Tuesday, March 20, 2012

100 Dice Rolls with Two 6-Sided Dice - Probability vs Reality

I decided on a whim to compare probability to reality and see what happened. So I rolled two six-sided dice 100 times and compared the percent rolled for each number to the statistical probability.  Now the numbers where never going to line up exactly with probably because the probability percentages aren’t whole numbers and by rolling the dice 10 times, every percent rolled was going to be a whole number. In fact whatever number of times a number was rolled was also its percent.  Nevertheless, in a 100 rolls the percents ought to be getting close.  Here’s what actually happened for each number rolled, between 2 and 12.

2: Probability 2.78%, Rolled 6%
3: Probability 5.56%, Rolled 18%
4: Probability 8.33%, Rolled 5%
5: Probability 11.1%, Rolled 8%
6: Probability 13.89%, Rolled 10&
7: Probability 16.67%, Rolled 15%
8: Probability 13.89%, Rolled 16%
9: Probability 11.1%, Rolled 10%
10: Probability 8.33%, Rolled 7%
11: Probability 5.56%, Rolled 3%
12: Probability 2.78%, Rolled 2%

So… okay the numbers weren’t ridiculously off (it’s not like any number was rolled half the time but neither were they really that close neither (rolling 3 more than any other number was statistically highly unlikely).  Conclusion: certainly consider the odds in games where you have to choose whether to roll dice or from what position, but don’t bet significant amount of money on any given dice roll.

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