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Texas Hold'em Probabilities
The hole-cards (the two opening cards dealt face down)
Concerning the hole-cards:
The probability of getting any given pair is 0,45249 % ,
while the probability of getting a random pair is 5,8824 % .
The probability of getting suited cards in given values is 0,30166
% ,
while the probability of getting randomly valued suited cards
is 23,529 % .
The probability of getting unsuited cards in given but different
values is 0,90498 % ,
while the probability of getting randomly but different valued
unsuited cards is 70,588 %
2 players
If you’re in a 2-player-game, and your hole-cards make
a pair, the probability
that your opponent doesn’t have a pair is 94,041 % .
Here are 3 tables about probabilities, they are as follows,
1. Your pair in comparisson with your opponents pair.
2. Your chances of leading with a pair before the flop.
3. Your chance to have the highest card, if no one have a pair.
Yet, if your opponent found a pair, the probabilities depend
on the value of your own pair and are distributed as follows:
(1)
Your Pair |
Better Pair |
Worse Pair |
Same Pair |
As |
- |
98,630 % |
1,3699 % |
Ks |
8,2192 % |
90,411 % |
1,3699 % |
Qs |
16,438 % |
82,192 % |
1,3699 % |
Js |
24,658 % |
73,973 % |
1,3699 % |
10s |
32,877 % |
65,753 % |
1,3699 % |
9s |
41,096 % |
57,534 % |
1,3699 % |
8s |
49,315 % |
49,315 % |
1,3699 % |
7s |
57,534 % |
41,096 % |
1,3699 % |
6s |
65,753 % |
32,877 % |
1,3699 % |
5s |
73,973 % |
24,658 % |
1,3699 % |
4s |
73,973 % |
16,438 % |
1,3699 % |
|
3s |
90,411 % |
8,2192 % |
1,3699 % |
2s |
98,630 % |
- |
1,3699 % |
The probabilities of you being ahead before the flop are distributed
as follows: (2)
Your Pair |
You're ahead |
You're trailing |
Same Hand |
As |
99,918 % |
- |
0,081633 % |
Ks |
99,429 % |
0,48980 % |
0,081633 % |
Qs |
98,939 % |
0,97960 % |
0,081633 % |
Js |
98,449 % |
1,4694 % |
0,081633 % |
10s |
97,959 % |
1,9592 % |
0,081633 % |
9s |
97,469 % |
2,4490 % |
0,081633 % |
8s |
96,980 % |
2,9388 % |
0,081633 % |
7s |
96,490 % |
3,4286 % |
0,081633 % |
6s |
96 % |
3,9184 % |
0,081633 % |
5s |
95,510 % |
4,4082 % |
0,081633 % |
4s |
95,020 % |
4,8980 % |
0,081633 % |
| 3s |
94,531 % |
5,3878 % |
0,081633 % |
2s |
94,041 % |
5,8776 % |
0,081633 % |
If your opponent doesn’t have a pair, the probabilities
for his or her high card depend on the value of your own high
card and are distributed as follows: (3)
Your High Card |
Better High Card |
Worse High Card |
Same High Card |
A |
- |
87,771 % |
12,229 % |
K |
15,958 % |
72,853 % |
11,188 % |
Q |
30,529 % |
59,324 % |
10,147 % |
J |
43,712 % |
47,181 % |
9,1067 % |
10 |
55,507 % |
36,427 % |
8,0659 % |
9 |
65,915 % |
27,060 % |
7,0252 % |
8 |
74,935 % |
19,081 % |
5,9844 % |
7 |
82,567 % |
12,489 % |
4,9436 % |
6 |
88,812 % |
7,2853 % |
3,9029 % |
5 |
88,812 % |
3,4692 % |
2,8621 % |
4 |
97,138 % |
1,0408 % |
1,8213 % |
| 3 |
99,219 % |
- |
0,78057 % |
2 |
- |
- |
- |
The 2s is not included because it would never be possible for
the 2s to be the highest card. You can have 2 and 3 in your
hand, then 3 is the highest card. If you have 2 and 2 it will
create a pair, then see table (1) and (2).
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