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Calculating the Odds of Winning
I
n poker, winning is all about having the best hand. Although strategy plays
an important part in the game, in the end it's all up to the draw of the
cards. Part of a winning strategy is knowing how to calculate the odds
of ending up with the cards that you need. The method of calculating
odds varies between the different games. Here's a look at the how it's done.
All of the odds below are based upon a 52 card deck with no Joker.
Odds for Five Card Draw
T
he table below shows the odds that you will be dealt any particular hand in
Five Card Draw:
| Hand |
Odds against it |
| Straight flush |
64,973 to 1 |
| Four-of-a-Kind |
4,164 to 1 |
| Full House |
693 to 1 |
| Flush |
508 to 1 |
| Straight |
254 to 1 |
| Three-of-a-kind |
46.3 to 1 |
| Two-Pair |
20.0 to 1 |
| Pair of A,K,Q,J |
6.69 to 1 |
A
fter the cards are dealt, the odds shift to the probability of you making a
hand from the cards that you held and the new cards that replaced your
discards. Here are some examples:
The odds against making Four-of-a-Kind or better by holding Three-of-a-Kind
and discarding two cards:
| Hand |
Odds against it |
| Four-of-a-Kind |
22.5 to 1 |
| Full House |
15.4 to 1 |
And here are the odds against drawing three cards to an existing pair:
| Hand |
Odds against it |
| Four-of-a-Kind |
359 to 1 |
| Full House |
97.3 to 1 |
| Three-of-a-Kind |
7.75 to 1 |
| Pair and an Ace |
5.26 to 1 |
Odds for Seven Card Stud
T
he table below shows the odds of being dealt various hands in the
first three cards:
| Combination |
Odds against it |
| 3 Aces |
5,524 to 1 |
| 3 Jacks through 3 Kings |
1,841 to 1 |
| 3 Sixes through 3 Tens |
1,104 to 1 |
| 3 Twos through 3 Fives |
1,380 to 1 |
| 2 Aces |
75.7 to 1 |
| 2 Jacks through 2 Kings |
24.6 to 1 |
| 2 Sixes through 2 Tens |
14.3 to 1 |
| 2 Twos through 2 Fives |
18.2 to 1 |
| Three parts of a Straight Flush |
85.3 to 1 |
| Three parts of Other Flush |
23.9 to 1 |
| Three parts of Other Straight |
4.76 to 1 |
| Any Three-of-a-Kind |
424 to 1 |
| Any Two-of-a-Kind |
4.90 to 1 |
Calculating the odds beyond the first three cards becomes very difficult
as they will vary widely depending upon what you are holding.
Odds for Texas Hold'Em
B
ecause of the way that the game is played, we have to use a two-part
formula when trying to calculate the odds of completing any given hand.
In order to do that, we have to first know the number of
"outs" available
to complete any given hand before we can calculate the odds of completing
that hand. "Outs" are the number of cards that
are potentially available in the deck to complete any given hand.
For example:
| Your Cards |
Wanted Hand |
Outs |
| A Pair |
Three-of-a-Kind |
2 |
| Two Pair |
Full House |
4 |
| Inside Straight |
Straight |
8 |
| Open-ended Straight |
Straight |
8 |
| Four Flush |
Flush |
9 |
| Open Straight Flush Draw |
Straight, Flush, Straight Flush |
15 |
O
nce you determine the number of available outs, you can use the table below
to determine the odds of actually catching one of those outs at either the
turn or the river.
| Outs |
Turn (X:1) |
River (X:1) |
Turn or River (X:1) |
| 20 |
1.35 |
1.30 |
0.48 |
| 19 |
1.47 |
1.42 |
0.54 |
| 18 |
1.61 |
1.56 |
0.60 |
| 17 |
1.77 |
1.71 |
0.67 |
| 16 |
1.94 |
1.88 |
0.76 |
| 15 |
2.13 |
2.07 |
0.85 |
| 14 |
2.36 |
2.28 |
0.96 |
| 13 |
2.62 |
2.54 |
1.08 |
| 12 |
2.92 |
2.83 |
1.22 |
| 11 |
3.27 |
3.18 |
1.40 |
| 10 |
3.70 |
3.60 |
1.61 |
| 9 |
4.22 |
4.11 |
1.86 |
| 8 |
4.88 |
4.75 |
2.18 |
| 7 |
5.71 |
5.57 |
2.59 |
| 6 |
6.83 |
6.67 |
3.14 |
| 5 |
8.40 |
8.20 |
3.91 |
| 4 |
10.75 |
10.50 |
5.07 |
| 3 |
14.67 |
14.33 |
7.01 |
| 2 |
22.50 |
22.00 |
10.88 |
| 1 |
46.00 |
45.00 |
22.50
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Odds for Omaha
T
he theory for calculating the odds in Omaha is the
same as in Texas Hold'Em. The difference lies in the fact that you have
more hole cards in Omaha. Here is a table
of probability of you catching one of the needed number of
outs:
| Number of Outs |
% in Turn |
% in River |
| 1 |
2.3 |
4.4 |
| 2 |
4.5 |
8.8 |
| 3 |
6.8 |
13.0 |
| 4 |
9.1 |
17.2 |
| 5 |
11.4 |
21.2 |
| 6 |
13.6 |
25.2 |
| 7 |
15.6 |
29.0 |
| 8 |
18.2 |
32.7 |
| 9 |
20.5 |
36.7 |
| 10 |
22.7 |
39.9 |
| 11 |
25.0 |
43.3 |
| 12 |
27.3 |
46.7 |
| 13 |
29.6 |
49.9 |
| 14 |
31.8 |
53.0 |
| 15 |
34.1 |
56.1 |
| 16 |
36.7 |
41.0 |
| 17 |
38.6 |
61.8 |
| 18 |
40.1 |
64.5 |
| 19 |
43.2 |
67.2 |
| 20 |
45.5 |
69.7 |
| 21 |
47.7 |
72.1 |
| 22 |
50.0 |
74.4 |
| 23 |
52.3 |
76.7 |
| 24 |
54.5 |
78.8 |
| 25 |
56.8 |
80.8 |
| 26 |
59.1 |
82.7 |
| 27 |
61.4 |
84.6 |
| 28 |
63.6 |
86.3 |
| 29 |
66.0 |
87.9 |
| 30 |
68.2 |
89.4 |
N
o matter what game you are playing, remember this: The odds listed are only a
probability of success or failure. Use them as a guideline but don't bet the
farm on them playing out as you expect!
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