Math - Statistical
Averages
To make things simple, all odds and statistics are based upon an American style Roulette
Wheel. I.E. A 38 position Double Zero wheel.
Most people will say that the odds of seeing two identical outcomes in a row is 1 in 1,444
(38*38). However, that's the odds of predicting the outcome of the next two spins.
For this Hit It Again bet, it doesn't matter what the current outcome is, only that the next
outcome is the same as the current outcome. As such, to get to the first payout level, only the
next outcome matters, therefore the odds of at least a single repeat, is 1 in 38.
With that in mind, the following are the odds that any of up to four repeated outcomes in a
row will occur. The 'Unique Spins' column shows the number of unique outcomes in 1, 2, 3, and 4 spins
following the current spin. The '4 Spin Wins' column shows the number of expected wins at that level
in all combinations of 4 spins. Note that the first three levels shows the probability and odds of
achieving only that level, without another repeat to get to the next level. The 'Unique Spins'
column is also the 1:X odds of achieving at least that level.
In all the math on this website, a maximum of 4 repeats is used, but casinos have the option to
set the maximum at more or less than 4 repeats.
Repeats |
Unique Spins |
4 Spin Wins |
Probability |
Odds - 1:X |
1 |
38 |
53,428 |
0.02562327 |
39.03 |
2 |
1,444 |
1,406 |
0.00067430 |
1,483.03 |
3 |
54,872 |
37 |
0.00001774 |
56,355.03 |
4 |
2,085,136 |
1 |
0.00000048 |
2,085,136.00 |
Only initial repeats matter. I.E. If the first spin is a repeat of the prior spin, and the second
spin is not a repeat, it doesn't matter if the third spin repeats either previous spin. Since the second
spin was not a repeat, new bets are accepted and the third spin is actually the first spin of the next
series. Therefore, the odds of winning anything, is the same as Roulette's regular single number odds:
1:38. Similarly, once any number of repeats is achieved, the odds of getting at least one more repeat,
remains at 1:38.
Probability for Total Spins
For every man that ever saw a history display at the roulette table and said, "Look honey,
eight reds in a row. Let's bet on black," you can find a man that, a few moments prior, said,
"Look honey, seven reds in a row. Let's bet on black." Not as often, but you can sometimes find
a man who says, "Look honey, eight reds in a row. It's HOT! Let's bet on red!"
Statistics will tell you that, discounting the possibility of a zero or double zero, in
ten spins, you should get five red and five black. However, probability tells you that the chance of
getting 5 and 5 is actually rather low. With a bigger sample, the results will be closer to 50/50.
But the chance of getting exactly 50/50 is still rather low.
The chart above discusses the statistical averages. Statistically, four repeats,
for a Level 4 win, will occur on average, every 2,085,136 times. However, the probability that
a Level 4 win will occur within the 2,085,136 trials, is only 63.2%.
Level 1 |
Level 2 |
Level 3 |
Level 4 |
Spins |
Probability |
Spins |
Probability |
Spins |
Probability |
Spins |
Probability |
1 |
2.6316% |
1 |
0.0693% |
1 |
0.0018% |
1 |
0.000047959% |
2 |
5.1939% |
10 |
0.6904% |
100 |
0.1821% |
100 |
0.0047957% |
3 |
7.6888% |
20 |
1.3760% |
200 |
0.3638% |
200 |
0.009591% |
4 |
10.1180% |
30 |
2.0568% |
300 |
0.5452% |
300 |
0.0144% |
