Poker is a game of chance. It's also a game of skill, and if you want to win at poker, thinking clearly about chance is one of the most important skills you can develop. Understanding the nature of probability will allow you to develop winning strategies, which you can then apply at the tables to make money – in the long run.
That last part is very important. In poker, you can make the correct play and still lose. Let's say you're playing no-limit Hold'em and you get all your money in preflop with AA, and your opponent has 7-2 offsuit for some reason. Your opponent is going to win that pot around one-ninth of the time. When it happens, and it will, should you get angry at yourself for not folding those Aces preflop? Of course not. You should get your money in again the next time, and the time after that, expecting to win much more often than not.
Great Expectations
That's why the concept of expected value is so powerful. In poker, you're presented with a standard set of choices: raise, call, or fold. If it's a “big bet” game like no-limit Hold'em, you also have to choose how big or how small your bet will be. How do you decide? Ideally, you'll be aware of the expected value (EV) of each possible decision. Then you can make the choice that is most plus-EV.
Of course, poker's too complicated for you to memorize all the EV numbers for all the situations you might find yourself in. Don't even try. Start at the beginning: Get comfortable with the basic concept of EV. Once you've wrapped your head around that, you'll already have made a big step toward improving your poker game. You'll be less likely to tilt when your Aces get cracked by 7-2 offsuit, for example.
Choosies
Let's start by looking at a much simpler game: odds and evens. You and your opponent each bet a dollar, then you each hold out either one or two fingers at the same time. If the sum of all those fingers is odd, you win the pot. If it's even, your opponent wins the pot. You have a decision to make: Do you hold out one finger, or two?
Think of it in terms of expected value. If you hold out one finger, you'll win the pot when your opponent extends two fingers, but you'll lose when they also hold out one finger. Let's assume your opponent is random, and there's a 50/50 chance they'll choose either one or two fingers. Your EV in this situation is zero: Half the time you'll take the pot for a profit of one dollar, and half the time your opponent will win, costing you one dollar.
What if you decide to extend two fingers instead? It's the same result. Your opponent is 50/50 to hold out one finger or two; you'll win the pot half the time, and you'll lose the pot the other half. Your EV here is still zero. As it turns out, it doesn't matter in this situation whether you extend one finger or two, since the EV of either choice is the same.
Aces High
Poker will put you in more complex situations than this, but you can use the concept of EV to help you decide what to do. Let's imagine a very easy (if unlikely) no-limit Hold'em hand: It's heads-up, you and your opponent, and you each start with $100. Your opponent goes first, and shoves all-in with any two cards. You look down at AA. Do you call, or do you fold?
We arrive at the answer by looking at the expected value for each decision. If you fold, your EV is zero. What about if you call? The math says pocket rockets will beat a random hand 85.2% of the time. That means 85.2% of the time, you'll earn $100 in profit by calling, and the other 14.8%, you'll lose $100.
EV(call) = (85.2% * $100) + (14.8% * –$100)
EV(call) = $85.20 – $14.80
EV(call) = $70.40
Since $70.40 is greater than zero, you have an easy choice: call. But what if you're holding 7-2 offsuit instead of AA? The math says 7-2 offsuit will beat a random hand 34.58% of the time. Let's plug that number into our simple formula:
EV(call) = (34.58% * $100) + (65.42% * –$100)
EV(call) = $34.58 – $65.42
EV(call) = –$30.84
In this case, the EV of calling is worse than the EV of folding, so you should fold. Again, most poker situations will be more complex than this. But if you think in terms of expected value, and if you're willing to analyze hands away from the table and do some simple math, you can begin making smarter decisions and winning more money. In the long run.