Computer Simulated Roulette

I'm a programmer and I've been doing some work in analyzing streaks in random roulette data. Anyway, the companion site WizardofOdds has a one million random generated of rolls. Just for fun I ran it through my summary program and below is the stats for that data set. (You can find the data here:)

For the bottom section on the straight numbers, for example, the number 14 has at least one streak of 5 consecutive hits; all the others have have 3-4. Also, while 0 and 00 each had streaks of 3, there was a green streak of 4 consecutive. That would be most interesting at the tables!


Session information:

System tested................: ReadFile (One million spin from a Mersenne Twister)
Run Date.....................: 09-18-2014
Number of spins..............: 1,000,000
Wheel slots..................: 38


Spin results breakdown (for all sessions):

Total RED....................: 473,041
Total BLK....................: 473,725
Total Even...................: 473,392
Total Odd....................: 473,374
Total Low (1-18).............: 473,041
Total High (19-36)...........: 473,725

Total GRN....................: 53,234

Longest Streaks:
Red.......................: 20
Blk.......................: 18
Grn.......................: 4

Even......................: 20
Odd.......................: 18
Low (1-18)................: 18
High (19-36)..............: 19

Column 1 (1-34)...........: 13
Colunm 2 (2-35)...........: 12
Column 3 (3-36)...........: 14
Dozen 1 (1-12)............: 11
Dozen 2 (13-24)...........: 11
Dozen 3 (25-36)...........: 11

Straight numbers:
# # Spun LgStreak
0: 26,403 3
00: 26,831 3
1: 26,301 4
2: 26,477 3
3: 26,355 5
4: 26,256 3
5: 26,290 3
6: 26,281 3
7: 26,302 4
8: 26,124 4
9: 26,124 3
10: 26,485 3
11: 26,285 3
12: 26,126 4
13: 25,898 3
14: 26,335 5
15: 26,491 3
16: 26,234 4
17: 26,433 3
18: 26,244 3
19: 26,167 4
20: 26,376 3
21: 26,334 4
22: 26,477 3
23: 26,386 3
24: 26,100 3
25: 26,180 3
26: 26,418 3
27: 26,468 3
28: 26,264 4
29: 26,280 4
30: 26,090 3
31: 26,289 3
32: 26,328 3
33: 26,373 3
34: 26,427 4
35: 26,418 3
36: 26,350 3

Quote: wicklunda

I'm a programmer and I've been doing some work in analyzing streaks in random roulette data. Anyway, the companion site WizardofOdds has a one million random generated of rolls. Just for fun I ran it through my summary program and below is the stats for that data set. (You can find the data here: https://wizardofodds.com/games/roulette/simulation/ )

For the bottom section on the straight numbers, for example, the number 14 has at least one streak of 5 consecutive hits; all the others have have 3-4. Also, while 0 and 00 each had streaks of 3, there was a green streak of 4 consecutive. That would be most interesting at the tables!


Session information:

System tested................: ReadFile (One million spin from a Mersenne Twister)
Run Date.....................: 09-18-2014
Number of spins..............: 1,000,000
Wheel slots..................: 38


Spin results breakdown (for all sessions):

Total RED....................: 473,041
Total BLK....................: 473,725
Total Even...................: 473,392
Total Odd....................: 473,374
Total Low (1-18).............: 473,041
Total High (19-36)...........: 473,725

Total GRN....................: 53,234

Longest Streaks:
Red.......................: 20
Blk.......................: 18
Grn.......................: 4

Even......................: 20
Odd.......................: 18
Low (1-18)................: 18
High (19-36)..............: 19

Column 1 (1-34)...........: 13
Colunm 2 (2-35)...........: 12
Column 3 (3-36)...........: 14
Dozen 1 (1-12)............: 11
Dozen 2 (13-24)...........: 11
Dozen 3 (25-36)...........: 11

Straight numbers:
# # Spun LgStreak
0: 26,403 3
00: 26,831 3
1: 26,301 4
2: 26,477 3
3: 26,355 5
4: 26,256 3
5: 26,290 3
6: 26,281 3
7: 26,302 4
8: 26,124 4
9: 26,124 3
10: 26,485 3
11: 26,285 3
12: 26,126 4
13: 25,898 3
14: 26,335 5
15: 26,491 3
16: 26,234 4
17: 26,433 3
18: 26,244 3
19: 26,167 4
20: 26,376 3
21: 26,334 4
22: 26,477 3
23: 26,386 3
24: 26,100 3
25: 26,180 3
26: 26,418 3
27: 26,468 3
28: 26,264 4
29: 26,280 4
30: 26,090 3
31: 26,289 3
32: 26,328 3
33: 26,373 3
34: 26,427 4
35: 26,418 3
36: 26,350 3

What no 30 losses in a row? Marty here I come, I only need about 2 million to make $10

You didn't notice that the number 3 is a 5-peat as well.

Aren't the odds of a single number occurring 5 times in a row significantly greater than a million to one? It happened twice in this sim, once to the 3 and also to the 14.

Also, see a lot of 4-peats. I can only think of one time I've ever seen that at the table.

You are right I didn't catch that on the 3. if you do a search of the page "14,14,14,14,14" you will find the spot; but if you search for "3,3,3,3,3" it won't hit. That's because a "3,3,3,3" appears at the end of a line, and the final "3" at the beginning of the next one. Good catch!

As for the odds of two numbers repeating five times, you are right the odds are against it, but on any given run it is certainly possible. I have had two numbers repeat five times in runs as low as 100,000; and many runs of a million that had none. By 10 million runs I usually get about 6 numbers repeating 5 times. If I run 10 sets of 1 billion runs, I will normally get 2 that have a number repeat 7 times, and for red or black, 29 repeats is the most I've ever gotten.

Wicklunda,

Excellent post. Thanks for showing your work. I do have a question did you by any chance chart single events vs. runs of 2 or more just on red/black. The reason I ask, my friend seems to think that runs/streaks of red and black outnumber single events in roulette.

Example:

Red

Black

Red

All three spins above would be consider single events.

________________________________________________________

Example:

Red

Red

Red

Red

Red

The above run/streak is considered a run of 2 or more.

_________________________________________________________

If you did chart the above streaks/runs of red and black vs. single of events. Could you please share your data with me.


Thanks!

Quote: darkoz

You didn't notice that the number 3 is a 5-peat as well.

Aren't the odds of a single number occurring 5 times in a row significantly greater than a million to one? It happened twice in this sim, once to the 3 and also to the 14.

Also, see a lot of 4-peats. I can only think of one time I've ever seen that at the table.

Here's what you have to look at:

The probability of a specific number five-peating is: (1/38)^5 = 1.26206585e-8

However, there are 38 numbers, so the probability of any non-specified number repeating is 1.26206585e-8 * 38 = 4.79585023e-7

While this may still seem ridiculously unlikely, there are 999,996 opportunities for this to happen within 1,000,000 spins. (It can't start with the 999,997 spin because there wouldn't be enough spins left).

The probability of this NOT happening, at least once, in 999996 attempts is: (1-4.79585023e-7)^999996 = 0.61904134229

Which means that, in one million spins, there is only a 61.904134229% probability that you will not see a five-peat at least once.

Yes like this post most interesting..... Was at a indian casino wheel when 1 came up 4 times in a row it scared me right up out of my seat......

Thanks again