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August 28th, 2015 at 10:44:42 AM
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This is with a doubt my absolute favorite gambling side. What a tremendous wealth of information!!

I would like to know how the number of decisions per hour in craps is calculated. I have typically seen a number that was 30% of the the rolls per hour.

What is the math behind arriving at this 30% number?

Steve in Newbury Park

I would like to know how the number of decisions per hour in craps is calculated. I have typically seen a number that was 30% of the the rolls per hour.

What is the math behind arriving at this 30% number?

Steve in Newbury Park

August 28th, 2015 at 11:08:31 AM
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There are about 3.376 rolls per passline decision, on average; 1/3.376 is about 30%. The math behind the 3.376 number is a good exercise though -- do you know how to calculate it?

"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563

August 28th, 2015 at 11:27:58 AM
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nice question for fun math (math IS fun)

i ask you back

Why you want to know the math?

ok

Donald Catlin (such a nice man, imo, and funny too, like Ed Sullivan funny)

answered this way back in

5 January 2000

wow!

http://catlin.casinocitytimes.com/article/how-long-is-a-craps-roll-1240

"Okay, we're ready to roll.

First let us calculate the expected number of rolls for a Pass Line decision.

To do this we will calculate the expected number of rolls for each of the possible things that will lead to a Pass Line decision and weight each one by the probability that it occurs."

so that 30% is close to 165/557

i due agree

now the distribution

the chance that on roll X (or by roll X) the craps game ends (round - pass line is resolved)

1/3 chance on the 1st roll or the come out roll

1 in 15 that the round requires more than 8 rolls

I have seen 20 rolls to a decision. point was 4 and it lost.

in Google Sheets

https://goo.gl/mySruK

Mully

i ask you back

Why you want to know the math?

ok

Donald Catlin (such a nice man, imo, and funny too, like Ed Sullivan funny)

answered this way back in

5 January 2000

wow!

http://catlin.casinocitytimes.com/article/how-long-is-a-craps-roll-1240

"Okay, we're ready to roll.

First let us calculate the expected number of rolls for a Pass Line decision.

To do this we will calculate the expected number of rolls for each of the possible things that will lead to a Pass Line decision and weight each one by the probability that it occurs."

Event | Probability | Expected Rolls | Product |
---|---|---|---|

Craps/Natural | 12/36 | 1 | 12/36 |

Point 4 | 3/36 | 1 + 36/9 | 3/36 + 3/9 |

Point 5 | 4/36 | 1 + 36/10 | 4/36 + 4/10 |

Point 6 | 5/36 | 1 + 36/11 | 5/36 + 5/11 |

Point 8 | 5/36 | 1 + 36/11 | 5/36 + 5/11 |

Point 9 | 4/36 | 1 + 36/10 | 4/36 + 4/10 |

Point 10 | 3/36 | 1 + 36/9 | 3/36 + 3/9 |

Totals | 1 | . | 1 + 392/165 |

so that 30% is close to 165/557

i due agree

now the distribution

the chance that on roll X (or by roll X) the craps game ends (round - pass line is resolved)

1/3 chance on the 1st roll or the come out roll

1 in 15 that the round requires more than 8 rolls

I have seen 20 rolls to a decision. point was 4 and it lost.

roll | ends on Nth roll | ends by Nth roll | still no decision | 1 in |
---|---|---|---|---|

0 | 0 | 0 | 1 | 1 |

1 | 0.333333333 | 0.333333333 | 0.666666667 | 1.50 |

2 | 0.188271605 | 0.521604938 | 0.478395062 | 2.09 |

3 | 0.134773663 | 0.656378601 | 0.343621399 | 2.91 |

4 | 0.096567311 | 0.752945911 | 0.247054089 | 4.05 |

5 | 0.0692571 | 0.822203011 | 0.177796989 | 5.62 |

6 | 0.049717715 | 0.871920727 | 0.128079273 | 7.81 |

7 | 0.035725128 | 0.907645855 | 0.092354145 | 10.83 |

8 | 0.025695361 | 0.933341216 | 0.066658784 | 15.00 |

9 | 0.018499325 | 0.95184054 | 0.04815946 | 20.76 |

10 | 0.013331487 | 0.965172027 | 0.034827973 | 28.71 |

11 | 0.009616645 | 0.974788673 | 0.025211327 | 39.66 |

12 | 0.006943702 | 0.981732374 | 0.018267626 | 54.74 |

13 | 0.005018575 | 0.98675095 | 0.01324905 | 75.48 |

14 | 0.003630703 | 0.990381653 | 0.009618347 | 103.97 |

15 | 0.002629179 | 0.993010832 | 0.006989168 | 143.08 |

16 | 0.001905753 | 0.994916585 | 0.005083415 | 196.72 |

17 | 0.001382697 | 0.996299282 | 0.003700718 | 270.22 |

18 | 0.001004149 | 0.997303432 | 0.002696568 | 370.84 |

19 | 0.000729922 | 0.998033354 | 0.001966646 | 508.48 |

20 | 0.000531076 | 0.99856443 | 0.00143557 | 696.59 |

21 | 0.000386754 | 0.998951184 | 0.001048816 | 953.46 |

22 | 0.000281906 | 0.99923309 | 0.00076691 | 1,303.93 |

23 | 0.000205665 | 0.999438755 | 0.000561245 | 1,781.75 |

24 | 0.000150175 | 0.99958893 | 0.00041107 | 2,432.67 |

in Google Sheets

https://goo.gl/mySruK

Mully

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