The fundamental theorem of poker

The fundamental theorem of poker

Famous poker theoretic and mathematician David Sklansky in his book 'The Theory of Poker' first put forward this theorem. In its essence, this is the most comprehensive and generalized theorem with the key to success in the game. Absolutely all your actions at the poker table must be made considering these thoughts.

Quoting theory right from the book, we can highlight basic moments of it:

'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 theorem is different to all the others poker theorems as this is one global theorem which applies to all the poker variations, unlike other theorems that offer certain decision X in the situation Y. Despite the fundamental theorem of poker being quite straightforward, it is the cornerstone that stands behind every winning poker player.

The author and professional poker player David Sklansky is a Godfather of Poker. His observations are astute, modest and well justified. The fundamental theorem of poker is one of the most famous pieces of wisdom of Sklansky, which includes all these qualities. After reading this definition and understanding it you will think: 'Of course! It makes sense!'. On some level you might think you knew it and probably used this knowledge. Or maybe (more probable) the brilliant clarity Sklansky uses to formulate his thoughts contradicts with the wisdom itself.

The fundamental theorem of poker comes to the conversation about the great battle for informational advantage in the game of incomplete information. The information is the main advantage in poker; unlucky cards or huge stack - is an info. The perceived information, to be precise. It is almost impossible to know cards of the opponents for sure in poker.

The fundamental theorem of poker explanation

The fundamental theorem of poker supposes all your actions in game must be made in order to get maximum EV to win in the long run. For instance, call of the bet from the opponent with the flush draw on the turn might look attractive but you must make it only having needed pot odds.

If you know cards of the opponent for sure, you will be able to play your hand with the maximum profit. Moreover in the context, not losing the certain amount of money/chips is also considered a win and winning with some hands could be a mistake in the long run. When you know the strength of the hand of the opponent, you get to choose the most profitable of three options - call, raise or fold and make the only right decision. On practice, you will never know the exact hand of the opponent so at times you will deviate from playing the hand in perfect way and won’t be able to get the maximum expected value (EV).

As you can see, the statement is idealized as it is impossible to play according to the fundamental theorem of poker. However, your winnings (or losses) will defend on how close to reality you will be able to assess opponents’ range. Adversely, you should disallow your opponents assessing your range correctly making him deviate from the fundamental theorem of poker.

This means that if you’re willing to become a successful poker players, you must train your hand reading skill basing on tells and observations of previous play of opponents. You should also hide the strength of your hand with balancing your ranges and lines. Everything in poker can be balanced.

Speaking simple, next time playing Texas Hold’em, imagine that all the hole cards of the opponent will be available for you to see. In this case you will be able to know the strength of your hand and the hand of the opponent and will always make a right decision: whether to play check, raise, call or fold. Anyways, your game will be in the following:

  • If you have the best hand, you will be betting (except for the cases you will be slow playing).
  • If you have a draw hand, you will play according to the pot odds.
  • If you have the worst hand, you will fold.

This means you will be playing showing maximum EV as you will follow the fundamental theorem of poker. Unfortunately, you won’t be able to say you are 100 percent sure you know the exact cards of the opponent in poker and that means you won’t be able to follow your perfect plan. So the key in poker is to try to play as good as it is possible without having an opportunity to see the cards of the opponents.

To sum up, the winning player in poker is the one who is able to play closely to the way he would play knowing the cards of the opponents. The more information on your opponents you will have, based on your reads of the opponents and their analysis of action during the game and after the game, the less your fame will be deviated to the ideal. That means it will be as profitable as it gets.

The example of the fundamental theorem of poker

You play at $1/$2 NL and all the players have $200 in stacks.

Our hand:    

Hand of the opponent:    

Board:      

Lets’ suppose we act last and our opponent bets $20 to the pot of $20. We can see the pocket cards of the opponent. What should we do according to the fundamental theorem of poker? You have three options:

  • Fold your hand
  • Make a call
  • Make a raise

According to the Fundamental theorem of poker, we have to define what is the right decision here.

Fold is not the option as we have a strong hand so we have to choose between the raise and the call.

The best option here is call. We will often be getting pure bluff from the opponent so if we make raise, it is highly unlikely the opponent will invest at least some money in the pot. By making the call, though we give our opponent an opportunity to make another bluff bet and invest more money in the pot on turn. We can win more money with this action. So call has a bigger expected value than raise, However, had the opponent had a hand like:     (two pair - more info can be found at the article poker hand rankings), raise would have been a more +EV decision in comparison with call. We would have been sure our opponent makes a call of the raise so we would get bigger amount of value making a raise.

As you could notice, knowing 2 pocket cards of the opponent in each case we can make the most profitable decisions.

Is the fundamental theorem of poker still relevant?

You can have no doubt about that - the fundamental theorem of poker will always be the basis of poker play so you have to know it.

What is the use of the fundamental theorem of poker?

Your task is to try to create an ideal situation. This makes your profits maximum in the long run. Opponents’ mistakes will always be in your favor. Mistakes lead to psychological dis-balance which leads to worse mistakes and the loss of profit.

To have a general idea of what the hand/range of the opponent is you should follow his game using the history of the hands and the stats. This is relevant for online games where different programs for gathering stats for analysis sufficiently simplify the process of the game.

You won’t be able to get rid of all your mistakes completely and that is ok as your opponents are also unable to do that. But if you learn to understand the tendencies of your opponents better and get to play closer to the fundamental theorem of poker than they will, in the end you will be able to outplay them in the long run.

The conclusions on the fundamental theorem of poker

The fundamental theorem of poker is not a small theorem describing a minor aspect of the game, that is the way of thinking and understanding the game.

If you play poker the way you would do that knowing the cards of your opponents, you will be winning. Nevertheless, poker is poker; you will never have complete information. Articles on strategy of the game or other study materials will help you to get closer to the fundamental theorem of poker basing on the incomplete information of your opponents.

What could be simpler!?

You can enter the strategy of poker section, get back to the theorems of poker or studying any other theorem.

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