Loaded dice: number being rolled twice before any other number being rolled twice


New Member

Not sure if this is the correct place for this.

What started as a simple question between my mates and I (to do with board gaming as it happens) has descended into ongoing annoyance!

We have one six sided die, lettered A to F.
A has 2/20 chance of coming up
B has 3/20
C has 3/20
D has 3/20
E has 4/20
F has 5/20

How would I calculate the odds of, say, B coming up twice (not necessarily in a row), before any other letter has come up twice?