Pot Odds

Pot Odds

Poker Fundamentals
Mathematics of Poker

Understanding some math basics will go a long way in helping you appreciate how it can affect your odds and your game. Learn your critical pot odds, and how to use this information to make the best possible decisions at the table. 

If you want a bankroll big enough to choke a T-Rex, you’re going to want to learn about pot odds. Try as you may, you can’t totally escape the all mighty power of math. Don’t get us wrong, you don’t have to be able to do complex calculus in your head, but understanding some math basics will go a long way in helping you appreciate how it can affect your odds and your game. 

When thinking about ‘odds’ in reference to poker, there are actually several types of odds we could be talking about, but they basically all boil down to hand odds and pot odds. Today, we’re going to be looking at both to see how you can use them to optimize your performance. 

The Deal with Pot Odds: Ratio and Percentage

Your pot odds help you decide whether or not it's worth it to act by illuminating the likelihood of your winning a drawing hand. Pot odds are usually broken down to a convenient ratio, so we’ll start with that method. 

If - for example - there is $100 in the pot and you call $10, your pot odds are 100:10 or 10:1. 

Easy peasey, right? Yes, but this is actually not all you need to know. You don’t want to be going all-in or, making a hefty bet or even calling on pot odds alone. Pot odds only show you part of the picture since they don’t account for the cards in your hand; they only account for the size of the pot and the size or your bet. To get a full picture, you are going to have to calculate your hand odds. 

To get a handle on hand odds (also called card odds) it's most helpful to look at a concrete example. 

Let's say you hold A♦, 9♦.

The flop comes in with 3♦, 10♣, Q♦. 

What you’re going to want to determine first is your chances of snagging another diamond on the turn. The easiest way to go about determining this is to work out the ratio of cards in the deck that we don't want against the cards in the deck we do. 

We see 5 of the cards (our hole cards and the board cards), which means there are 47 cards left of indeterminate rank and value. What we do know, however, is that 9 out of those remaining 47 cards will make the flush and 38 won't. (There are 13 cards of every suit in a deck and we can see 4; hence the 9 remaining saviours, or 'outs'.) When put into ratio form, this gives us 38:9, or about 4:1 (38/9 = 4.2222). 

Compare for Yourself

Your pot odds are 10:1 and your hand odds are 4:1. In this instance, you should definitely act since the odds of connecting on your flush (your hand odds) are better than your pot odds. You have a 1 in 4 chance of making your flush as opposed to a 1 in 10 chance with your pot odds. As a general rule, you should only call when the pot odds are greater (not better, remember, just bigger) than your card odds. 

Another way to look at calculating pot odds is using percentage. 

Using the same example, we are going to determine our card equity, which is exactly the same as our card odds. If you remember, we found we had 9 outs. If we want to find out what our chances of making the flush using percentages, just double your outs, then add 1. 

So, 9 x 2 = 18.

18 + 1 = 19. 

You have a 19% chance of making your flush. 

Again, you’re going to want to compare this with your pot odds. The pot is $100 and you call $10, giving you a total pot size of $110. Since 10 is 9% of 110, you can easily deduce your pot odds are 9%. 

So, your hand odds are 19% and your pot odds are 9%. If your card equity is better than your pot odds, you should bet. If it is worse, you should fold. 

Of course, it can take years for some players to be able to quickly work out the math in their heads, and while it is certainly worth practicing to achieve this goal, you can also use odd, ratio and percentage charts to soften the learning curve in the meantime. 

Ratio Odds Chart (from the flop)

Chart Legend:

  • Flop → Turn is your odds of hitting an out from the turn card
  • Turn → River is your odds of hitting an out from the river card
  • Flop → River is your odds of hitting an out with two cards remaining (turn & river)
  • 4 outs is a gutshot straight draw 
  • 8 outs is a open-ended straight draw
  • 9 outs is a flush draw
  • 15 outs is a open-ended straight or flush draw