5 |
12.4834% |
40 |
2.7330% |
400 |
0.7263% |
400 |
0.0192% |
6 |
14.7864% |
50 |
3.4045% |
500 |
0.9071% |
500 |
0.0240% |
7 |
17.0289% |
75 |
5.0630% |
750 |
1.3575% |
750 |
0.0360% |
8 |
19.2123% |
100 |
6.6931% |
1,000 |
1.8059% |
1,000 |
0.0479% |
9 |
21.3383% |
125 |
8.2952% |
1,250 |
2.2523% |
1,250 |
0.0599% |
10 |
23.4084% |
150 |
9.8697% |
1,500 |
2.6966% |
1,500 |
0.0719% |
12 |
27.3865% |
200 |
12.9382% |
2,000 |
3.5793% |
2,000 |
0.0959% |
14 |
31.1580% |
250 |
15.9022% |
2,500 |
4.4539% |
2,500 |
0.1198% |
16 |
34.7335% |
300 |
18.7653% |
3,000 |
5.3205% |
3,000 |
0.1438% |
18 |
38.1234% |
350 |
21.5310% |
3,500 |
6.1794% |
3,500 |
0.1677% |
20 |
41.3372% |
400 |
24.2025% |
4,000 |
7.0304% |
4,000 |
0.1917% |
22 |
44.3841% |
500 |
29.2757% |
5,000 |
8.7094% |
5,000 |
0.2395% |
24 |
47.2728% |
600 |
34.0093% |
6,000 |
10.3580% |
6,000 |
0.2873% |
25 |
48.6603% |
700 |
38.4261% |
7,000 |
11.9769% |
7,000 |
0.3351% |
26 |
50.0114% |
800 |
42.5473% |
8,000 |
13.5665% |
8,000 |
0.3829% |
27 |
51.3269% |
900 |
46.3927% |
9,000 |
15.1275% |
9,000 |
0.4307% |
28 |
52.6077% |
1,000 |
49.9807% |
10,000 |
16.6602% |
10,000 |
0.4784% |
29 |
53.8549% |
1,250 |
57.9349% |
12,500 |
20.3720% |
12,500 |
0.5977% |
30 |
55.0692% |
1,444 |
63.2248% |
15,000 |
23.9186% |
15,000 |
0.7168% |
32 |
57.4029% |
1,750 |
70.2497% |
17,500 |
27.3071% |
17,500 |
0.8358% |
34 |
59.6153% |
2,000 |
74.9807% |
20,000 |
30.5448% |
20,000 |
0.9546% |
36 |
61.7129% |
2,500 |
82.3052% |
25,000 |
36.5939% |
25,000 |
1.1918% |
38 |
63.7015% |
3,000 |
87.4855% |
30,000 |
42.1162% |
30,000 |
1.4285% |
40 |
65.5868% |
3,500 |
91.1492% |
35,000 |
47.1575% |
35,000 |
1.6645% |
42 |
67.3742% |
4,000 |
93.7403% |
40,000 |
51.7597% |
40,000 |
1.9001% |
44 |
69.0687% |
5,000 |
96.8690% |
50,000 |
59.7966% |
50,000 |
2.3694% |
46 |
70.6753% |
6,000 |
98.4339% |
54,872 |
63.2124% |
60,000 |
2.8365% |
48 |
72.1984% |
7,000 |
99.2166% |
70,000 |
72.0767% |
70,000 |
3.3014% |
50 |
73.6424% |
8,000 |
99.6082% |
80,000 |
76.7288% |
80,000 |
3.7640% |
55 |
76.9327% |
9,000 |
99.8040% |
90,000 |
80.6058% |
90,000 |
4.2244% |
60 |
79.8123% |
10,000 |
99.9020% |
100,000 |
83.8369% |
100,000 |
4.6827% |
65 |
82.3324% |
12,500 |
99.9827% |
125,000 |
89.7516% |
125,000 |
5.8187% |
70 |
84.5379% |
15,000 |
99.9969% |
150,000 |
93.5019% |
150,000 |
6.9411% |
75 |
86.4681% |
17,500 |
99.9995% |
175,000 |
95.8798% |
175,000 |
8.0502% |
80 |
88.1573% |
20,000 |
99.9999% |
200,000 |
97.3875% |
200,000 |
9.1461% |
90 |
90.9295% |
25,000 |
100.0000% |
250,000 |
98.9497% |
250,000 |
11.2988% |
100 |
93.0528% |
30,000 |
100.0000% |
300,000 |
99.5777% |
300,000 |
13.4004% |
110 |
94.6790% |
35,000 |
100.0000% |
350,000 |
99.8302% |
350,000 |
15.4523% |
120 |
95.9246% |
40,000 |
100.0000% |
400,000 |
99.9318% |
400,000 |
17.4556% |
130 |
96.8785% |
45,000 |
100.0000% |
450,000 |
99.9726% |
450,000 |
19.4114% |
140 |
97.6092% |
50,000 |
100.0000% |
500,000 |
99.9890% |
500,000 |
21.3209% |
160 |
98.5975% |
75,000 |
100.0000% |
750,000 |
99.9999% |
750,000 |
30.2107% |
180 |
99.1773% |
100,000 |
100.0000% |
1,000,000 |
100.0000% |
1,000,000 |
38.0960% |
200 |
99.5174% |
125,000 |
100.0000% |
1,250,000 |
100.0000% |
1,250,000 |
45.0904% |
220 |
99.7169% |
150,000 |
100.0000% |
1,500,000 |
100.0000% |
1,500,000 |
51.2945% |
240 |
99.8339% |
175,000 |
100.0000% |
1,750,000 |
100.0000% |
1,750,000 |
56.7976% |
260 |
99.9026% |
200,000 |
