Calculating Odds
To determine the odds against improving your hand on the next card,
compare the total number of cards that will not help you to the number of cards or
"outs" that will.
For example, you hold 7 ♥ 6 ♥; with a flop of A ♣
T ♥ 5 ♥. On the flop there are
47 unseen cards. Out of these 47, there are nine hearts remaining that will
improve your hand to a flush and 38 cards that won't; therefore, the odds against
improving to a flush are 4.2 to 1 (38/9). An open-ended straight draw has eight outs,
which is 4.9 to 1 against improving (39/8). An inside straight draw, a.k.a.
gut-shot draw, has four outs, which is 10.75 to 1 (43/4).
If you don't improve on the turn and want to know the odds that the
river can will improve your hand, the odds will improve just slightly as one more care
has been seen. There are only 46 unseen cards on the turn; therefore, a flush draw
is now 4.1 to 1 (37/9), which is just slightly better than the 4.2 to 1 odds you had
when drawing on the flop.
To determine the probability of improving on the next card, simply
divide your outs by the total number of cards left in the deck. For example, the
probability of improving to a flush on the next card is 19% (9/47). You will improve to
an open-ended straight 17% of the time (8/47), and a gut-shot straight 8.5% of the
time (4/47). I prefer to know the odds are 11 to 1 rather than the probability is
8.5%, because it is easier to compare to the pot odds you are receiving.
Sometimes on the flop, you want to know the probability that either the
turn or the river card will improve your hand with two cards to come. These
calculations are slightly more complicated. The best way is to multiply the probability of
missing on the turn by the probability of missing on the river. For example, for a
flush draw you would multiply 38/47 by 37/46, which equals 1406/2162 or .6503;
therefore, 65% of the time you will not improve and 35% of the lime you will. [To convert
this to odds, invert the percentage and subtract 1 to get 1/.35 -1 = 1.9 to 1 against
improving.]
This section looked briefly at how to calculate simple odds and
probabilities; however, calculating odds in your head during a poker game can be
quite cumbersome. In reality, all you need to do is memorize the following
chart.
| Number of Outs |
Two cards |
One card* |
| 20 |
.5 to 1 |
1.3 to 1 |
| 19 |
.5 |
1.5 |
| 18 |
.6 |
1.6 |
| 17 |
7 |
1.8 |
| 16 |
.8 |
1.9 |
| 15(Flush draw with overcard) |
.8 |
2.1 |
| 14 |
1 |
2.4 |
| 13 |
1.1 |
2.6 |
| 12(Flush draw with overcard) |
1.2 |
3 |
| 11 |
1.4 |
3.3 |
| 10 |
1.6 |
3.7 |
| 9(Flush draw) |
1.9 |
4 |
| 8(Open-ended straight draw) |
2.2 |
5 |
| 7 |
2.6 |
6 |
| 6(Two Overcards) |
3 |
7 |
| 5 |
4 |
8 |
| 4(Gut-shot draw) |
5 |
11 |
| 3 |
7 |
15 |
| 2(Trying to hit a pocket pair) |
11 |
23 |
| 1 |
23 |
46 |
The one card column looks at drawing on the flop. When drawing one card on the turn, the odds
are slightly better since one more card has been exposed
NEXT...
Determining the Number of Discounted Outs
