Poker Theorems
Jeffrey Poker Articles, Poker Mathematics, Poker Strategy
The Fundamental Theorem of Poker was formulated by David Slansky. It encapsulates the essential nature of poker as a game of decision making under the conditions of incomplete information and volatility. The Fundamental Theorem of Poker is usually stated in natural language but is actually based on strong mathematical foundations (Law of Iterated Expectation). Because poker is a Zero Sum game. Common Poker Theorems The dictionary defines a theorem as “A general proposition not self-evident, but proved by a chain of reasoning. A truth established by means of accepted truths.” Over the years several poker theorems have been proposed by strong players and students of the game.
The following massive piece of work on poker theorems was submitted by Conrad. Poker theorems are pieces of fundamental poker strategy and advice, usually expressed in poker literature and forums. An ‘objective’ poker strategy is hard come to come by – the generation of hyper aggressive internet hotshots have caused us to revamp our ideas as to what constitutes an ‘optimum’ strategy. Internet star Dusty ‘Leatherass’ Schmidt, who posted the world’s highest win rate for $5/$10 NL in 2007 and 2008, even released a book entitled ‘Don’t listen to Phil Hellmuth: correcting the 50 worst pieces of poker advice you’ve ever heard’. Due to the evolution of the game, advice from the ‘old guard’ of is often considered dated, and players such as Hellmuth have been heavily scrutinised for their cash game performances. That said, books such as Doyle Brunson’s Super System and the Harrington on Hold’em Series are still well respected. Although their doctrines are contested, poker theorems are good as general rules of thumb. They may not be a substitute for things like poker training, but are useful nonetheless. They are not concepts that a player should stick to religiously, but ideas that a player should
always have in mind.
The fundamental theory of poker by David Sklansky
The Fundamental Theorem of Poker is described by esteemed poker player, theorist and author, David Sklansky. Sklansky is considered to be a leading voice on gambling and poker theory in general. The theorem states:
‘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.’
This is a very basic theorem, stating that every decision we make should be in accordance with maximizing EV (expected value). In the long term, this is what counts. So even though chasing a flush on the river may be tempting, we should only call if our opponent is giving us the correct pot odds.
Morton’s addition to Sklansky’s theorem
Sklansky’s theorem is only applicable in heads up situations. Morton’s theorem, articulated in a poker newsgroup by Andy Morton, explains why Sklansky’s theorem is not applicable in a multi-way pot. It often occurs when one player has the best hand, and two players are on draws. The player with the best hand might make more money in the long run when an opponent folds to a bet, even if that opponent is making a correct fold and would be making a personal mistake to call the bet. For instance, Player A holds Ac-Qc, player B Ah-9h, and player C Js 3s on a Ad-Jh- 4h board. Player A has a made hand – top pair, and when he bets the pot Player B with the flush draw is going to call. In the long run, Player A would make profit in a heads up situation with Player B. His odds are dashed and Player B’s enhanced, however, if player C, with his mid pair, makes the call. This is because he has 6 outs to improve his hand. This concept is sometimes referred to as implicit collusion.
The Beluga Whale Theorem
Other popular theorems are documented in community site twoplustwo. The Beluga Whale Theorem states that when you are a pre-flop raiser, and your top-pair hand is raised/check-raised on the turn, it is time to re-evaluate your hand. This is because your opponent is often trying to build a pot to get paid off with his monster. If you have AK on a K-10-5-9 board, and you face a raise on the turn, it is quite conceivable your opponent has two pair or better. This theorem is reliable against weaker opposition, however shrewder players can exploit this by floating.
Zeebo’s poker theorem
Zeebo’s Poker Theorem states that nobody ever folds a full house. So, if you have any inclination that your opponent has a weaker full house, bet out. People tend to overestimate boats because in a large number of situations they tend to be good. If you have KK on a board which includes AAA, bet out even if you put your opponent on something as low as 22.
Clarkmeister’s Theorem
Clarkmeister’s Theorem argues that when you are out of position heads-up on the river, and a 4 to a flush card comes, always bet (unless you have something with realistic showdown value). This is a perfect bluff spot, and an opponent will fold something like a weak/middle flush a large percentage of the time.
To find out about more obscure poker theorems, or the mathematical explanation behind some of the ones stated in this article, be sure to browse twoplustwo along with other poker forums.
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What about the yeti theorem, a 3bet bluff on the flop is a bluff? It’s not true, but hell these aren’t either.
Hey Mark,
As you seem to be math prone, in order to prove a theorem false, you need to provide a counterexample.
When is the Zeebo Theorem not true? Or the fundamantal therorem no true?
Oh yes, I know, one time there was a drunk player who had a full house but as his eyes could not see his cards well, he thought he had two pairs, so he folded a boat. Ok, fine, Zeebo is not true.