# of Decisions/Hour in Craps

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

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?

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."

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