December 22nd, 2018 at 8:47:31 AM
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Hello,

I have a poker related question of the probability distribution of coin flips when playing poker.

If you run bad for a long period of time at the poker tables and you loosing way more coin flips then you should loose, what is the probability of winning only

1 out of 30?

5 out of 30?

The average is 15, but how can I calculate this? The distribution should be around 15. So it can not be a linear path, right?

Thanks,

I have a poker related question of the probability distribution of coin flips when playing poker.

If you run bad for a long period of time at the poker tables and you loosing way more coin flips then you should loose, what is the probability of winning only

1 out of 30?

5 out of 30?

The average is 15, but how can I calculate this? The distribution should be around 15. So it can not be a linear path, right?

Thanks,

December 22nd, 2018 at 9:10:56 AM
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The probability of winning exactly K out of N coin flips is (N)C(K) / 2

For 1 out of 50, that is 50 / 2

For 3 out of 50, this is 19,600 / 2

^{N}For 1 out of 50, that is 50 / 2

^{50}, or about 1 in 22.5 trillion.For 3 out of 50, this is 19,600 / 2

^{50}, or about 1 in 57.4 billion.
December 22nd, 2018 at 9:21:21 AM
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there are really not that many hands that are exactly 50/50 in a "coin flip"Quote:masterjI have a poker related question of the probability distribution of coin flips when playing poker.

(so poker players really are talking about a biased coin flip)

I can think of 1 after the flop and 1 after the turn that are exactly 50/50.

poker players say something like 51/49 is a coin flip.

and it is.

they just do not say what kind it is.

but with all these biased coin flips, poker players still think they "should win" 50% of them.

30, should win 15 of them, when the only thing the math says about that is the ratio of wins to attempts will approach 50%

the actual number of wins is meaningless

winsome johnny (not Win some johnny)

December 22nd, 2018 at 9:24:37 AM
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1 out of 30?Quote:ThatDonGuyThe probability of winning exactly K out of N coin flips is (N)C(K) / 2

^{N}

For 1 out of 50, that is 50 / 2^{50}, or about 1 in 22.5 trillion.

For 3 out of 50, this is 19,600 / 2^{50}, or about 1 in 57.4 billion.

for a 50/50 event

about 1 in 35,791,394

using pari/gp calculator

(08:54) gp > 1/(binomial(30,1)/2^30.)

%6 = 35791394.133333333333333333333333333332

5 out of 30?

about 1 in 7,535

(08:55) gp > 1/(binomial(30,5)/2^30.)

%7 = 7534.71309278205829929

winsome johnny (not Win some johnny)

December 22nd, 2018 at 11:44:25 AM
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Quote:7craps1 out of 30?

My bad - I though it said "out of 50" for some reason

December 22nd, 2018 at 11:47:23 AM
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Quote:ThatDonGuyThe probability of winning exactly K out of N coin flips is (N)C(K) / 2

^{N}

For 1 out of 50, that is 50 / 2^{50}, or about 1 in 22.5 trillion.

For 3 out of 50, this is 19,600 / 2^{50}, or about 1 in 57.4 billion.

Is the 2 the same as (1/p)?

Could you do say

(N)C(K) / (1/p)

^{N}?

# Свободный Натан

December 22nd, 2018 at 11:53:31 AM
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at first I thought so too.Quote:ThatDonGuyI thought it said "out of 50" for some reason

it seemed like a weird question

a spreadsheet (Excel) can give the total distribution of 30 trials at 50%

quite easily.

many still do not understand the binomial probability distribution

(it is just a special case of the multinomial probability distribution. we all should have leared that in early math classes)

for the OP, one would have to know the hands to continue down that road

successes | prob | 1 in |
---|---|---|

0 | 9.31323E-10 | 1,073,741,824.00 |

1 | 2.79397E-08 | 35,791,394.13 |

2 | 4.05125E-07 | 2,468,372.01 |

3 | 3.78117E-06 | 264,468.43 |

4 | 2.55229E-05 | 39,180.51 |

5 | 0.000132719 | 7,534.71 |

6 | 0.000552996 | 1,808.33 |

7 | 0.001895986 | 527.43 |

8 | 0.005450961 | 183.45 |

9 | 0.013324572 | 75.05 |

10 | 0.027981601 | 35.74 |

11 | 0.050875638 | 19.66 |

12 | 0.080553093 | 12.41 |

13 | 0.111535052 | 8.97 |

14 | 0.13543542 | 7.38 |

15 | 0.144464448 | 6.92 |

16 | 0.13543542 | 7.38 |

17 | 0.111535052 | 8.97 |

18 | 0.080553093 | 12.41 |

19 | 0.050875638 | 19.66 |

20 | 0.027981601 | 35.74 |

21 | 0.013324572 | 75.05 |

22 | 0.005450961 | 183.45 |

23 | 0.001895986 | 527.43 |

24 | 0.000552996 | 1,808.33 |

25 | 0.000132719 | 7,534.71 |

26 | 2.55229E-05 | 39,180.51 |

27 | 3.78117E-06 | 264,468.43 |

28 | 4.05125E-07 | 2,468,372.01 |

29 | 2.79397E-08 | 35,791,394.13 |

30 | 9.31323E-10 | 1,073,741,824.00 |

winsome johnny (not Win some johnny)

December 22nd, 2018 at 12:06:52 PM
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that should say 'fair coin flips'Quote:ThatDonGuyThe probability of winning exactly K out of N coin flips is (N)C(K) / 2

^{N}

one could do say when p = 1/2Quote:RSIs the 2 the same as (1/p)?

Could you do say

(N)C(K) / (1/p)^{N}?

for those that want to know more

(N)C(K) is just the binomial coefficient found in Pascal's Triangle, for example

the number of ways an event could happen where order doesn't matter

it is A in A/B

B = the total ways an event could and could not happen (in the example 2^30 = 1,073,741,824)

Last edited by: 7craps on Dec 22, 2018

winsome johnny (not Win some johnny)