odds of 7
July 20th, 2011 at 10:07:45 AM
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What are the odds of a 7 being hit 3 times in a row, 3 differnt times on the same table in the same night in craps?
Thanks,
doublek
Thanks,
doublek
July 20th, 2011 at 10:12:25 AM
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need more data, such as how many total rolls. But I would say this would happen very frequently, perhaps nearly every night on average.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
July 20th, 2011 at 10:42:05 AM
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From your Bllog
In just 3 consecutive rolls it would be 1/(1/6)^3 = 1 in 216 or odds of 215 to 1 against.
The probability increases as the number of trials also increases. Meaning the odds go down as the number of trials increases.
See my 2nd post on this page for more information.
yes, number of rolls would be nice. 400 rolls about 4 to 5 hours of play.
These are very close estimates as the exact answers math is quite messy.
Here is a breakdown per 100, 200, 300 and 400 rolls using POISSON() in Excel. (My simulations show these to be quite accurate) Number in () = expected number of runs of length 3 or more per N trials
The more rolls increases the chance of seeing more runs of length 3 or higher.
simulations for 400 rolls results:
Quote: doublekIm new here so forgive me if this has been coverd,,I have not learned how to navigate this site yet. But here is the question:
What are the odds of a 7 comming 3 times in a row in 1 night at 1 table?
Thanks,
doublek
In just 3 consecutive rolls it would be 1/(1/6)^3 = 1 in 216 or odds of 215 to 1 against.
The probability increases as the number of trials also increases. Meaning the odds go down as the number of trials increases.
See my 2nd post on this page for more information.
Quote: doublekWhat are the odds of a 7 being hit 3 times in a row, 3 differnt times on the same table in the same night in craps?
Thanks,
doublek
yes, number of rolls would be nice. 400 rolls about 4 to 5 hours of play.
These are very close estimates as the exact answers math is quite messy.
Here is a breakdown per 100, 200, 300 and 400 rolls using POISSON() in Excel. (My simulations show these to be quite accurate) Number in () = expected number of runs of length 3 or more per N trials
The more rolls increases the chance of seeing more runs of length 3 or higher.
100 rolls
1 in Prob (0.379) Times
or more 0.685 0
3.2 0.31535 0.259 1
17.9 0.05597 0.049 2
146.3 0.00684 0.006 3 <<--
1581.7 0.00063 0.001 4
22456.1 0.00004 0.000 5
200 rolls
1 in Prob (0.765) Times
or more 0.465 0
1.9 0.53436 0.356 1
5.6 0.17842 0.136 2
23.6 0.04233 0.035 3 <<--
130.8 0.00765 0.007 4
986.1 0.00101 0.001 5
300 rolls
1 in Prob (1.150) Times
or more 0.316 0
1.5 0.68230 0.364 1
3.1 0.31819 0.209 2
9.2 0.10874 0.080 3 <<--
35.2 0.02842 0.023 4
188.1 0.00532 0.005 5
400 rolls
1 in Prob (1.536) Times
or more 0.215 0
1.3 0.77983 0.331 1
2.2 0.44925 0.254 2
5.1 0.19532 0.130 3 <<--
15.3 0.06529 0.050 4
65.2 0.01534 0.015 5
simulations for 400 rolls results:
group freq freq/100
---------------------------------------------
0 210191 21.02%
1 332069 33.21%
2 258576 25.86%
3 130822 13.08%
4 49370 4.94%
5 14630 1.46%
6 3551 0.36%
7 642 0.06%
8 122 0.01%
9 3 0.00%
10 4 0.00%
sessions: 1,000,000
p: 1/6
run length: 3 or more
trials: 400
minimum value: 0.00
first quartile: 1.00
median: 1.00
third quartile: 2.00
maximum value: 10.00
mean value: 1.54
sample variance (n): 1.50
sample std dev (n): 1.22
July 20th, 2011 at 10:42:57 AM
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The odds of rolling three 7s in a row are 1/216, so the odds of doing it three times in a night wouldn't be too terribly high. We'd need the number of rolls in the night to get a good estimate.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
July 20th, 2011 at 10:59:17 AM
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Quote: rdw4potusThe odds of rolling three 7s in a row are 1/216, so the odds of doing it three times in a night wouldn't be too terribly high. We'd need the number of rolls in the night to get a good estimate.
I also agree. Remember the 1/216 is just for any 3 consecutive rolls.
The average number of rolls to see one streak of 3 7s (a run of length 3) is 258.
added: The math for this is just the sum of a geometric series.
There are other formulas, this one is easy one to remember. (1/p)+(1/p^2)+(1/p^3)
Also, Here is a link to a popular steak calculator for at least 1 run of a certain length or more. (example: 3 or higher in a row)
CLICK Here
rolls / probability of at least 1 streak of 3 or more
5 / 1.234568%
76 / 25.182633%
180 / 50.186532%
357 / 75.071712%
591 / 90.018007%
July 20th, 2011 at 11:40:17 AM
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A streak of three sevens begins with the first seven so every time we see a seven, we can look for the next two rolls to be a seven. I expect that after each seven, there is one chance in thirtysix that the next two rolls will be sevens which is equal to seeing boxcars right after a seven. Not too unusual.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
