the FTOP is a useful conceptual tool for understanding how poker works and why I do the things I do (for example, why I am much less likely than other players to overbet the pot and push all-in in an attempt to knock out draws in NLHE).

[Ed Miller]

I think this debate is meh. FWIW, we revisit the FTOP in the new NL book.

Honestly, I think the people who take issue with the FTOP are taking issue with its pseudo-mathematical formulation... not the concept behind it.

The idea is this:

Generally when you play poker, you want your opponents to make a different play than they would if they knew your cards. If you actually have AK, but they make a different play than the one they'd make if they knew you had AK, then that's USUALLY good for you.

It highlights the value of deception... if you actually have ace-no-kicker, don't make a play such that the natural response your opponents will usually make is that they'll fold all worse hands and raise with all better hands. Make a different play, one that sometimes your opponents will call with a worse hand or fold a better one.

Of course, this isn't always the best way to play. Sometimes, due to stack sizes, the exact hands, or whatever, you can't really help but make a play your opponent will tend to respond to "perfectly." You shouldn't bend over backwards and throw loads of EV out the window just to try to get your opponent to make a mistake every once in a while.

And as Bloch pointed out (or, IMO, way overemphasized), OCCASIONALLY in multiway pots, your opponent can play differently than if he had seen your hand, and it will still cost you money.

So yes, if I were to write the FTOP chapter in TOP, I'd write it in a way that says something like, "You know exactly what you have, but your opponents will only be able to put you on a range of hands. Recognize what range they are likely to put you on, then make a play that will encourage them to make a mistake GIVEN THE ACTUAL HAND YOU HAVE. They may be playing ok based on their knowledge... but you know that their play is wrong because you have more information. This isn't the be all and end all, but it's something to think about every time you make a play."

[Ed Miller]

FWIW, I think Bloch's comments are out of line in general. The Theory of Poker is a very good, if perhaps slightly flawed, book that has taught countless people how to think about poker. Suggesting that it's not worth reading to an audience (the WPT fan site) who clearly crave to learn the basics about how to play poker is, IMO, slightly irresponsible.

[O_Witty]

maybe this whole thing is over my head but according to Mr. Prock folding when you are a 64% to win is the optimal play. How is this so?