Dice Probability – The Myth

Ever had the idea that your dice were against you? That you had to swap out to different dice to get ‘better results’? What can you do to test this theory?

In my experiment, I’ve thrown Guild dice and collected their numbers to see their odds. My experiment used N=400, so I rolled 400 dice per Guild. After getting all data, I’ve calculated the probability of hitting a 2+, 3+, 4+, 5+ and 6+, and checked the difference with the theoretical average. In this post, I’ll subtract my findings from the theoretical averages. These theoretical averages are 16.67% for 6+, 33.33% for 5+, 50% for 4+, 66.67% for 3+ and 83.33% for 2+. This gives an approximation to how much these probabilities are alike.

VERY IMPORTANT: my experiment uses N=400, so this is but an approximation of the actual averages. To get absolute results, N should be near infinite, but I would like to still have a life. 😉

Engineers dice:
2+: -0.33%
3+: +1.58%
4+: +1.50%
5+: +2.92%
6+: +1.58%

Masons dice:
2+: -0.33%
3+: -2.42%
4+: -3.75%
5+: -2.08%
6+: -0.67%

Morticians dice:
2+: +1.92%
3+: +2.58%
4+: -0.25%
5+: -1.83%
6+: -0.17%

Union dice:
2+: +1.42%
3+: -0.67%
4+: +1.00%
5+: +0.17%
6+: -1.67%

Ratcatchers dice:
2+: +2.42%
3+: +3.83%
4+: +2.72%
5+: +1.67%
6+: +2.58%

Alchemists dice:
2+: +0.42%
3+: -0.92%
4+: -2.00%
5+: -4.83%
6+: -1.42%

Blacksmith’s dice:
2+: -1.08%
3+: -0.92%
4+: -1.50%
5+: +4.92%
6+: +2.58%

Inspiring Hat dice:
2+: +1.42%
3+: -0.92%
4+: -1.75%
5+: -1.08%
6+: +0.33%

Obviously, these percentages are more important the higher you go in your Target Number (TN). If the assumption that N=400 is decent enough for the approximation of the dice averages, there are some main take-aways.

Masons dice are constantly below the curve.
Ratcatchers dice are constantly above the curve.
Engineers dice are very decent in hitting high numbers.
Morticians dice fall off when trying to hit the high numbers.
Union dice are very much alike the theoretical averages.
Alchemists dice are abominable at hitting high numbers.
Blacksmiths are quite good at hitting high numbers.
My own dice are champs at hitting 2’s and 6’s.

When looking at N=3200, so basically at all dice rolled up to this point, I get the following numbers.

2+: +0.57%
3+: +0.15%
4+: -0.59%
5+: -0.08%
6+: +0.36%

N=3200 should give a far better approximation to the theoretical averages than N=400, and it seems that this indeed is the case. Almost are averages are within 0.60% of their theoretical point.

So next time you try to hit those high numbers and you come up short, know that it’ll always average out eventually!

Good luck, and until next time!