Math in Poker

On this page you will learn about using mathematics in poker. A solid understanding of probability and poker odds is vital, but you will need to know how to properly calculate those odds that are fundamental to making most decisions at the poker table.

In poker, when the cards are dealt on the flop there will be many situations where you don’t expect to have the best hand. But if your hand falls into the drawing category, it means you can still make the winning hand, and this is one of the situations in which math in poker becomes important to know.

The next step you need to do is to identify the cards you need to improve in order to complete the draw. If you can figure out your odds of improving, you can compare it with the pot odds you’re getting to make the call in order to determine whether it’s a profitable play.

To calculate your odds of improving your drawing hands, you first need to understand the concept of “outs”. Your outs are the cards that you need in order to improve your hand to the winning one.

For example, the following is often the common drawing hands that you will make on the flop:

  • Flush draw – 9 Outs
  • OESD (open-ended straight draw) – 8 Outs
  • Two Overcards – 6 Outs
  • A pair as a three of a kind or two pair – 5 Outs
  • Gutshot (inside straight draw) – 4 Outs

Knowing the number of outs for the most common draws you will flop will definitely help, but quite often you will flop combo draws, so will need to consider your additional outs and odds of improving your hand.

The 2/4 Poker Rule

With this information at your disposal, you can use the 2/4 rule to work out the percentage odds of making the best hand.

To calculate your percentage odds can be done on the fly and is worked out by:

  • Multiplying your outs by 2 when you’re working out your odds for the next card.
  • Multiplying your outs by 4 when you’re working out your odds for both the turn and river (opponent is all-in on the flop).

Pretty much always though you are multiplying your outs by 2 to see the next card because you can’t anticipate what the future betting action will be like you may have to call more bets. So, for example, you are on a flush draw, you have 9 outs to improve, so 9 x 2 = 18%, which is the equity you have in winning the pot. Keep in mind the 2/4 rule calculates percentage odds and not ratio odds. So, this just means you will need to convert your pot ratio odds to a percentage so you can compare the two and decide whether to make the call.

Calculating Your Pot Odds

Now that you know how to calculate hand odds for improving to the best hand, the only thing that it doesn’t help you with is to make the correct decision whether to call or not. This is when you need to calculate the pot odds.

Pot odds are the ratio between the amount of money you can win and the money you have to call to continue playing in the hand. This ratio also represents risks and profits. By comparing the pot odds to the odds you have of making your hand, you can decide whether to continue in the hand.

Suppose you are playing a No Limit Hold’em game. On the flop the amount in the pot is $10. Your opponent bets $2. To keep playing you must at least call the $2 bet. So, is calling to see the next card in this situation beneficial or not?

First let us consider the following four factors:

  • Amount in the pot before the bet : $10
  • The bet amount: $2
  • The money that can be won: $12 (current pot)
  • The amount to call: $2

In this situation, you must pay $2 to win $12 so the pot odds are 12:2 or 6:1. This means the player would need to win the hand one in seven times to break even on the call. As a percentage this converts to around 14%.

If the percentage odds of making your hand is greater than the odds the pot is giving you, then you should make the call. If you were on a flush draw, we already know from the example above that we will complete the flush 18% of the time by the next card, so the call is profitable in this situation!

In general, we can decide whether to call in a particular situation or not by comparing the pot odds and odds of making what you expect to be the best hand. If the percentage odds of making your hand are greater than the percentage odds the pot is giving you, you will make money in the long run, and making mathematically correct decisions is integral to being a winning poker player.