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acpa
Posted by acpa
Jul 15, 2010

Confidence level of sample

I know the odds of getting the perfect pyramid of possibilities out of 36 rolls is very remote. ie 1 2, 2 3s, 3 4s, 4 5s, 5 6s, 6 7s, 5 8s, 4 9s, 3 10s, 2 11s and 1 12.

My knowledge of sampling is fairly small however.

We all know that the House Advantage on a pass line bet is only 1.41%. Can someone help me understand what percentage of confidence I could have with say 9,000 decisions that my results would be within 90% of the expected. i.e. 1.269% to 1.551%.

Same question, but expected range varies by 100%, i.e. break even 0.0000% to 2.82% loss.

Can someone refer me to somewhere on the web I could find out more about this concept.

Thanks in advance.

acpa

Comments

ruascott
ruascott Jul 16, 2010

I don't know the exact answer, but you'll get a lot better responses posting in the forums rather than the blgo.

PapaChubby
PapaChubby Jul 16, 2010

I can get you in the ballpark based on a biased coinflip analogy. I'm a probability guy, not a statistics guy.



In 9000 decisions, the standard deviation will be about 95 decisions. 95 decisions out of 9000 is about 1 percent. So you can expect a return between -0.41% and -2.41 percent about 65% of the time. Your 0.14% spread can be expected much less often, I'd estimate around 10-15%. Your 1.4% spread will probably occur around 85% of the time. Ish.

7winner
7winner Jul 17, 2010

"I know the odds of getting the perfect pyramid of possibilities out of 36 rolls is very remote. ie 1 2, 2 3s, 3 4s, 4 5s, 5 6s, 6 7s, 5 8s, 4 9s, 3 10s, 2 11s and 1 12"



This gave me something to do. Hope the math is correct.



Thought I'd throw out this distribution table for the perfect 36. Was made in Excel. very simple to do.



=C2*C2*C3*C3*C4*C4*C5*C5*C6*C6*C7



0.000015931223909174% or...

1 in 6,276,982 Groups of 36 rolls

225,971,339 rolls

2,259,713.3 hours/ at 100 rolls per hour 24/7

94,154.7 days

257.95 years to see it happen on one craps table.



30000 dice rolls per hour in Vegas per day / There are over 300 tables in Las Vegas, so...

7532.37 hrs

313.8 days

so it can happen every year in Vegas between all the tables.

One would not know that it happened since nobody tracks all dice rolls.






#exactly eachProbabilityagainst or less or more #
2,12137.31%62.69%036.27%226.42%100.00%2,12
3,11227.85%72.15%139.83%332.32%100.00%3,11
4,10323.40%76.60%241.34%435.26%100.00%4,10
5,9420.72%79.28%342.19%537.09%100.00%5,9
6,8518.90%81.10%442.73%638.37%100.00%6,8
7617.59%82.41%543.09%739.33%100.00%7