At the Poker Tables: Mathematics Series 001 - Pot Odds

Maths is everywhere, isn't it? Without it, my computer wouldn't compute, my brain wouldn't process and, most important for us here, my poker playing wouldn't yield success. That's because this is the first instalment of the Riverboat Gaming "At the Poker Tables: Mathematics Series". In this series, we'll be looking at the importance of using and understanding maths when you are playing poker, and explaining how some key concepts shape the game and will be the difference between a winning and a losing player.

Note: Not everyone likes maths as much we do so we will keep this series as jargon-free as possible.

The first concept that we are going to look at is vital to understand if you are going to be making smart bets and is one of the most fundamental concepts of the game. 

Pot Odds

Pot = The poker chips that are currently in play in the centre of the poker table and which you will win if you take down the hand, either by having the strongest cards or by outplaying opponents with betting strategies.

Odds = The probability of one eventuality happening in relation to another eventuality.

Pot Odds = A ratio of the amount that you have to call to the amount that is in the pot.


This idea is easily clarified with some simple examples:

Poker Table 1:

Pot = £100

Amount to Call = £20

Odds Given by the Pot: 5:1

An easy way to think about this is: How many times can you multiply the call amount by before you reach the pot amount? A: 20 x 5 = 100


Poker Table 2:

Pot = £750

Amount to Call = £300

Odds Given by the Pot: 2.5:1

How many times can you multiply the call amount by before you reach the pot amount.? A: 300 x 2.5 = 750


Poker Table 2:

Pot = £1000

Amount to Call = £900

Odds Given by the Pot: 10:9

This one is a bit more awkward to calculate mentally but you end up with a pot odds of 1: 1.1.11111 recuring. These odds would usually be considered very tight as they are getting close to "evens" or 1:1. At 1:1 odd you don't make any money, but you also don't lose any money, on average given that situation.


The key here is not to be able to necessarily do complex mental arithmetic (though these days many professional poker players are also mathematicians) but to get in the habit of thinking about the size of the call you are making vs the size of the pot. Rather than just thinking about the size of the call. A £1000 call is more than a £100 call in absolute terms. However, a £1000 call into a £10,000 pot is a much more attractive proposition than a £100 call into a £100 pot in terms of pot odds!

To summarise: You need to have a good reason to call a bet when the pot odds are bad (as they approach 1:1 or evens), and a less good reason to call as the pot odds improve.

So for example in the "Poker Table 1" example, you are going to have to win one out of every 6 hands in order to "break even" This is because, when you win, you will win £120, but you are only betting £20.

In "Poker Table 3" example you will have to win in this situation 9 out of every 19 times in order to break even. You, therefore, need a stronger hand relative to your opponent to call this bet than you would do in example 1.

It is worth clarifying here that it doesn't matter if some of those poker chips in the centre of the table were yours originally, that you bet them in an earlier round. They are communal now and should be included exactly as if they were no longer yours. The pot is there to win in this round or future rounds, and the previous betting become irrelevant (except from the point of view of information on what other players have of course).


The better you are at calculating these pot odds, the more precisely will you be able to make astute decisions at the poker table. Plus you will be more likely to be able to make these decisions under pressure when it really matters! Try occasionally just tracking the pot odds through a whole hand - seeing how the ratio changes and develops over the betting rounds. You don't need to be too precise, rough and ready calculations will do the job!

Once you know and understand pot odds the next step is to then start to compare those odds to your believed or known odds of being ahead of the other players. It is this comparison which will ultimately determine whether or not you should continue in the hand. We will visit these skills in detail in our explanations of "drawing odds" and "implied odds" which will be coming soon!

In the meantime start getting a feel for when pot odds are good and think about how to get involved in those hands!

Mathematics Series

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