Cainan18

It’s the grand opening of Triple Sevens at Isleta Resort and Casino with live music, food and drink specials all night long July 27 and July 28.
7 before a 6 or 8 = 6/16 =.375 3 times in a row =.375^3 (.375.375.375) = 0.052734375 or 1 in 18.96 trials But each trial is not 1 roll long (of 6,7 and 8s only) That is the sum of a geometric series 1+(6/16)+(6/16)^2 = 1.515625 = length of each trial Multiply the two together 18.96. 1.515625 = 4 the average number of rolls of 6,7,8s.

Can you please educate me on what the exact odds are in the following scenario(s).
1. What is the odds of (3) consecutive Sevens appearing before either a 6 or an 8 appears.
2. What is the odds of (4) consecutive Sevens appearing before either a 6 or an 8 appears.
Thank you for your help.
Cainan

Sep 29, 2015 Charlie Murphy & EXIT O @ Isleta Casino Charlie Murphy & EXIT O @ Isleta Casino & Triple 7's Bar 2015 Albuquerque New Mexico USA. On the scene at Triple 7 lounge inside the Isleta Resort & Casino for the Fight Night 5 weigh-ins. The event is a 12-fight card including 7 amateur and 5 professional mixed martial arts contests. Twenty-four fighters stepped on the scales with three having issues.

7craps

Nice questions.
I get
1 in 18.96 trials for 3 in a row
1 in 50.57 trials for 4 in a row
Each trial is NOT one roll long
A bit more math to the questions

We can ignore any roll other than a 6,7 or 8 for now.
There are 6 ways to throw a 7
5 ways each for the 6&8
7 before a 6 or 8 = 6/16 = .375
3 times in a row
=.375^3 (.375*.375*.375) = 0.052734375
or 1 in 18.96 trials
But each trial is not 1 roll long (of 6,7 and 8s only)
That is the sum of a geometric series
1+(6/16)+(6/16)^2 = 1.515625 = length of each trial
Multiply the two together
18.96 * 1.515625 = 28.74074074 the average number of rolls of 6,7,8s
For the average number of total rolls (your total wait time)
28.74074074 * (36/16) = 64.667 rolls on average
For 4 in a row just extend the math
(6/16)^4 = 0.019775391 or 1 in 50.56790123 (1/0.019775391)
The length of each trial
1+(6/16)+(6/16)^2+(6/16)^3 = 1.568359375
product = 79.30864198 (50.56790123*1.568359375)
This is just the average number of 6,7 and 8s
now Times 2.25
(2.25 is the average number of rolls to see either a 6,7 or 8)
178.44 = average number of total dice rolls
A quick look at the Zumma Craps Tester Book (35097 actual dice roll file) shows
at least 3 in a row 7s before a 6 or 8 happened 536 times, avg=65.48
at least 4 in a row 7s before a 6 or 8 happened 196 times, avg=179.07

I gots a feeling I know why you asked the questions.
Good Luck

rudeboyoi

Isleta Resort And Casino

I gots a feeling I know why you asked the questions.
Good Luck

yep. hes prob gonna try some martingale-esque system placing the 6&8.

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