Actually...

I agree. Sometimes the generators are just too damn random -- even displaying bias amongst themselves

And you are correct in that regard - each wheel is almost certainly flawed, and the results are not truly random. But you're missing my point which is that you can't tell that from the data you're given!

The fact that 20,000 random spins generates the same spikes and dips as this alleged biased wheel means that even if the biased wheel is biased, you can't say that for sure. The signal doesn't break free of the noise at 20,000 spins. By 100,000 it looks pretty good, though:

10,000 spins, random:
http://img9.imageshack.us/img9/2443/45823529.png

100,000 spins, random:
http://img96.imageshack.us/img96/9316/90483961.png

10,000 spins, 38 (37 = 0, 38 = 00 for the nits) biased 10%:
http://img191.imageshack.us/img191/1022/15786005.png

100,000 spins, 38 biased 10%:
http://img84.imageshack.us/img84/2006/25022377.png

The more data you gather, the flatter the left section is and the sharper the rise to the right appears to be. The smaller the bias, the larger of a sample size you will need to be able to detect it.

Let's say one number had a 10% bias. You'd be looking at a 2.9% chance for that to hit vs 2.6% chance for the other numbers. If you're looking for the standard deviation of that biased number to be 10% of the difference in counts between biased and unbiased, you'd want:


sqrt(0.029n) / (0.029n - 0.026n) = 0.1
n = 322k spins

So....the postive here would be that if one discovered a bias the casino, using above methodology, would not discover the bias for over a year?

The piont Im making is that a computer can produce a ramdom sequence of numbers. A physical wheel mad of wood metal and other earthly materials can't.

So the question I'm asking is how large a bias is there, can the bias be discovered with a reasonable amount of effort, and if discovered can it be exploited for profit without an insane amount of varaince.

Wow, it's not often that someone says the *opposite* of the truth, instead of just being wrong.

What do you mean?

"If I somehow magically knew there was a bias in the wheel, the casino wouldn't be able to detect the same bias for another year?" (correct)

"If I mathematically figured out the bias in the wheel, the casino wouldn't have been doing the same thing and would only start looking after they knew I knew?" (incorrect)

The casino (a) gathers more information than you're capable of gathering, so from a mathematical standpoint the casino will know before you know, and (b) doesn't need to mathematically detect a bias when they see you winning way too much money to be just lucky. If you start winning thousands of dollars a day, they don't really care how you're doing it, they'll just switch the wheel / switch the dealers / shut down the table until you stop. The casino is a business, not an educational center.

Some of the best lessons I ever learned in life came from a casino.

FYP

Never married, eh?

I think what's missing here that someone pointed out a little earlier is that there are lots of things happening in the pit during the day to day action that is going to influence the wheel. Examples like people bumping into the table, wheel being moved around slightly, maintenance, etc.

You won't be able to get enough spins in even if you have a slight edge without something changing.

Thanks for the correction and the extra info. I wonder why they changed the title. Probably sales-pitch related. I actuall prefer The Eudaemonic Pie.

It must have been so exciting to be involved in a scheme like that.

Ok I know this is pretty much a pipe dream but if anyone is interested, if for no other reason then following an insane person waist some time, I started collecting data on a wheel.

First obseveraions I made. The wheel has a pretty good nick on the rim of the bowl it is 100 degrees to the right of the label. This doesnt effect ball roll at all but will allow me to identify the wheel to make sure I am collecting data on the same wheel. Also the thing is filthy. I mean this thing is covered in dirt and dust. It looks as if it has never been cleaned. There is noticable build up of loose lint type material in some of the pockets. Im not sure if this is a good thing or a bad thing.

I collected data on 145 spins over the course of about 7 hours. I played poker and when ever I took a smoke break I just walked by the wheel and recorded a voice memo. When I got home I transferd the numbers into excel. Just for kicks I hoped on you tube and figured out to chart a histogram and frequency chart. I dont think 145 spins can give me any relaible data just though I would learn something new.
Im gonna stay here for 2 weeks I think and Im going to try to get 200 spins per day so I shoud have 2800 data points to make a graph with just to see what it looks like.

If nothing else, it's cheap entertainment.

After 130 spins
30 9
19 8
24 7
15 6
1 5
3 5
7 5
35 5
6 4
9 4
13 4
16 4
17 4
21 4
23 4
34 4
36 4
2 3
4 3
5 3
10 3
12 3
18 3
20 3
26 3
31 3
38 3
11 2
14 2
27 2
29 2
33 2
22 1
25 1
28 1
37 1
8 0
32 0

After 330 spins
Bin Frequency
23 22
16 15
7 14
10 13
15 13
21 13
3 12
5 12
6 12
14 12
17 12
24 12
30 12
9 11
11 11
19 11
34 11
31 10
1 9
2 9
13 8
20 8
22 8
4 7
18 7
26 7
29 7
35 7
36 7
38 7
28 6
33 6
12 5
25 5
27 5
32 5
37 5
8 4

after 469 spins
Bin Frequency Sorry for the crude format.
23 24
14 19
6 18
2 16
10 16
16 16
24 16
5 15
7 14
15 14
17 14
19 14
21 14
30 14
9 13
11 13
31 13
34 13
1 12
3 12
13 12
18 12
20 12
22 12
35 12
28 11
29 11
4 9
8 9
36 9
38 9
12 8
26 8
33 8
25 7
32 7
37 7
Sorry for the crude format. Not sure how else to transfer the data. I just copied and pasted from excel. 37=0 38=00

This could be interesting. Is it an automatic wheel?

No
This the next 289 spins independt of the first of the 489.
Bin Frequency
22 13
32 12
13 12
35 11
31 11
26 11
1 11
36 10
5 10
2 10
33 9
30 8
27 8
25 8
21 8
19 8
15 8
14 8
34 7
20 7
11 7
9 7
6 7
3 7
37 6
28 6
18 6
17 6
10 6
7 6
24 5
8 5
4 5
38 4
29 4
23 4
16 4
12 4
More 0
Can you see the pattern?

lol

Playing the wheel sections 2-14-23-35 and 5-22-17-34 over a total of 919 spins show a 16.52% edge. The test will be the next 1000 spins.

Calipyan you're really good at math. How likely is it that all the numbers in these sections come out at better than 36-1(36-1 is break even)? And if the next 1000 spins show a similar advantage what are the odds of that?

You're trying to spoil a perfectly rational disbelief in randomness -- how dare you!

Im think im testing my sanity. Which is not random.