How To Calculate Pot Odds

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While tournament poker is a game of situations and psychology, do your maths homework and you'll be leaving less to chance. Human calculator Phil Shaw examines the odds and reveals the most common confrontations with percentages to help maximise your chances when it counts.

Every time you make a decision or respond to what another player does in poker you are taking and laying odds. While a game like No Limit Hold'em often comes down to a 'Do they have it or don't they' scenario, there are many games and situations in poker where the odds alone that you are getting on a hand will dictate your action. For example, in a game like Limit Hold'em or Omaha many of the decisions you make will be highly mathematical ones based on the 'pot odds,' and in some situations there might even be no point trying to bluff a player because of the odds, whereas in others you could virtually call blind.

It's therefore important to have a strong idea of the odds of making or defending your hand in any given situation, and the ability to quickly compare them to the 'pot odds' you are getting or giving. Tournament poker, in particular, is one area where all top players know inside out the odds of their hand winning an all-in against other hands, because these confrontations come up so frequently. Most of them don't like playing all-ins that are close to even money, and some will even fold as a decent favourite rather than risk a big all-in early on, because they expect to have a better chance of outplaying amateurs in smaller pots. But even for the greats there comes a point in a tournament when playing an all-in is necessary, and - needless to say - you should always be looking to be a clear favourite when this happens.

Poker odds can be examined in a variety of ways, and we have split them into sections below to make the process easier, as well as listing some common confrontations with percentages for you to learn and remember. I've omitted odds from flop to turn, and on the turn, as these can simply be calculated by counting the outs for or against you out of the remaining cards.

BASIC ODDS
In Hold'em there are 1,326 possible two-card combinations for your starting hand, and 1,225 for any one of your opponents after you look at your cards. If you play a hand through, there are then 19,600 possible flops and 2,118,760 total full board combinations. This means that you could play for a lifetime and not see exactly the same thing happen twice!

With these parameters the chances of getting a pocket pair are 16/1, and of making it into trips or quads on the flop 12%. The chances of getting Aces are 220/1 against and AK about 1.2%, and, given you don't have a pair, you will make one on the flop about one third of the time and about 49% of the time by the river. With suited cards, you will make a flush 8.4% of the time by the river but only flop a flush 0.84% of the time, and flop a flush draw nearly 11% of the time of which it will be completed with a frequency of 38.3%. If you flop an open-ended straight draw, it will complete 34% of the time. The flop will be all of one suit some 5% of the time, two suited cards 55% and rainbow 40%.

All of this is interesting to know, and there are many other interesting facts in poker, but often such information is of limited use since your equity in a situation also depends on what cards your opponents are holding in any given situation. Because of this, in some games (especially Omaha) you may ignore 'redraws' if only looking at one side of the equation and overestimate your chances. On the other hand, you may be in a better position than you think. For example, in Hold'em the chances of completing your flush draw after the flop are low, but if you also have a live Ace they are much better. So basic odds are certainly important, because they give you a framework to think within, but you mustn't forget that poker is also about situations and psychology as well as mathematics - so although the chances of any given player having Aces pre-flop in Hold'em may be 220/1 against, unless they raise blind every hand, when they do raise the true odds are going to be a whole lot shorter.

PRE-FLOP, ALL-IN HAND MATCH-UPS
The key here is to spot hands that are likely to dominate, and those that are likely to be dominated. This is mainly useful for the purposes of tournament all-ins because a bad hand may be getting the odds to outdraw a good one on the flop and thereafter, but your equity in a pre-flop all-in is fixed and not affected by whatever entertainment the board throws up.

If you're considering a call, compare this information with the pot odds you are getting and decide if the risk is worth it with a marginal hand, and consider whether you are likely to be pot-committed if raising or facing a re-raise all-in.

Everyone is familiar with the concept of 50-50s or race situations in Hold'em where a pair takes on two overcards, and because these are unavoidable you should always be looking to get the money in during situations where you can be evens or better. For example, AK may run up against AQ as well as 88 and therefore be a good all-in investment, whereas the best 22 can hope for is overcards and a bigger pair would be a 9/2 against disaster. You can raise all-in but not call an all-in with it.

Notice from the odds listed that the emphasis is therefore on drawing to 'live' cards in a showdown - such as with A6 v 77 only the A is a live out and in A7 v AK only the 7 is live, putting both hands in very bad shape. When there are no pairs or duplications, things are much closer with AK v 89s and AJ v Q9 being 3/2 shots, and middle connectors like 89s v A4 being virtually evens shots.

ON THE FLOP
These odds demonstrate popular confrontations when all the money goes in on the flop and illustrates the importance of not risking a situation where you are a massive underdog. In order to do this you will need a good idea of what you are up against, which means protecting your hand pre-flop and understanding just how big a draw you have on the flop, as well as how your opponents play certain hands.

For example, if you have a combination hand like a live ace and flush draw against a pair, a straight and flush draw, or a pair and a draw, you're likely to be in reasonable shape unless you run into a monster, whereas the wrong end of a straight draw or a second best flush could obviously cost you dear. Similarly, running a big pair into trips or going up against someone with two pair or a better pair is likely to be disastrous for your bankroll.

We are grateful for this article to Inside Poker Magazine.