More on UB Dice

Another article about UB Dice statistics! Hurrah!!

This article was inspired by 3 things.

  1. Nick Williams’s article about UB dice.
  2. A comment by Dan King during a commentary on a UB game in which he suggested that rolling a nerve check and then immediately re-rolling the nerve check due to inspiring leads to a higher than average chance of rolling the same numbers.
  3. My game against Moonraker Andy last night which came down to a turn 7 game-defining nerve test in which I rolled a 9, immediately re-rolled it and scored the same numbers again thus turning a draw into a very unlikely win.

I started by rolling a single dice a lot of times. It immediately became apparent that the number 5 was grossly under-represented in the results, but as I rolled more dice this corrected itself and, within the bounds of the statistical sample, I could see no long term bias. I recorded the numbers of repeat rolls and ended up with the highest chain being 5 consecutive 6s. There is, I think, about a one in 1,296 chance of rolling the same number 5 times in a row and given the size of sample used, rolling one chain of 5 is not unexpected.

These tables show how the numbers rolled on one D6 varied over time. Sample 2 used the data from Sample 1 and then added more rolls.

I then moved on to rolling 2 X D6s to replicate nerve checks to see how often the same combination of dice arrived consecutively, for example 1 and 4 followed by another 1 and 4. I rolled pairs of dice in quick succession to see if this had any bearing on the outcome. Interestingly, had I stopped after my first rolls, the statistics would suggest there is a 100% chance of rolling the same numbers as I rolled 3 and 4 immediately followed by 3 and 4.

In fact I rolled a much larger sample and was quite surprised by the results. Ten % of the successive rolls resulted in the same numbers appearing. This was split exactly between rolls made immediately and those not rolled immediately with 5% for each. This struck me as a much higher percentage than I would have expected. And so I did some maths (did I tell you that I had to resit my maths A level at school?).

If you have a blue dice and a red dice, the chance of rolling exactly the same number on each in the next roll is 1 in 36. But, UB dice does not let us know which of the 2 dice rolled scored which number and so the chance of repeating ant particular roll such as 3 and 4 is in fact 2 in 36 as you can roll 3 and 4 or 4 and 3. For doubles such as 1 and 1 (6 in 36 occasions), the chance remains one in 36.

The chance of repeating the same dice roll is therefore (I think):
[(6 x 1/36) + (30 x 2/36)] / 36 = 5.1%

So the theoretical chance of repeating the same double dice roll in the next turn is about 5%, or about one on 20, which is probably more than most people expect but is only half of what I observed in my trial. It is possible that the difference is due to the sample size and that a larger sample size might produce results that more closely match the theoretical result.


  1. Individual dice rolls do not favour any particular number.
  2. The theoretical chance of rolling the same numbers in consecutive nerve tests is about 5%. This is probably more than players might expect.
  3. In the practical experiment, 10% of nerve test rerolls resulted in the same numbers. This is double the theoretical result but might be due to sample size issues.
  4. In the practical experiment, there was no difference in the chance of rolling the same number in a reroll whether the reroll was made immediately or if there was a delay.

Hope this helps!



Great post & very interesting and does sound pretty suspicious. I hope someone (else, not me, haha) delves into this further one day :slight_smile:

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