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   Calculating Odds
Hand odds are the odds, probability or chance of you successfully competing your hand. For example, if you hold two spades in your hand and there are two additional spades in the flop giving you 4 spades to the flush, your hand odds for making a flush are about 2 to 1 and is represented as 2:1. This can be read as you will fail to make your hand 2 times for every time you do, or you will succeed 1 out of 3 times, or 33%.

The 1st thing you must do when calculating hand odds is to determine how many cards are left in the deck and how many will complete your hand.

Calculating Outs

How many cards are left in the deck is very simple. The deck starts with 52 cards and only those cards that you know the value of are considered removed, therefore, since the two pocket cards and 3 flop cards are the only cards you know, the remaining cards are 52 – 5 or 47. Yes, it is true that other players have pocket cards. You don’t know the value of these cards so you must assume they are all available to do the statistics.

How many cards that will complete your hand, called “outs”, is also very simple. If, between you pocket cards and the flop, you have 4 to a flush, there are 13 – 4 or 9 cards that will complete the flush. If you have 4 cards to an up and down straight, that is to say you have 3,4,5, and 6 giving you the up card 7 and the down card 2 that will complete the straight, there are 4 sevens and 4 twos for a total of 8 outs.

It gets a little more complicated when you have two different draws. Let’s say you have a flush and straight draw, such as 3, 4, 5, and 6 of hearts. You are drawing to a flush and a straight. The cards that will complete your hand are any 7 or any 2 to make the straight and any heart to complete the flush. There are 4 sevens and 4 twos available to make the straight and 13 hearts to make the flush, however, one of the 7’s and one of the 2’s are hearts and can’t be counted twice. To calculated the outs there are 4 sevens and 4 twos and 13 hearts minus the 1 seven of hearts and the 1 two of hearts so it’s 4 + 4 + 9 – 1 - 1 = 15 outs.

Calculating Hand Odds

So to continue with the calculation, the percentage of you completing your hand is calculated by dividing the number of outs by the number of cards remaining and can be calculated for the next card, the turn, the last card, the river, or both.

The probability of making the flush on the turn would be 9 outs / 47 remaining cards = .19 or 19%. The probability of making the flush on the river, assuming you didn’t make it on the turn would be 9 outs / 46 remaining cards = .2 or 20%. Keep in mind, there was one additional card reveled on the turn making the total cards left in the deck 46.

These probability are normally converted to a ratio in the format X:Y, for example 2:1. To convert a probability to this more typical format use the formula (1 / X ) - 1 where x is the decimal percent calculated above. In our flush example, we calculated the chance of completing our hand on the turn as 19%. So we calculate the hand odds as (1 / .19) – 1 = 4.3 or the odds are roughly 4:1 meaning you will complete your hand 1 time for every 4 times you miss.

Now I’m not sure how many people can do all this math in their head during a poker game. I sure can’t. What I do is study the probability chart and remember the probability for specific hands. See Table 1 below.

Calculating Pot Odds

So now you know the hand odds of making your flush is 4:1 on the turn. What good is that? This is where pot odds come into play. If you stand to earn more than 4:1 on your money, that is for every dollar you have to bet, you will receive more than $4 in return, then statistically this is a good bet. Lets say there is $90 in the pot and the player before you bets $10 to make the total pot $100. If you call the $10 bet, you will be getting $100/$10 or 10:1 on your bet making this a very good bet for your flush draw. If the player ahead of you bets more, say 50% of the pot or $45 making the total pot $135, you will be earning 135/45 or 3:1 on your money and statistically, the flush draw will cost you more than you will earn in the long.

Table 1: Hand Odds

Outs Turn River Turn+River
1 46:1 45:1 22.5:1
2 22.5:1 22:1 10.9:1
3 14.7:1 14.3:1 7:1
4 10.8:1 10.5:1 5.1:1
5 8.4:1 8.2:1 3.9:1
6 6.8:1 6.7:1 3.1:1
7 5.7:1 5.6:1 2.6:1
8 4.9:1 4.8:1 2.2:1
9 4.2:1 4.1:1 1.9:1
10 3.7:1 3.6:1 1.6:1
11 3.3:1 3.2:1 1.4:1
12 2.9:1 2.8:1 1.2:1
13 2.6:1 2.5:1 1.1:1
14 2.4:1 2.3:1 1:1
15 2.1:1 2.1:1 .8:1
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