ProbabilitiesProbabilities
in PokerBelow are the number of ways to draw each hand
and the probability of drawing for the first draw in five-card
draw and in seven-card stud.
Another good source of Gambling Odds, Gambling
Probabilities and Top Casino Guide is the House of Odds.
|
Five Card Stud
|
|
Hand |
Combinations |
Probability |
|
Royal flush
|
4 |
0.00000154 |
|
Straight flush
|
36 |
0.00001385 |
|
Four of a kind
|
624 |
0.00024010 |
|
Full house
|
3,744 |
0.00144058 |
|
Flush
|
5,108 |
0.00196540 |
|
Straight
|
10,200 |
0.00392465 |
|
Three of a kind
|
54,912 |
0.02112845 |
|
Two pair
|
123,552 |
0.04753902 |
|
Pair |
1,098,240 |
0.42256903 |
|
Nothing
|
1,302,540 |
0.501177394
|
|
Seven Card Stud
|
|
Hand |
Combinations |
Probability |
|
Royal flush
|
4,324 |
0.00003232 |
|
Straight flush
|
37,260 |
0.00027851 |
|
Four of a kind
|
224,848 |
0.00168067 |
|
Full house
|
3,473,184 |
0.02596102 |
|
Flush
|
4,047,644 |
0.03025494 |
|
Straight
|
6,180,020 |
0.04619382 |
|
Three of a kind
|
6,461,620 |
0.04829870 |
|
Two pair
|
31,433,400 |
0.23495536 |
|
Pair |
58,627,800 |
0.43822546 |
|
Ace high or less
|
23,294,460 |
0.17411920 |
|
Total
|
133,784,560 |
1.00000000
|
Derivations for Five Card Draw
|
Five Card Draw High Card Hands
|
|
Hand |
Combinations |
Probability |
|
Ace high
|
502,860 |
0.19341583 |
|
King high
|
335,580 |
0.12912088 |
|
Queen high
|
213,180 |
0.08202512 |
|
Jack high
|
127,500 |
0.04905808 |
|
10 high
|
70,380 |
0.02708006 |
|
9 high
|
34,680 |
0.01334380 |
|
8 high
|
14,280 |
0.00549451 |
|
7 high
|
4,080 |
0.00156986 |
|
Total
|
1,302,540 |
0.501177394
|
Probabilities in Bingo
The following table shows the probability of
forming a bingo, black out, or four corners within a specified
number of calls. For example the probability of a single player
forming a bingo within 25 calls is 0.06396106, or about 6.4%.
|
Probabilities in Bingo
|
|
Number
of Calls |
Bingo |
Black Out |
Four Corners |
X |
|
1 |
0.00000000 |
0.00000000 |
0.00000000 |
0.00000000 |
|
2 |
0.00000000 |
0.00000000 |
0.00000000 |
0.00000000 |
|
3 |
0.00000000 |
0.00000000 |
0.00000000 |
0.00000000 |
|
4 |
0.00000329 |
0.00000000 |
0.00000082 |
0.00000000 |
|
5 |
0.00001692 |
0.00000000 |
0.00000411 |
0.00000000 |
|
6 |
0.00005215 |
0.00000000 |
0.00001234 |
0.00000000 |
|
7 |
0.00012492 |
0.00000000 |
0.00002880 |
0.00000000 |
|
8 |
0.00025632 |
0.00000000 |
0.00005759 |
0.00000000 |
|
9 |
0.00047305 |
0.00000000 |
0.00010367 |
0.00000000 |
|
10 |
0.00080783 |
0.00000000 |
0.00017278 |
0.00000000 |
|
11 |
0.00129986 |
0.00000000 |
0.00027150 |
0.00000001 |
|
12 |
0.00199521 |
0.00000000 |
0.00040726 |
0.00000003 |
|
13 |
0.00294715 |
0.00000000 |
0.00058826 |
0.00000008 |
|
14 |
0.00421648 |
0.00000000 |
0.00082356 |
0.00000018 |
|
15 |
0.00587167 |
0.00000000 |
0.00112304 |
0.00000038 |
|
16 |
0.00798905 |
0.00000000 |
0.00149739 |
0.00000076 |
|
17 |
0.01065272 |
0.00000000 |
0.00195812 |
0.00000144 |
|
18 |
0.01395440 |
0.00000000 |
0.00251759 |
0.00000259 |
|
19 |
0.01799309 |
0.00000000 |
0.00318894 |
