The Fundamental Theorem of Poker

Royal Flush Poker Hand and Math Equations

My friend Larry called me the other day to ask me some questions about switching from online poker to live poker. He knows I’m a poker player, and he also knows that I write about poker extensively for work. The first thing I asked him was if he was familiar with the Fundamental Theorem of Poker.

David Sklansky coined the phrase “The Fundamental Theorem of Poker.” The idea was to sum up the nature of the game clearly and quickly.

Here’s how Sklansky expressed the Theorem:

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.

I suggested to Larry that he thoroughly study Sklansky’s book The Theory of Poker. I suggest that if you’re serious about poker, you should do the same thing.

Until you can get your copy of that book and start reading it, here are some of my own observations about The Fundamental Theorem of Poker.

The Fundamental Theorem of Poker Is Essentially Mathematical in Nature

Even though the Theorem is clearly written without numbers, the idea behind it is based on logic, math, and probability. It also clarifies the nature of the game – poker is essentially about making positive expectation gambling decisions in situations where you have incomplete information.

This, after all, is the difference between poker and games of pure skill like chess. In a game like chess, you have a lot of variables, but you know everything there is to know. The pieces can only move in specific patterns, and they’re located wherever they’re located on the board.

It’s possible for an inferior poker player to win a hand against an expert. It’s even possible for an inferior poker player to have winning sessions against experts. That’s because of the random nature of the game. You can make incorrect decisions in poker and still win.

Poker Cards With a Chess Backing

This isn’t the case in a game like chess.

When you make a decision in poker, you should be thinking about the mathematical expectation of that decision. The decision with the largest expected value is always the correct decision because the goal of poker is to win money.

If you were playing with all your opponents’ cards face-up, you’d know exactly which decision would have the highest expected return. Even if you didn’t know what to do intuitively, you’d be able to eventually figure it out with some minor calculations.

Here’s another way to look at it:

Suppose your opponent is playing with his cards face-up, but you’re playing with your cards face-down.

Do you see how you’d have a mathematical advantage over your opponent?

An Example of the Fundamental Theorem of Poker in Action

Let’s say my buddy Larry is playing Texas holdem. He gets a pair of sevens preflop. He calls the big blind, and everyone else folds. The big blind checks.

On the flop, an ace, a king, and a jack are showing.

Larry has to decide what to do next. He should probably fold because of how unfavorable the flop is to him. The big blind is likely to have any of those three cards – an ace, king, or jack – which means that the big blind has Larry beat.

Also, I didn’t mention this, but two of the flop cards were of the same suit, so the big blind might also have a flush draw. The possibility that the big blind might have a draw to a straight shouldn’t be ignored, either. The big blind might even have a queen and a 10, which means he might already have hit a straight.

Poker Player David Sklansky

Even if a seven shows up on the turn or the river, Larry might lose this hand – his three of a kind might not be good enough to beat the potential flush or straight. And there are only two sevens left in the deck, which means he’s a lot less likely to hit his hand than the big blind is.

But what about this?

Suppose the big blind is playing with his cards face-up, and he has a suited six and seven. Larry now knows that the big blind has a flush draw. The correct decision for the big blind now is to raise.

If Larry folds in this situation, he’s making a mistake because he’s playing his hand differently than he would if he knew what the big blind was holding.

Your goal in poker is to avoid mistakes, but your goal is also to encourage your opponents to make mistakes.

This is also a classic example of a semi-bluff. The big blind wins in this situation if Larry folds, but he also wins if he hits one of his nine outs.

So, Should I Always Play My Hand Deceptively?

A beginner poker player might read about The Fundamental Theorem of Poker and assume that he should always play his hand differently from what its strength might warrant.

He might think that he should check his pair of aces in the hopes that one of his opponents will be or raise against him.

He might think that he should bet and raise every time he gets 27 offsuit.

This is NOT the correct application of the Fundamental Theorem of Poker, though.

For one thing, the Fundamental Theorem of Poker applies directly to heads-up poker, but in multi-way pots, its utility decreases because of what happens when the other players make decisions.

Stack of Chips and Cash on a Poker Table

For example, if you have a strong hand, but several other players have drawing hands, you can be an underdog just because you have so many opponents. This is one of the reasons you should bet and raise with strong preflop hands – you want to thin the field to make winning more likely and to simplify your decision making in later rounds of the game.

On the other hand, if you ARE heads-up with an opponent and have a weak hand, it CAN make sense to bet and raise with it. In fact, it’s essential if you want to avoid being predictable. Face it. If you always play your hands perfectly according to the hands’ strength, you might as well be playing with your cards face-up anyway.

Having an idea of your opponents’ tendencies help with these decisions, too. I’ve played with all types of poker players, and there are those who consider themselves “sheriffs.” Even with the weakest of hands, they’ll call you down to the river just to make sure you’re not putting one over on them.

Trying to bluff a “sheriff” is an exercise in futility regardless of what cards you’re holding. They rarely fold.

On the other hand, if you know they’ll fold unless they’re holding premium cards, if you can get heads-up with them and have position on them, it makes sense to bluff and semi-bluff as often as possible.

Another Way to Explain This Concept

Suppose you’re playing Texas holdem for real money, and you can see all your opponents’ hole cards.

But they can’t see yours.

Since you know how strong or weak your opponents’ cards are, you can decide with a lot of precision whether to bet, call, check, fold, or raise.

For the most part, this means that if you have the strongest hand, you’d bet and/or raise.

If you have the weakest hand, you would call or fold, depending on how strong your draw is and how many other players are in the pot.

Mathematically, you’d be making the decision with the highest expected value in every situation.

Since you don’t have perfect information on every poker hand, your goal is to get good enough at reading your opponents that you’re able to make decisions as close to perfectly as possible. This requires a good understanding of the math behind the game.

But, just as important, it requires a lot of attention on your part. You can’t ascertain your opponents’ tendencies unless you’re paying attention to their play on every hand – even the ones you’re not involved.

I see players like Larry watching television or engaging in a lot of idle chit-chat at the table when they’re not involved in a hand. They’re not playing optimal poker. They’re missing out on a lot of information they should be paying attention to.

Your goal is to play as closely as possible to the way you’d play if you could see your opponents’ cards.

Your other goal is to get your opponents to deviate from how they’d play if they could see your cards.

That sums up in a nutshell how to play profitable poker.

Conclusion

The Fundamental Theorem of Poker is something that seems simple but is actually more complex than you might think. Putting the Theorem into action presupposes that you understand pot odds and outs well enough to play correctly if you have perfect information.

Without those fundamentals, you can’t apply the Fundamental Theorem of Poker at all.