The 'repeat window' - Math vs Reality

[redhot]

Mathematically, roulette can't be beaten. This is a fact.

However, this is under the assumption that roulette will behave in a mathematically expected way defined by probability. If it doesn't, the above statement no longer holds true.

If we could find a situation where roulette results do not conform to the mathematical expectation, we may have a chance to beat the game.

A simple example is a biased wheel, certain numbers/sectors hit above the mathematical expectation. Betting on these numbers gives an advantage.

Another example is what I call the 'Repeat Window' -

In a 38 spin cycle, a repeat is guaranteed however we don't know when it will occur.

Mathematically, the repeat can occur on any spin up to and including spin 38. Mathematically it is possible to see all 37 numbers appear with a repeat coming on spin 38.  If this is true, then roulette can't be beaten. It's impossible to benefit from a repeat at spin 38.

Interesting fact 1 -  we all know this isn't true! All 37 numbers appearing without a repeat has NEVER and will NEVER happen. Mathematically this is possible but in reality it's not possible, so here we have an example of roulette results that do not conform to mathematical expectation.

Can this give an advantage? Well, let's take 1,000,000 cycles of 38 spins and see when the repeat occurs:

Cycle Length 1: 26839 --- 2.6839%
Cycle Length 2: 52544 --- 5.2544%
Cycle Length 3: 74880 --- 7.488%
Cycle Length 4: 91570 --- 9.157%
Cycle Length 5: 101780 --- 10.178%
Cycle Length 6: 105320 --- 10.532%
Cycle Length 7: 103471 --- 10.3471%
Cycle Length 8: 96449 --- 9.6449%
Cycle Length 9: 84391 --- 8.4391%
Cycle Length 10: 70998 --- 7.0998%
Cycle Length 11: 57243 --- 5.7243%
Cycle Length 12: 43701 --- 4.3701%
Cycle Length 13: 31892 --- 3.1892%
Cycle Length 14: 22293 --- 2.2293%
Cycle Length 15: 14934 --- 1.4934%
Cycle Length 16: 9430 --- 0.943%
Cycle Length 17: 5640 --- 0.564%
Cycle Length 18: 3245 --- 0.3245%
Cycle Length 19: 1788 --- 0.1788%
Cycle Length 20: 874 --- 0.0874%
Cycle Length 21: 411 --- 0.0411%
Cycle Length 22: 177 --- 0.0177%
Cycle Length 23: 84 --- 0.0084%
Cycle Length 24: 29 --- 0.0029%
Cycle Length 25: 12 --- 0.0012%
Cycle Length 26: 2 --- 0.0002%
Cycle Length 27: 2 --- 0.0002%
Cycle Length 28: 1 --- 0.0001%
Cycle Length 29: 0 --- 0%
Cycle Length 30: 0 --- 0%
Cycle Length 31: 0 --- 0%
Cycle Length 32: 0 --- 0%
Cycle Length 33: 0 --- 0%
Cycle Length 34: 0 --- 0%
Cycle Length 35: 0 --- 0%
Cycle Length 36: 0 --- 0%
Cycle Length 37: 0 --- 0%

As expected, a repeat on spin 38 (cycle length 37) never happened. In fact, the furthest it went to was spin 29 (cycle length 28) which happened once in 1 million cycles.

Mathematically the repeat can appear at spin 38, but in reality the limit is spin 29.

The mathematical 'repeat window' is 38/38 = 100% of the cycle - the repeat can appear on all spins

The real 'repeat window' is 29/38 = the repeat can only occur in 76% of the cycle.

Unfortunately, 76% is still quite a large proportion of the cycle and when adding in table limits, this is still difficult to create an advantage from.

We need to make the 'repeat window' smaller so we're only betting in a small section of the cycle.

Interesting fact 2 - Increasing the number of options, decreases the repeat window! Try it out for yourself - imagine if roulette had 74 numbers, what happens to the repeat window?

