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woods101

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Hi Maths heads,

Flat betting on dozens. At what point do you say ‘this is a winning system’ as opposed to ‘this is random swing/bias in my favour’?
Example: betting 1 unit on 1 dozen per spin, at what point of profit do you conclude it’s a method that works ? 50u profit? 100u profit? 500u profit?

TIA
Woods.

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ati

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To me it's more about predictability than units won. A winning system always wins and adapts to the variance, no matter what numbers come out.
So in order to conclude that something is a winning system, I have to be able to say that new bankroll high is guaranteed within X number of spins.

This is the chart of one of my recent tests, it's basically a dozen bet but on inside numbers. It's a no zero test and there is a bet on every spin.
Did it win? Yes
Do I think it's a playable winning system? No
There are big draw downs, difficult to track, and it may lose for thousands of spins. That may not seem a big deal, but when you have to actually play spin by spin, it matters a lot. I tried playing it on rng casino, it took 1 and a half hour to play 100 spins and ended up -150 units. At one point I lost 21 bets in a row.

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Joe

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Flat betting on dozens. At what point do you say ‘this is a winning system’ as opposed to ‘this is random swing/bias in my favour’?

In general the more bets the better. If your edge is very small you will need to get more spins to verify an edge, and the same goes for betting few numbers, so if betting on one or two numbers you will need more results to confirm the edge. A dozen bet covers quite a lot of numbers so you shouldn't need more than a few hundred spins. By that time any edge should have manifested as long as you use the correct test. The data needed for the test is the number of wins, the number of bets, and the probability of a win. This software will calculate the edge for you (if any) :

http://www.roulettecoder.com/utilities.html

You just need to enter how many numbers you're betting, and update the W/L each spin.

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woods101

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Thanks for the input guys.
I guess what I'm wanting to know is, betting on dozens, what would be the maximum standard deviation that it would be possible to witness and what would be the result in units based on a 1 unit bet on one of 3 dozens if that deviation was in my favour?
Apologies - I figure some numbers might help, so for example, say I placed a bet every spin for 500 spins. Would it be possible to come away with say a 100u profit due to sheer luck or does the maths deem it impossible? If impossible what would be the maximum profit (if any) I could hope to achieve with standard deviation on my side based on those parameters?

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Herby

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what would be the maximum standard deviation that it would be possible to witness
There is no maximum standard deviation, but probabilities get smaller and smaller for greater  standard deviations.
Tables in math books reach most of the time from -3STD to +3STD.

  I placed a bet every spin for 500 spins. Would it be possible to come away with say a 100u profit due to sheer luck .
You can calculate the exact probability by binomial distribution, for large numbers you can approximate by normal distribution.

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Herby

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500 spins.  100u profit or above due to sheer luck
3.93 STDs above Mean
probability for this event: 0.000033

What does it mean ?
Lets say this board has 1000 visitors per day. They play each day 500 spins for one month.
Only 1 person could reach this result.

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Joe

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so for example, say I placed a bet every spin for 500 spins. Would it be possible to come away with say a 100u profit due to sheer luck or does the maths deem it impossible? If impossible what would be the maximum profit (if any) I could hope to achieve with standard deviation on my side based on those parameters?

I ran a simulation betting a dozen (starting bank = 0) for 10,000 sessions each of length 500 bets. Here's the frequency distribution of the bank at the end of the sesssion :

Code: [Select]
Frequency distribution for bank, obs 1-10000
number of bins = 29, mean = -13.0418, sd = 31.0783

       interval          midpt   frequency    rel.     cum.

           < -132.50   -137.00        1      0.01%    0.01%
   -132.50 - -123.50   -128.00        1      0.01%    0.02%
   -123.50 - -114.50   -119.00        4      0.04%    0.06%
   -114.50 - -105.50   -110.00        8      0.08%    0.14%
   -105.50 - -96.500   -101.00       18      0.18%    0.32%
   -96.500 - -87.500   -92.000       50      0.50%    0.82%
   -87.500 - -78.500   -83.000      105      1.05%    1.87%
   -78.500 - -69.500   -74.000      162      1.62%    3.49%
   -69.500 - -60.500   -65.000      273      2.73%    6.22%
   -60.500 - -51.500   -56.000      423      4.23%   10.45% *
   -51.500 - -42.500   -47.000      660      6.60%   17.05% **
   -42.500 - -33.500   -38.000      835      8.35%   25.40% ***
   -33.500 - -24.500   -29.000     1037     10.37%   35.77% ***
   -24.500 - -15.500   -20.000     1160     11.60%   47.37% ****
   -15.500 - -6.5000   -11.000     1137     11.37%   58.74% ****
   -6.5000 -  2.5000   -2.0000     1062     10.62%   69.36% ***
    2.5000 -  11.500    7.0000      948      9.48%   78.84% ***
    11.500 -  20.500    16.000      727      7.27%   86.11% **
    20.500 -  29.500    25.000      517      5.17%   91.28% *
    29.500 -  38.500    34.000      355      3.55%   94.83% *
    38.500 -  47.500    43.000      238      2.38%   97.21%
    47.500 -  56.500    52.000      141      1.41%   98.62%
    56.500 -  65.500    61.000       83      0.83%   99.45%
    65.500 -  74.500    70.000       34      0.34%   99.79%
    74.500 -  83.500    79.000       11      0.11%   99.90%
    83.500 -  92.500    88.000        6      0.06%   99.96%
    92.500 -  101.50    97.000        1      0.01%   99.97%
    101.50 -  110.50    106.00        1      0.01%   99.98%
          >=  110.50    115.00        2      0.02%  100.00%

So on average you will lose about 13 units each session. Compare this with theory which says it should be 500 * -0.027 = -13.5, so pretty close  ;). You won at least 100 units 3 times in the 10,000 sessions, so it's possible, but very unlikely.

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Joe

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To work out what a profit of 100u after 500 bets would mean in terms of standard deviations, first find the number of wins :

2w - L > 100
w + L = 500

Solving simultaneously, you get w = 200 and L = 300. (Check :  200 * 2 - 300 = +100)

The expected number of wins is 12/37 * 500 = 162.

The standard deviation is sqrt(500 * 12/ 37 * 25/37) = 10.4675

Now find the number of standard deviations from the mean (expectation) :

(200 - 162) / 10.4675 = 3.63

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woods101

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@ Joe and Herby (and Ati) many thanks.

It's been a while since I passed through here. I used to have a bit of a grasp of standard deviation etc but it's all a bit hazy these days. There's a fine line between fluke, a seemingly good system and a disaster waiting to happen. I do feel somewhat enlightened now though.
Many thanks
Woods

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Herby

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all a bit hazy these days
me too, I made a mistake in calculating of the STD, so Jo is right.  :thumbsup:

 

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