0.00000448 |
|
20 |
0.02287445 |
0.00000000 |
0.00398618 |
0.00000747 |
|
21 |
0.02871003 |
0.00000000 |
0.00492410 |
0.00001206 |
|
22 |
0.03561614 |
0.00000000 |
0.00601835 |
0.00001895 |
|
23 |
0.04371249 |
0.00000000 |
0.00728537 |
0.00002906 |
|
24 |
0.05312045 |
0.00000000 |
0.00874244 |
0.00004359 |
|
25 |
0.06396106 |
0.00000000 |
0.01040767 |
0.00006411 |
|
26 |
0.07635261 |
0.00000000 |
0.01229997 |
0.00009260 |
|
27 |
0.09040799 |
0.00000000 |
0.01443910 |
0.00013159 |
|
28 |
0.10623163 |
0.00000000 |
0.01684561 |
0.00018423 |
|
29 |
0.12391628 |
0.00000000 |
0.01954091 |
0.00025441 |
|
30 |
0.14353947 |
0.00000000 |
0.02254720 |
0.00034692 |
|
31 |
0.16515993 |
0.00000000 |
0.02588753 |
0.00046759 |
|
32 |
0.18881391 |
0.00000000 |
0.02958575 |
0.00062345 |
|
33 |
0.21451154 |
0.00000000 |
0.03366654 |
0.00082296 |
|
34 |
0.24223348 |
0.00000000 |
0.03815542 |
0.00107617 |
|
35 |
0.27192783 |
0.00000000 |
0.04307870 |
0.00139504 |
|
36 |
0.30350759 |
0.00000000 |
0.04846353 |
0.00179362 |
|
37 |
0.33684876 |
0.00000000 |
0.05433790 |
0.00228842 |
|
38 |
0.37178933 |
0.00000000 |
0.06073059 |
0.00289866 |
|
39 |
0.40812916 |
0.00000000 |
0.06767123 |
0.00364670 |
|
40 |
0.44563111 |
0.00000000 |
0.07519026 |
0.00455838 |
|
41 |
0.48402328 |
0.00000001 |
0.08331894 |
0.00566344 |
|
42 |
0.52300269 |
0.00000001 |
0.09208935 |
0.00699602 |
|
43 |
0.56224021 |
0.00000003 |
0.10153441 |
0.00859511 |
|
44 |
0.60138685 |
0.00000007 |
0.11168785 |
0.01050513 |
|
45 |
0.64008123 |
0.00000015 |
0.12258423 |
0.01277651 |
|
46 |
0.67795818 |
0.00000031 |
0.13425892 |
0.01546630 |
|
47 |
0.71465810 |
0.00000063 |
0.14674812 |
0.01863888 |
|
48 |
0.74983686 |
0.00000125 |
0.16008886 |
0.02236665 |
|
49 |
0.78317588 |
0.00000245 |
0.17431898 |
0.02673088 |
|
50 |
0.81439191 |
0.00000472 |
0.18947715 |
0.03182247 |
|
51 |
0.84324614 |
0.00000891 |
0.20560286 |
0.03774293 |
|
52 |
0.86955207 |
0.00001654 |
0.22273644 |
0.04460528 |
|
53 |
0.89318170 |
0.00003023 |
0.24091900 |
0.05253511 |
|
54 |
0.91406974 |
0.00005441 |
0.26019252 |
0.06167165 |
|
55 |
0.93221528 |
0.00009654 |
0.28059978 |
0.07216896 |
|
56 |
0.94768080 |
0.00016894 |
0.30218438 |
0.08419712 |
|
57 |
0.96058846 |
0.00029180 |
0.32499074 |
0.09794358 |
|
58 |
0.97111353 |
0.00049778 |
0.34906413 |
0.11361456 |
|
59 |
0.97947539 |
0.00083912 |
0.37445061 |
0.13143645 |
|
60 |
0.98592639 |
0.00139853 |
0.40119709 |
0.15165744 |
|
61 |
0.99073928 |
0.00230569 |
0.42935127 |
0.17454913 |
|
62 |
0.99419379 |
0.00376192 |
0.45896170 |
0.20040826 |
|
63 |
0.99656346 |
0.00607694 |
0.49007775 |
0.22955855 |
|
64 |
0.99810354 |
0.00972311 |
0.52274960 |
0.26235263 |
|
65 |
0.99904080 |
0.01541468 |
0.55702826 |
0.29917406 |
|
66 |
0.99956626 |
0.02422308 |
0.59296557 |
0.34043944 |
|
67 |
0.99983122 |
0.03774293 |
0.63061418 |
0.38660072 |
|
68 |
0.99994699 |
0.05832999 |
0.67002756 |
0.43814749 |
|
69 |
0.99998812 |
0.08943931 |
0.71126003 |
0.49560945 |
|
70 |
0.99999861 |
0.13610330 |
0.75436670 |
0.55955906 |
|
71 |
1.00000000 |
| |