[Herby]

To get an idea following diagram, any repeat position in %:
37 numbers higher maximum
74 numbers lower maximum
calculated results

[Steve]

If we could find a situation where roulette results do not conform to the mathematical expectation, we may have a chance to beat the game.

True. So create automated software to perform analysis, use cross referencing to reduce the data needed for sufficient confidence, and determine in what conditions the anomalies occur.

Its not rocket science.

[Firefox]

True. So create automated software to perform analysis, use cross referencing to reduce the data needed for sufficient confidence, and determine in what conditions the anomalies occur.

Its not rocket science.

There's a fundamental difference between your approach to that and what redhot is talking about. You gather data on specific wheels, anticlockwise and clockwise spins, and scatter distances etc. He seems to work with only the pure results. Trying to work with cycles in numbersets. Such numbersets as I understand it can come from anywhere, even RNG.

Maybe the two can meet somewhere, but as I see it, you're barking up different trees at the moment.

[Steve]

Yes his parameters are as relevant as how many birds fly past the window.

[Anastasius]

 :girl_to:Bet from spin 18 to 30 with a long progression 1unit x 5 bets 2 units x 5 bets 3 units x 5 bets ... Hope then u eventually ahead lol

unless u also organise the repeats into categorys like even chance and choose the dominant one to have a longer progression

[Anastasius]

Redhot

Out of curiousity how many 6 unique bets were lost in a row in ur million spins

[redhot]

There's a fundamental difference between your approach to that and what redhot is talking about. You gather data on specific wheels, anticlockwise and clockwise spins, and scatter distances etc. He seems to work with only the pure results. Trying to work with cycles in numbersets. Such numbersets as I understand it can come from anywhere, even RNG.

Maybe the two can meet somewhere, but as I see it, you're barking up different trees at the moment.

Correct. The stats presented above are true for any random numberset consisting of 37 unique possible outcomes.

Those results do not need to come from a wheel, they can be from RNG, random.org, picked out of a hat etc...

There's no concern for any physical variables because the physical wheel is not required.

Back to the topic...

Results for "74 number roulette" over 1,000,000 cycles below:

Cycle Length 1: 13304 --- 1.3304%
Cycle Length 2: 26682 --- 2.6682%
Cycle Length 3: 38595 --- 3.8595%
Cycle Length 4: 49786 --- 4.9786%
Cycle Length 5: 58584 --- 5.8584%
Cycle Length 6: 66219 --- 6.6219%
Cycle Length 7: 70545 --- 7.0545%
Cycle Length 8: 72921 --- 7.2921%
Cycle Length 9: 73418 --- 7.3418%
Cycle Length 10: 72189 --- 7.2189%
Cycle Length 11: 68070 --- 6.807%
Cycle Length 12: 62735 --- 6.2735%
Cycle Length 13: 57523 --- 5.7523%
Cycle Length 14: 50872 --- 5.0872%
Cycle Length 15: 44516 --- 4.4516%
Cycle Length 16: 37691 --- 3.7691%
Cycle Length 17: 31290 --- 3.129%
Cycle Length 18: 25650 --- 2.565%
Cycle Length 19: 20263 --- 2.0263%
Cycle Length 20: 15896 --- 1.5896%
Cycle Length 21: 12362 --- 1.2362%
Cycle Length 22: 9256 --- 0.9256%
Cycle Length 23: 6752 --- 0.6752%
Cycle Length 24: 4870 --- 0.487%
Cycle Length 25: 3325 --- 0.3325%
Cycle Length 26: 2345 --- 0.2345%
Cycle Length 27: 1529 --- 0.1529%
Cycle Length 28: 1098 --- 0.1098%
Cycle Length 29: 677 --- 0.0677%
Cycle Length 30: 432 --- 0.0432%
Cycle Length 31: 258 --- 0.0258%
Cycle Length 32: 163 --- 0.0163%
Cycle Length 33: 87 --- 0.0087%
Cycle Length 34: 43 --- 0.0043%
Cycle Length 35: 30 --- 0.003%
Cycle Length 36: 8 --- 0.0008%
Cycle Length 37: 6 --- 0.0006%
Cycle Length 38: 5 --- 0.0005%
Cycle Length 39: 2 --- 0.0002%
Cycle Length 40: 2 --- 0.0002%
Cycle Length 41: 1 --- 0.0001%
Cycle Length 42: 0 --- 0%
Cycle Length 43: 0 --- 0%
Cycle Length 44: 0 --- 0%
Cycle Length 45: 0 --- 0%
Cycle Length 46: 0 --- 0%
Cycle Length 47: 0 --- 0%
Cycle Length 48: 0 --- 0%
Cycle Length 49: 0 --- 0%
Cycle Length 50: 0 --- 0%
Cycle Length 51: 0 --- 0%
Cycle Length 52: 0 --- 0%
Cycle Length 53: 0 --- 0%
Cycle Length 54: 0 --- 0%
Cycle Length 55: 0 --- 0%
Cycle Length 56: 0 --- 0%
Cycle Length 57: 0 --- 0%
Cycle Length 58: 0 --- 0%
Cycle Length 59: 0 --- 0%
Cycle Length 60: 0 --- 0%
Cycle Length 61: 0 --- 0%
Cycle Length 62: 0 --- 0%
Cycle Length 63: 0 --- 0%
Cycle Length 64: 0 --- 0%
Cycle Length 65: 0 --- 0%
Cycle Length 66: 0 --- 0%
Cycle Length 67: 0 --- 0%
Cycle Length 68: 0 --- 0%
Cycle Length 69: 0 --- 0%
Cycle Length 70: 0 --- 0%
Cycle Length 71: 0 --- 0%
Cycle Length 72: 0 --- 0%
Cycle Length 73: 0 --- 0%
Cycle Length 74: 0 --- 0%

