The Basics of Calculating Poker Odds

Oct 18 2012 |

The game of Texas Hold’em Poker is half art and half science. The art part is mastered through many hours of sitting at the poker tables (or in front of a monitor with poker tables). Learning the science is more straightforward, but is a crucial first step. Understanding the numbers will build solid fundamentals to underpin your game. And it can make learning the art part a less costly experience.

The most important concept in poker odds is the “out.” An out is a card you don’t see in your hand or on the table. For instance, if you have the Ace of hearts in your hole cards and are looking to at least pair it, there are exactly three outs that can do that – the Aces of clubs, diamonds and spades.

Good poker play includes always knowing how many outs you need to get a desired hand and knowing the probability you have to hit those outs. Odds calculation usually happens after the flop. There are far too many possibilities pre-flop and consideration is mainly focused on the relative strength of your starting hand.

After the flop, you have seen five cards – the two in your hand and the three community ones. Out of the deck of 52 cards, that leaves exactly 47 that are “out there.” Your odds of hitting a desired hand on the turn is thus the number of outs you need, divided by 47. If you don’t see what you are looking for on the turn, you have one more chance on the river. Now you’ve seen 6 cards (including the turn), so your odds are your outs divided by 46. Let’s quickly consider an example.

Calculating poker odds with poker flash cards

You are holding QsJs. The flop comes in KsTs2c. You have an open-ended straight draw. It can be completed by either an Ace or a 9. There are four Aces and four 9s in the deck, so you have eight outs. Divide that by 47 and you see you have a 17% chance of completing a straight on the turn. It also happens that you have a spades flush draw. There are a total of 13 spades, two are in your hand and two are on the table, leaving you with nine outs. Divided by 47, you have a 19.2% of making a flush on the turn, and a 36.2% chance of making either a flush or a straight. Let’s say the turn is 3h. Now on the river, following the calculation above but with 46 remaining cards, you have a 17.4% chance to hit a straight, 19.6% to hit a flush and 37% chance to hit either.

This is all well, but in reality making divisions by 47, while you are simultaneously trying to read other people and your blood is probably boiling with tension, is not the most convenient calculation. Furthermore, if you want the odds that you will make your hand either on the turn or on the river involves a conditional probability even Albert Einstein on his best day couldn’t calculate accurately in his head.

Fortunately, there is a shortcut. As a quick calculation, multiply your outs by 2 to get the probability to make a hand on the turn or on the river and multiply by 4 to get the odds of making the hand either on the turn or on the river. This quick calculation gives a good ballpark number for three to 13 outs. Its accuracy diminishes with fewer than 3 or more than 13, but in any event if you have more than 13 outs (as in the open-ended straight flush draw case above) you should probably be more worried about betting and raising than about making calculations.

Poker Flash Cards

As a last note, bear in mind that the calculations described measure the chances of hitting a certain hand, not of it being the winning hand. You might hit your flush draw just to find yourself beat by a higher flush. Once you have crunched the numbers in your head, you need a make a winning play out of them. And that’s where the art part kicks in.

For more practice with counting your outs and making decisions about how to play, use our Hand Odds deck of pokerflash cards.

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