Need a statistician (or, the dicebot is broken!)

[GeorgeBates]

Actually, no you can’t say that at all since that distribution isn’t “unusual” by any accepted statistical definition. In fact, it’s well within the range of “expected” for 600 rolls.

Certainly felt unusual. How do we know it is within the expected range?

 

[DVexile]

Certainly felt unusual. How do we know it is within the expected range?

There are some more complicated and accurate ways to evaluate a distribution of die rolls, but a reasonable and conservative approximation is to simply take the square root of the expected number of rolls of a particular value as a "common" variation from the expected number. In this "common" means about 1/3 of the times you play the variation will be this big or larger. This "common" variation is know as the "standard deviation".

Looking at the values that are suspicious to you:

• Sevens - Expected: 100, Difference from expected: 3, Standard deviation: 10 - Your variation is much smaller than what we'd expect to happen 1/3 of the time.
• Sixes and Eights - Expected: 83, Difference from expected: 5.5, Standard deviation: 9 - Your variation is still smaller than what we'd expect to happen 1/3 of the time.
• Fives - Expected - 67, Difference from expected: 6, Standard deviation: 8 - Your variation is still smaller tan what we'd expect to happen 1/3 of the time.

So nothing is even remotely unusual here. Again, you should see variations worse than this 1/3 of the times you play!

Within science and engineering fields results that aren't at least two standard deviations away from the expectation are typically simply consider insignificant, this is because even two standard deviations variation (so for example only getting 80 sevens when you expected 100) happens 5% of the time, so one out of every twenty trials. For people that play a lot of games they should then of course expect to see that multiple times per year.

Please note a few things so my quick summary doesn't lead you astray:

• The quick square root rule of thumb isn't useful when the expected numbers get quite small (e.g. less than say 10).
• The actual statistics for all these interrelated result counts are more complicated than this. For example, if we get more sevens than expected we must get fewer of some other number. But this quick rule of the thumb is more of a worst case. In other words, this rule of thumb is likely to make you think there is a problem more frequently than there actually is.
• As mentioned above, really two standard deviations is a better threshold for determining if someone has been particularly "unlucky" as that would be a 1/20 occurrence. Of course we encounter 1/20 chances all the time in life, so it isn't super unlucky, but one could reasonably complain it was a bad day.

 

[GeorgeBates]

There are some more complicated and accurate ways to evaluate a distribution of die rolls, but a reasonable and conservative approximation is to simply take the square root of the expected number of rolls of a particular value as a "common" variation from the expected number. In this "common" means about 1/3 of the times you play the variation will be this big or larger. This "common" variation is know as the "standard deviation".

Thanks so much. This is the missing piece needed to address the suspicion and put it to rest.
I was probably looking down someone's blouse when this was explained in class years ago.