Frequency of Come Out Rolls

I am interested in knowing how often a come out roll will occur in craps (once every x rolls). According to the Wizard of Odds, the probability of a DECISION on the pass line is once in every 3.38 rolls. That would include rolling a natural on the come out roll. I'm not necessarily looking for pass line decisions, but rather the frequency of come out rolls in craps.

the probability of a roll being a comeout roll
should be 165/557
that would be 1 in 3.375376 rolls on average

Here
35,097 Zumma actual dice rolls
10,635 come out rolls

and my super 1 million actual dice roll collection
296,192 come out rolls

rolls/come out rolls (the program tracks this for us)
Zumma = 1 in 3.30 rolls
super 1 million = 1 in 3.3761884 rolls

hope this is clear
Zumma

super 1 million


Sally

Thanks so much Sally!

Hi Sally:

Can you explain the 165/557?? I am racking my brain to figure out the 3.38 rolls .

thankx very much!!

barry

Quote: Barry

Hi Sally:

Can you explain the 165/557?? I am racking my brain to figure out the 3.38 rolls .

you are not alone. this article shows how this is calculated. Donald Catlin been gone now for some time but his articles and math lives on.

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

"Since 1 = 165/165, the total is (165 + 392)/165 or 557/165.
This fraction is approximately 3.376.
In other words, if you played many, many Crap games (each decision is a game), kept track of the total number of rolls, and divided the number of rolls by the number of games, the result would be approximately 3.376.
According to Stewart Ethier from the University of Utah as quoted in Peter Griffin's book (Extra Stuff: Gambling Ramblings, Huntington Press, Las Vegas, 1991, p. 168), this result was first published in the American Mathematical Monthly in 1909."

took me sometime to actually have the data table sink in, then I was free.
good luck

added: the distribution (up to 30 rolls)

roll N	ends on Nth roll	ends by Nth roll
0	0
1	0.333333333	0.333333333
2	0.188271605	0.521604938
3	0.134773663	0.656378601
4	0.096567311	0.752945911
5	0.0692571	0.822203011
6	0.049717715	0.871920727
7	0.035725128	0.907645855
8	0.025695361	0.933341216
9	0.018499325	0.95184054
10	0.013331487	0.965172027
11	0.009616645	0.974788673
12	0.006943702	0.981732374
13	0.005018575	0.98675095
14	0.003630703	0.990381653
15	0.002629179	0.993010832
16	0.001905753	0.994916585
17	0.001382697	0.996299282
18	0.001004149	0.997303432
19	0.000729922	0.998033354
20	0.000531076	0.99856443
21	0.000386754	0.998951184
22	0.000281906	0.99923309
23	0.000205665	0.999438755
24	0.000150175	0.99958893
25	0.000109751	0.99969868