Calculating Hand Odds and Outs

Hand odds are the chance of making a particular hand. In order to calculate your hand odds, you first need to know how many outs your hand has. Outs are defined as a card in the deck that helps to make your hand. For example, if you hold AK of hearts and there are 2 hearts on the flop, which leaves 9 remaining hearts that, would complete your flush, since there are 13 cards of each suit. It may be the case that other players have already folded a number of the remaining hearts, in which case there would be less than 9 remaining hearts in the deck. If you know for sure that someone is holding or has folded a heart then you can take that into account when calculating your odds, but in most situations you will not know, and therefore, must do the calculations only with the knowledge that is available to you; that knowledge being your hand and the cards on the table.

When calculating your outs, it is important not to over count your outs. An example of such a situation would be a flush draw in addition to an open straight draw. You hold J-T of hearts and the board shows 8h Qh Kd. A Nine or an Ace gives you a straight, of which there are 8 outs, while any heart gives you the flush, of which there are 9 outs. However, there is an Ace of hearts and a Nine of hearts, so you don’t want to count these twice toward your straight draw and flush draw. The true number of outs is actually 15 instead of 17.
When drawing to a hand you always want to be drawing to the nuts, i.e. the best possible hand. The situation in which you will lose the most money is where you draw to and make a hand, but your opponent makes a better hand. This is known as reverse implied odds, where you take into account future betting assuming you make the best hand when in fact you don’t have the best hand. An example would be an open ended straight draw when two of a particular suit (of which you have none) are on the table. Where you would normally have a total of 8 outs, 2 of those outs will result in three to a suit on a table, making a possible flush for an opponent. As such whilst you would have 8 outs to make your straight, you only really have 6 outs for a nut straight draw. These 6 outs are referred to as true outs.

Once you know how many outs you have on a hand, you can calculate your hand odds, i.e. what percent of the time you will hit you hand either on the turn, the river, or by the river (on the turn or river). When calculating the probability of a single event there is a shortcut calculation that will make it much easier to calculate odds on the fly. After you have found the number of outs you have, multiply by 2 and you will get a close estimate to the percentage of hitting that hand on every street. Multiply by 2 instead to get a percentage estimate for the Turn and River, i.e. outs x 2 x 2. For example, for a flush draw with 9 outs on the flop, multiplying 9 x 2 x 2 you get 36%. In other words there is about a 36% chance of hitting the flush draw by the river.