Low-limit texas hold’em is mostly a game of math. In the
long run, players who understand the probabilities will take money
from those players who willingly bet their money on long shots.
To start learning the probabilities in texas hold’em, it
is necessary to understand the concept of "outs". The
number of "outs" that you have is the number of cards
in the deck that can complete your hand. For example, say you hold:
 
and the flop is:
  
If a 6 or a Jack comes on either the turn or the river, you will
have made the "nut" (best possible) straight. You therefore
have 8 outs (4 sixes plus 4 jacks) to make your hand. The probability
(as can be seen in the table) that you will make your straight by
the river is 31.45%.
Odds:
| Outs |
Flop to Turn |
Turn to River |
Flop to River |
| 1 |
2.13% |
2.17% |
4.27% |
| 2 |
4.26% |
4.35% |
8.42% |
| 3 |
6.38% |
6.52% |
12.49% |
| 4 |
8.51% |
8.70% |
16.47% |
| 5 |
10.64% |
10.87% |
20.35% |
| 6 |
12.77% |
13.04% |
24.14% |
| 7 |
14.89% |
15.22% |
27.84% |
| 8 |
17.02% |
17.39% |
31.45% |
| 9 |
19.15% |
19.57% |
34.95% |
| 10 |
21.23% |
21.74% |
38.39% |
| 11 |
23.40% |
23.91% |
41.72% |
| 12 |
25.53% |
26.09% |
44.96% |
| 13 |
27.66% |
28.26% |
48.10% |
| 14 |
29.79% |
30.43% |
51.16% |
| 15 |
31.91% |
32.61% |
54.12% |
You are probably wondering, “How can I be expected to memorize
all those numbers?”. Well—you don’t have to. If
you look at the table, you can see that there are some easy “rough
estimates” that you can make also. After the flop, the odds
of making your hand with one card to come is approximately 2 times
the # of outs. The odds of making your hand with two cards to come
is approximately 4 times the # of outs. The most common situations
where it’s is necessary to know your odds happen all the time,
and they will be easy to remember:
Open-ended Straight Draw: 8 outs
Flush Draw: 9 outs
Flush draw and Open-ended Straight Draw: 15 outs
Flush draw with an Inside Straight Draw: 13 outs
A few other interesting numbers to know are:
Probability of being dealt a pocket pair: 5.88%
Probability of being dealt suited cards: 23.5%
Probability of hitting a three of a kind or better on the flop
when you hold a pocket pair: 11.8%
Probability of making a pair on the flop with two unpaired hole
cards: 32.4%
Probability of making a gutshot straight draw from by turn or river:
16.5%
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