100.0000% |
2,000,000 |
100.0000% |
2,085,136 |
63.2121% |
280 |
99.9428% |
250,000 |
100.0000% |
2,500,000 |
100.0000% |
2,500,000 |
69.8493% |
300 |
99.9665% |
300,000 |
100.0000% |
3,000,000 |
100.0000% |
3,000,000 |
76.2777% |
325 |
99.9828% |
350,000 |
100.0000% |
3,500,000 |
100.0000% |
3,500,000 |
81.3355% |
350 |
99.9912% |
400,000 |
100.0000% |
4,000,000 |
100.0000% |
4,000,000 |
85.3150% |
375 |
99.9955% |
500,000 |
100.0000% |
5,000,000 |
100.0000% |
5,000,000 |
90.9094% |
400 |
99.9977% |
600,000 |
100.0000% |
6,000,000 |
100.0000% |
6,000,000 |
94.3725% |
450 |
99.9994% |
700,000 |
100.0000% |
7,000,000 |
100.0000% |
7,000,000 |
96.5164% |
500 |
99.9998% |
800,000 |
100.0000% |
8,000,000 |
100.0000% |
8,000,000 |
97.8435% |
550 |
100.0000% |
900,000 |
100.0000% |
9,000,000 |
100.0000% |
9,000,000 |
98.6650% |
600 |
100.0000% |
1,000,000 |
100.0000% |
10,000,000 |
100.0000% |
10,000,000 |
99.1736% |
The formula for the above chart is: Probability = 1 - ( ( 1 - ( 1 / 38 ^ Level ) ) ^ spins )
The values in blue are the point where statistics dictates that, on average, the event will occur.
Probability says that only about a 63% of the time will it occur by that time.
The values in green are the point where probability says that only about 50% of the time
the event will have occurred.
The values in black are 100% due to a rounding error. It is impossible to guarantee that the
event will occur at any point.
Probability - Spins Required
The following chart shows the same info, but from the other direction. It shows the number of
spins required for the chance the Level will be achieved at least as the probability show.
For reference, the 50% and 62.3% rows are colored green and blue as above. Additional significant
rows are in yellow.
Probability |
Spins |
Level 1 |
Level 2 |
Level 3 |
Level 4 |
1.0% |
0.38 |
14.51 |
551.48 |
20,956.31 |
5.0% |
1.92 |
74.04 |
2,814.54 |
106,953.47 |
10.0% |
3.95 |
152.09 |
5,781.29 |
219,690.95 |
15.0% |
6.09 |
234.60 |
8,917.66 |
338,873.99 |
20.0% |
8.37 |
322.11 |
12,244.22 |
465,284.54 |
25.0% |
10.79 |
415.27 |
15,785.55 |
599,856.10 |
30.0% |
13.37 |
514.86 |
19,571.29 |
743,715.59 |
33.3% |
15.19 |
584.57 |
22,221.05 |
844,407.38 |
35.0% |
16.15 |
621.84 |
23,637.70 |
898,240.75 |
40.0% |
19.15 |
737.38 |
28,029.77 |
1,065,140.64 |
45.0% |
22.42 |
862.98 |
32,804.21 |
1,246,571.15 |
50.0% |
25.99 |
1,000.56 |
38,034.03 |
1,445,305.79 |
60.0% |
34.36 |
1,322.67 |
50,278.25 |
1,910,590.33 |
63.2% |
37.49 |
1,443.03 |
54,853.52 |
2,084,452.29 |
65.0% |
39.37 |
1,515.42 |
57,605.31 |
2,189,021.38 |
66.6% |
41.12 |
1,582.96 |
60,172.87 |
2,286,589.38 |
70.0% |
45.15 |
1,737.93 |
66,063.79 |
2,510,446.44 |
75.0% |
51.98 |
2,001.12 |
76,068.05 |
2,890,611.59 |
80.0% |
60.35 |
2,323.22 |
88,312.27 |
3,355,896.13 |
80.5% |
71.14 |
2,738.49 |
104,097.82 |
3,955,752.23 |
90.0% |
86.34 |
3,323.78 |
126,346.30 |
4,801,201.92 |
95.0% |
112.33 |
4,324.34 |
164,380.32 |
6,246,507.71 |
98.0% |
146.69 |
5,647.00 |
214,658.57 |
8,157,098.05 |
99.0% |
172.68 |
6,647.56 |
252,692.60 |
9,602,403.84 |
99.9% |
259.03 |
9,971.34 |
379,038.60 |
14,403,605.76 |
The formula for the above chart is: Spins = LOG ( 1 - ( Probability ) ) / LOG ( 1 - ( 1 / 38 ^ Level ) )
Download the Excel
document containing the charts above, as well as the charts on the Standard Payout and Progressive
Payout pages.
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