Math in Poker

5 Ways Math Can Help Your Online Poker Game

While you can enjoy online poker profitably without any high-level math – having a basic grasp of the numbers is never a bad thing. The most obvious way in which math is used in online poker is for probability, with odds and outs both coming into play – as well as bet sizing. There are several other ways which math can help you. These include concepts of expected value, ICM and even bankroll management. This page takes you through the key areas of online poker where math can improve your play.

Poker Math #1 – Pot Odds

Every time you put chips into the pot in poker you are either offering odds to an opponent, or taking odds yourself. To put this in concrete terms, if you bet $100 on the river, into a $200 pot, then your opponent is getting odds of 3-to-1 on the call. If he believes his chances of winning the hand are greater than this, he should call – otherwise he should fold.

This is known as pot-odds – the odds you are getting at the time you are making the bet.

Things are more complicated when there are more cards to come. You might be getting a ‘price’ that does not work for your winning chances right now – though the potential for winning chips if you do win the hand might make the call worthwhile.

This is known as you ‘implied odds’. It can work before the flop. For example, you see a raise from a tight player and ‘know’ that he has aces or kings. You have a pair of 4’s. Since you have the worst hand at the moment, no current pot odds make this a good call. If you do hit your 4 on the flop, you can win 20x or even 30x your bet from your opponent. Those future wins make the immediate call worthwhile.

Poker Math #2 – Outs

The number of cards in the deck which will complete your hand are known as ‘outs’. You can combine your outs with the pot-odds (and sometimes implied odds) on offer to work out the best play.

Here are some examples:

• You have pair of 2’s on the turn. With just the river card to come you have seen 6 of the 52 cards in the deck. Of the 46 remaining cards, two of them are deuces – this gives you a 1 in 23 chance of making your hand on the river (just under 5%).
• You have 4 cards to a flush on the flop. Two in your hand, and two on the flop. You have seen 47 of the 52 cards, and 4 of them are your suit. This leaves 9 cards in your suit out of 47. That is around 19%. You have a 19% chance of making your hand on the turn, and a little bit higher than that on the river (since you will have seen one more card not of your suit).
• You have 2 pair on the flop, pairing both of your hole-cards. There are now 4 ‘outs’ which will make you a full house of the 47 unseen cards. There are two streets of betting to come.

Learning the number of outs and probability of making a hand is vital if you are going to profit in the long term. In each spot, you can compare your chances of making the hand to the odds on offer – and make the best decision about whether to call, raise or fold.

Poker Math #3 – Expected Value

In poker, things do not always go your way. You can get your money into the pot as 80% favorite, and still lose the hand. Over the long run, these swings of fortune will even out. In the short term, they can often be frustrating.

You need to keep in mind that variance is beyond your control, though putting the chips into the pot while you have an edge is very much in your control.

It can pay to think of each situation as having either a positive or negative ‘expected value’. Betting your trips against an overpair of your opponent has a huge expected value over time, this is said to be +ev. By comparing the odds, outs and tendencies of opponents, you can work out when calling a bet will have a positive or negative expected value over time.

Poker Math #4 – ICM, Chips Change Value

The Independent Chip Model is used in poker tournaments to describe the way that chips change value in relation to the prize pool. While this topic is advanced in some ways, the principle behind it is simple enough.

If you imagine at the start of a tournament, everyone has 1000 chips for a $10 buy-in. Each chip is worth 1c. Now fast forward to the end of the game, a player won the tournament, and accumulated the 100,000 chips along the way. He won $500. You can see that each chip is now worth half a cent!

ICM comes into play at the bubble of sit n go tournaments, though can also be used to guide your decisions in multi-table tournaments – particularly as you reach the final table.

Poker Math #5 – Bankroll Management

One way to survive the swings of fortune in poker is to use bankroll management. Again, some math is required. The idea is that you have enough buy-ins to survive even the biggest downswings, and use this as a guide for when you move up levels too.

For cash game players, 20 buy-ins is the standard guideline. If you play tournaments, then the requirements are stricter – with up to 100 buyins the norm.