Pot odds - how, when, what?

Some people like to play Texas Hold'em poker from a mathematical perspective. Basically what this means is calculating the pot odds - the statistical likelihood of your making a hand by either the turn or river card.

Before we go into the specifics of explaining how this is calculated, we feel we need to make you understand that this isn't a foolproof method of winning a poker hand. 99% of poker is not about the cards at all - which is why it is a game of skill, not of chance.

Most of the time, percentage odds of a particular hand coming up do not factor into the game at all. In fact, a recent study into online poker that analysed the hand data of over 3000 online players concluded that around 70% of all games of Texas Hold'em were resolved by one player folding out long before the River card.

If you understand and accept that pot odds are not a sure thing, then it is safe to use them because you then also understand that they are simply a guide. They are a mathematical indicator of what might happen, but they in no way guarantee that it will come to pass, even if they seem favourable.

Now that we've got that settled, let's look at the two main methods of calculating odds on the fly.

It's not called “betting” for nothing

When you place a bet on a sports fixture, there are two factors at play. The first is your insider knowledge in placing the bet in the first place - everything you know about the sport, and the reasons that you are placing this particular bet.

The second is the odds that the bookie is giving you. The odds help you decide whether or not the bet is worthwhile. For example, if you are sure that you will win, but the odds available are even, it might not even be worth your while to pursue the issue, especially if there is even the remotest doubt that you might be wrong.

However, if the odds are a phenomenal and you could quadruple your money or better, then it's worth doing.

Here's how to assess pot odds. Suppose that you're playing No Limit Hold'em, and due to some pre-flop betting, by the time the flop arrives there are only two of you left in the hand. The pot is already sitting at $2000, and your opponent raises $500.

This brings the total pot to $2500. You require $500 to call. Total pot divided by call amount gives the pot odds. In this case, $2,500 divided by $500 gives you 5:1.

Now, you're holding a flush draw at this point thanks to the suited King-8 of spades in your hand and two more spades on the table. The 8 of diamonds also currently gives you middle pair, since the highest table card is an Ace of spades, plus a loose 4 of spades.

Now, you feel pretty sure that your opponent is bluffing, and 5:1 feels like good odds. But is it worth calling him?

The odds of success

You see, your opponent may have the ace after all, which would sink your pair of eights. What are the chances of you completing your flush draw before the river?

Here's how you calculate these odds.

Okay, by the time the flop comes down you have seen a total of five cards out of a deck of 52. Four of these are spades. Now, with a total of 13 spades possible in a single deck, that leaves 9 that you haven't seen, any one of which completes your hand, beating the possible pair of eights.

This is called having 9 "outs". The formula is simple - number of outs divided by total number of unseen cards. In this case it's 9 divided by 47, which is 0.1914 – or 19.14% chance of hitting a spade on the turn.

The same formula applies at the river – only by that stage you've seen six cards leaving 46 in the deck. Assuming you haven't got your flush yet, your odds of hitting it on the river are: 9 divided by 46 which is 0.1956 – or 19.56%.

Bear in mind, please, that these are just statistics. They have no effect on psychology, which is most of what the game is about.