TurboGenius When does it lose ?

Here is the video if anyone is interested...

 

Hey, if you listen to the first sentence in the video from Dr Hume, I think he is a distant relative of Benas

 

If you want to do this at home in excel the formula to use is the BINOM.INV and it provides the critical values to determine if the spin count for a number is over or under what is expected by random (using a 95% confidence interval):

Maximum threshold:

Code:

=BINOM.INV(trials,1/37,0.975)

Minimum threshold:

Code:

=BINOM.INV(trials,1/37,0.025)

Where trials is the total number of spins you want to test against. It was pretty simple to make a reference card for bias detection so I have attached one.

 

Your question was : "How many probability distributions do you think the wheel has?" implying that there is only one, namely the Binomial.

You could argue that the discrete uniform is even more fundamental because in roulette there are 37 possible outcomes all equally likely, and this is a more basic description of roulette than that which the Binomial gives, which is concerned with the number of failures and successes in a fixed number of trials. But aside from that, the probability distribution you choose depends on what you want to know, that's all. For example, if you want to know how the Law of the Third works, the Binomial won't help you, and neither will it help if you want to know the chances of exactly 2 hits for Dozen 1, 4 hits for Dozen 2, and 4 hits for Dozen 3 in 10 spins. And suppose you want to know the probability that it takes between 20 and 30 spins before a certain street hits 3 times? The Binomial can't be used because it needs a fixed number of trials.

There are many other examples I could have used but I think you get the point. You answer to all probability questions seems to revolve around the Binomial. But that's a very limiting perspective.

 

Nice.
I saved it to my hard drive a long time ago. It was important enough to save it.

 

They have to be related lol

 

Twoup,

Before tracking a single spin, we knew that the wheel was biased, why it was biased, and where most of the biased numbers were. We did not use the chi square to determine a yes or no if the wheel was biased, but more as one of the indicators to determine just how biased it was. Determining the standard deviation of each number hit was also important.

The reason so many numbers are collected is because once we find the wheel we want to monitor it through periodic cleanings/maintenance. That why we have so many spins on some wheels.

By the way, the wheel is a double zero wheel.

 

--- Actual #'s hit ---
Count
# entered Other data Total Ratio St. dev.
37 416 0 416 42.26 -2.20
27 456 0 456 38.55 -0.31
10 445 0 445 39.51 -0.83
25 453 0 453 38.81 -0.45
29 444 0 444 39.59 -0.88
12 471 0 471 37.32 0.39
8 481 0 481 36.55 0.87
19 438 0 438 40.14 -1.16
31 458 0 458 38.38 -0.22
18 437 0 437 40.23 -1.21
6 444 0 444 39.59 -0.88
21 413 0 413 42.57 -2.34
33 470 0 470 37.40 0.35
16 448 0 448 39.24 -0.69
4 467 0 467 37.64 0.21
23 496 0 496 35.44 1.57
35 462 0 462 38.05 -0.03
14 442 0 442 39.77 -0.97
2 441 0 441 39.86 -1.02
0 457 0 457 38.47 -0.27
28 439 0 439 40.05 -1.11
9 478 0 478 36.78 0.72
26 433 0 433 40.60 -1.40
30 442 0 442 39.77 -0.97
11 451 0 451 38.98 -0.55
7 565 0 565 31.12 4.82
20 464 0 464 37.89 0.06
32 478 0 478 36.78 0.72
17 446 0 446 39.42 -0.78
5 517 0 517 34.00 2.56
22 483 0 483 36.40 0.96
34 504 0 504 34.88 1.95
15 468 0 468 37.56 0.25
3 412 0 412 42.67 -2.39
24 388 0 388 45.31 -3.52
36 444 0 444 39.59 -0.88
13 622 0 622 28.26 7.51
1 507 0 507 34.67 2.09

Total 17,580 0 17,580

High 622 0 622 7.51
Low 388 0 388 -3.52

Chance of
random (1/x) 7.723E+12 7.723E+12
Chi square 138.31 138.31

Average 462.63 0.00 462.63
Break even 488.33 0.00 488.33

80% hi conf. 515.69 0.00 515.69
95% hi conf. 526.30 0.00 526.30
80% low conf. 409.57 0.00 409.57
95% low conf. 398.96 0.00 398.96

Best ratio 28.26 28.26
Worst ratio 45.31 45.31

 

Dr the dreamer

 

@regular, remind me again .. how did you pass you math test ..
copying neighbours results? someone took the exam for you? you had a sudden moment of brightness that has long gone vanished?

 

A very straight forward and conclusive post by Dr. Sir A A .

Greatly appreciated .


ND

 

With this you simply show your not understanding...

 

The distribution calculation won't provide the spins required to meet a desired number of hits with a specified confidence, but than can be easily performed using the probability directly.

I have written about how the normal distribution can provide answers more readily for certain cases such as ranges and situations that are impractical with the discrete distribution when the number of trials gets large due to the factorial.

Most of what I need to do with roulette is best done with the binomial distribution given every event is independent and the probability is known/fixed and I am only interested in mutually exclusive probabilties win or lose.

 

I adjusted the critical value test to account for 38 pockets. Pretty much the same areas were identified.


I would be interested in the results in your first 190 spins, 380 spins for the above dataset to see if the bias is present and detectable based on the binomial test.

 

I have included a table that also shows the p-value. I'm using 0.025 as significant (allowing for over and under tails), so any p-value under 0.025 is exceeding the critical value. The p-value provides a direct metric on how significant the result is. As we can see the numbers 20 and 1 are quite significant.

 

I prefer a standard deviation graph

 

The first 380 spins

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

 

Why are we doing this ?

 

Because Twoup wanted to see some of the data, so I decided to post some of it.