Calculating Pot Odds

Poker can be played from a mathematical perspective. It's possible to calculate the odds of a poker hand being successful using algebra.

Back to school

And to think, you once questioned the usefulness of having to learn algebra in school. Little did you know that later in life it would be a huge contradicting factor in your successful poker playing career.

Yes, what you have heard is true. Using a simple pocket calculator, or your brain if you are super smart, you can use a formula to calculate the probability of successfully hitting any given poker hand, based on your hole cards.

Before we go on, two small notes of practicality.

First, unless you are a genius level mathematician, it won't necessarily help you very much in live poker situation, because you will be fiddling with a pocket calculator every time you get dealt new cards. People will point and laugh at you. But if you like to play online, no one can see you pressing buttons, and the information can be quite helpful.

Secondly, calculating the percentage odds of success is a really weird way to think about poker. Most people do it by learning the behaviour of their opponents and trying to deduce what they might be holding through their actions. Statistical probability is a useful addition to your arsenal of poker skills, but it is by no means a magic bullet.

Having said that, let's look at how it's done.

How many outs are there?

Step one in calculating pot odds is working out how many outs you have. What this means is, which cards would you need to make your hand successful? Let's give you an example.

Suppose that you are dealt the six of clubs and the six of hearts. As a low pair, it's probably rubbish. Could anything make it better? The flop comes down four of clubs, ten of spades, two of clubs. Oh boy.

So, to turn this into a set, there are two possible outs – either the six of diamonds or the six of spades on the turn or river. Get it? The number of outs is the number ways a hand could resolve to something decent.

My brain hurts

Now there is, if you google it, a long and convoluted mathematical algorithm for calculating pot odds. It goes something like this. There are 52 cards in a deck. By the time the flop comes down, you've seen 7 – that leaves 47.

So, your odds are: total cards left, minus number of outs, divided by total cards left. This a actually calculates the odds of failure. Subtract it from one, which gives you the percentage odds that you'll hit what you need.

There's a shorter, less accurate way

Luckily there's also a quickie method. Number of outs, multiplied by 4 gives you the approximate percentage odds from the turn. Multiply by 2 instead from the river.

Reality check

The thing to remember when calculating pot odds is that this is the percentage likelihood that you will hit the hand you're after. This does not mean that someone else won't have a stronger hand. You still need the foresight and maturity to recognise whether the hand you're trying to hit is strong enough to win.