Introduction to Poker Odds and Probability

Deck of Cards and Spread of Poker Cards on Table
This post is aimed at poker newcomers who understand how to play but lack the knowledge of the intricacies of odds and probability in the game. Since Texas holdem is the most popular poker game in the United States now, I’ll use that game for all of the examples.

If you want to win a poker game at home, in a casino cardroom, or at one of the best US casinos, you need to understand how the odds work. Don’t worry, though, they’re not as confusing as you might think.

1 – What Are Poker Odds?

If you place a bet that pays off at 2 to 1 odds, it means that if you bet $1 and win, you get $2 in winnings. You could say that odds are a ratio of how much money you’ll win if you place a bet contrasted with how much money you’ll lose.

But the term is also used to describe the probability that something will happen.

If you say that you have a 2 to 1 shot at winning a hand, you’re saying that there are two ways to lose and one way to win.

In this respect, odds are just a way of re-phrasing a probability, which is a fraction. The fractional equivalent of 2 to 1 odds is 1/3, or 33.33%. If you’re good at probability math, you can convert odds from one format to another.

Here are a couple of other things to consider when discussing or thinking about odds:

An event’s probability is always a number between 0 and 1. Also, when you add up the probability that something will happen with the probability that something won’t happen, you’ll always get a total of 1.

So, if something only has a 1/3 probability of happening, it has a 2/3 probability of NOT happening.

Finally, odds and probabilities can be reduced, just like fractions. If something has a 4/6 probability of happening, that’s the same thing as having a 2/3 probability of happening.

2 – Why Are Odds Important in US Poker?

One of the ways to win in poker is to repeatedly put yourself into what’s called +EV situations and repeatedly avoid -EV situations.

What does that mean? Well, +EV means a bet with positive expectation value, and –EV refers to a bet with negative expectation value.

The way you calculate the expected value of a bet is to compare the odds of winning with the payout odds for the bet.

In poker, the payout odds are represented by the pot odds. The amount of money in the pot compared to the amount of money it costs you to stay in the hand are the pot odds.

Colored Casino Chips in a Pile, Queen of Hearts and Stack of Poker Cards

Here’s an example:

There’s $50 in the pot. Someone before me has bet $10. If I call, the pot pays me $50 on a $10 call. That’s 5 to 1 odds.

If I think I can win that hand 1 time out of 6, that’s even money. If I can win that hand 1 time out 5, I will profit in the long run, even though I’ll still lose most of the time. And if I figure I can only win that hand 1 time out of 7, I’ll lose money in the long run.

The thing about odds in poker is you don’t know what your opponents’ cards are. If, for example, I have the seven and the eight of hearts, I have suited connectors. Let’s say I snuck into the hand, and the flop comes with two cards that are also hearts.

I have four cards to a flush, which is a strong hand. Since there are 13 cards in each suit, there are nine cards in the deck which will fill my flush.

Since I know there are 47 cards left unaccounted for, the odds of getting another heart are 9/47, which is close to 5 to 1 odds. But I also have to account for the possibility that someone else will have a higher flush or a better hand.

If I had the ace and the king of hearts, I’d be almost a lock if I hit my flush. But with middle suited connectors like that, it’s trickier. I do know, though, that I need at least 5 to 1 pot odds to make it worth calling here.

Also, I get two shots at it—the turn and the river—so really, I don’t even need that.

3 – The Concept of Outs in Poker

Those nine cards that were hearts are my “outs.” Those are cards that will make your hand the winner.

The problem with outs is that you should discount them sometimes. In the example I gave above, where one of your opponents might have a higher flush, you might only count those nine outs as five outs, making the pot odds you’d need for a call that much higher.

Also, outs vary based on what your opponent is holding, but you don’t know what cards your opponent has.

The poker player’s solution to this is to put his opponent on a range of hands, and he also assigns a probability to that range.

For example, a tight player who raises from early position probably has a monster—aces, kings, or ace-king suited. You might give him an 80% probability of that holding. You might put him on a 20% probability of having a pair of jacks or queens.

A loose player, on the other hand, might have anything, but you still put him on a range of hands. You might conclude that there’s a 50% probability that he has nothing worth having at all, and maybe he flopped a small or medium pair.

This is why you discount the outs, to contend with the idea that even if you make your hand, it might not be good enough to beat your opponent at the showdown.

You could just fold until you got the absolute nut hand, but you’ll lose money from the blinds if you use that strategy.

4 – There Are Shortcuts, Too

One of the ways to get a rough estimate of your probability of hitting your hand is to multiply your number outs by four on the flop and by two on the turn. That’s the percentage chance of hitting your hand.

Dealer and Players Around Poker Table, Four Poker Aces Spread Out

Here’s an example:

You have four cards to an outside straight draw. This means that there are eight cards that will fill your straight. If you’re on the flop, the probability that you’ll fill your straight is 4 x 8, or 32%. If you’re on the turn, the probability that you’ll fill your straight is 16%.

That’s roughly 2 to 1 odds and roughly 4 to 1 odds at those stages of the game, so those are the odds you’re looking for when calculating pot odds.

5 – Poker Bluffing

When you add bluffing to the equation, the calculation of odds and probabilities gets even more complex. You might have an idea based on your observations about how likely someone is to fold in the face of your naked bluff, or you might not. If you don’t, you shouldn’t bluff.

The problem is that bluffing is rarely a profitable move against more than two opponents. That’s because for a bluff to succeed, everyone has to fold except you.

If you’re facing two players who you think have nothing in their hands, and who you estimate have a roughly 60% probability of folding, the probability that BOTH will fold is 60% X 60%, or 36%.

So, you need 3 to 1 odds from the pot to make that a profitable bluff.

?
But what happens if you’re facing three other players?

The probability drops to 36% X 60%, or about 22%. Now you need 4 to 1 or 5 to 1 pot odds to justify bluffing.

A semi-bluff is a better strategy. The idea behind a semi-bluff is that you bet and/or raise with a hand which probably isn’t the best hand now, but if you get the right cards, it will be.

You have two ways to win—if you make your hand, AND if your opponents all fold.

If you have a roughly 36% probability of filling a straight and a 22% probability that everyone will fold when you bet or raise, you’ll win that hand 58% of the time. Even if it’s even money when it comes to pot odds, your move is going to be wildly profitable here.

Conclusion

Odds, probability, and counting outs are integral to a solid poker strategy. It’s not enough to just play tight aggressive poker, not anymore. You also need to know when to get your money into the pot for +EV situations on a consistent basis.