The limit for a repeat was spin 42 however mathematically the limit is spin 75.

The repeat window is 42/75 = 56% of the cycle.

By increasing the options, the repeat window has decreased and is moving further and further away from the mathematical expectation.

[quos]

Hi Redhot, very interesting. It is clear that as the options increase, the repeat window decreases. But going back to European roulette for example. Would it be possible in some way to decrease that repeat window ?.

Thanks!

[Anastasius]

How do u use 74 spins?

Does it decrease again at 111 spins

[redhot]

Does it decrease again at 111 spins

It's not spins, it's options but - Yes, increasing the options decreases the repeat window:

"111 number roulette"

The repeat window is 50/112 = 44% of the cycle.

[redhot]

Hi Redhot, very interesting. It is clear that as the options increase, the repeat window decreases. But going back to European roulette for example. Would it be possible in some way to decrease that repeat window ?.

Thanks!

The roulette wheel is just a random number generator.

Use the outcomes to create your own game. Create "74 number roulette" or "111 number roulette" or "1000 number roulette" whatever you like to get your desired repeat window.

[quos]

The roulette wheel is just a random number generator.

Use the outcomes to create your own game. Create "74 number roulette" or "111 number roulette" or "1000 number roulette" whatever you like to get your desired repeat window.

But how is that possible? We only have 37 numbers. That is, only 37 options. It is not possible to create a window of 1000 roulette numbers.
Thanks for continuing explaining!!!

[redhot]

But how is that possible? We only have 37 numbers. That is, only 37 options. It is not possible to create a window of 1000 roulette numbers.
Thanks for continuing explaining!!!

You can create any amount of options you like.

For example, "74 number roulette":

Take the result of 2 spins, for the first spin record if it's red or black, then for the second spin record the straight number.

Now you have 74 possible outcomes - R0, R1, R2....R36 and B0, B1, B2... B36

[RayManZ]

You can create any amount of options you like.

For example, "74 number roulette":

Take the result of 2 spins, for the first spin record if it's red or black, then for the second spin record the straight number.

Now you have 74 possible outcomes - R0, R1, R2....R36 and B0, B1, B2... B36

But you did not provide the statistics for that option. That should be the same as 1/37. Because now you do 2/74