Winning Runs

[GH]

Hi,

Further to Bricoman’s request  ("Losing Run" thread),for lengths of winning runs expected in 1000 bets, see below.

Number of THEORETICAL WINNING runs in 1000 bets <br>                      <br>length of                           Strike Rate <br>win run       80%   70%   60%   50%   40%   30%   20%

1                  32      63      96      125    144    147    128 <br>2                  26      44      58       62      58       44     26 <br>3                  21      31      35       31      23       13      5 <br>4                  16      22      21       16       9          4     1     <br>5                  13      15      12       7.8     3.7     1.2    0.2<br>6                  10      11     7.5       3.9     1.5     0.4<br>7                  8.4     7.4    4.5         2      0.6     0.1 <br>8                  6.7     5.2    2.7         1      0.2             <br>9                  5.4     3.6    1.6       0.5     0.1<br>10                4.3     2.5       1       0.2<br>11                3.4     1.8    0.6       0.1<br>12                2.7     1.2    0.3       0.1 <br>13                2.2     0.9    0.2<br>14                1.8     0.6    0.1<br>15                1.4     0.4    0.1 <br>16                1.1     0.3<br>17                0.9     0.2<br>18                0.7     0.1<br>19                0.6     0.1 <br>20                0.5     0.1 <br>21                0.4 <br>22                0.3<br>23                0.2 <br>24                0.2<br>25                0.2 <br>26                0.1<br>27                0.1<br>28                0.1<br>29                0.1

If anyone is interested, I’ll explain how they were determined.

Graham

[Bricoman]

Thanks for all your efforts GH…I for one would be interested to find out how your stats were determined.

I honestly find it hard to believe that you would only have 26 winning doubles for both 80% & 20% strike rates and 62 doubles for only a 50% strike rate…I’m obviously missing something important here.

Regards

Bricoman

[GH]

Hi Bricoman,

Yes, you have missed something important, you have forgotten that for a winning run of 3, you have 2 successful rolling doubles, for a winning run of 4, you have 3 successful doubles and so on.

Although there is the same expected amount of winning runs of 2 for both 20% & 80% strike rate, there are far more winning doubles for the 80% strike rate (as you would expect).

Graham<br>

[GH]

Hi again,

I’ll try to explain how the figures were arrived at by two examples.

Example 1.<br>Assume a 70% win rate = 0.7 chance of winning<br>therefore there is a 30% chance of losing = 0.3

A winning run of exactly 2 can only occur if the following sequence of results occur, LWWL.

The mathematical chance of that occuring is:-<br>0.3×0.7×0.7×0.3 = 0.0441 = 1 in 22.6757

Therefore in 1000 bets, a run of exactly 2 will occur:-<br>1000 divided by 22.67 = 44.1 times ( on average )

Example 2.<br>Assume a 70% win rate = 0.7 chance of winning<br>therefore there is a 30% chance of losing = 0.3

A winning run of exactly 3 can only occur if the following sequence of results occur, LWWWL.

The mathematical chance of that occuring is:-<br>0.3×0.7×0.7×0.7×0.3 = 0.03087 = 1 in 32.393

Therefore in 1000 bets, a run of exactly 3 will occur:-<br>1000 divided by 32.39 = 30.9 times ( on average ).

To compare the theory with practice, I ran my random number programme 5 times = 5000 bets for 20% strike rate and it gave the following results:-

length of             Run number                       Result<br>win run        1    2       3         4         5   average  theory

1              132    132   127      118    127    127.2    128 <br>2               10      21    36        34      25      25.2     25.6 <br>3                 0       9      5          3        6        4.6      5.1 <br>4                 0       0      1          1        0        0.4         1 <br>5                 0       0      0          0        1        0.4     0.2

If this hasn’t bored everyone to sleep, you will see that the theory is borne out by the practice.

Hope this is of use.

Regards,

Graham

[Author]

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