Something along these lines occurred to me and I wondered if there would be any advantage to casting lots early or late.

So I reduced it to a simple scenario, 3 players, 3 available numbers. Then made a little table and plotted out who would win for each scenario. x.y.z where x is the first persons roll, y is the second.. and you can work out what z is.

[1.2.3] - third wins
[1.3.2] - second wins
[2.1.3] - third wins
[2.3.1] - second wins
[3.1.2] - first wins
[3.2.1] - first wins

OK, so seems that there are an equal number of winning scenarios for the person rolling 1st, 2nd or 3rd, with an equal chance of each occurring.

AH! But there's more numbers in the roll pool that players in the party, might that affect anything?




1.2.3 -3rd wins
1.2.4 -3
1.3.2 -2
1.3.4 -3
1.4.2 -2
1.4.3 -2
2.1.3 -3
2.1.4 -3
2.3.1 -2
2.3.4 -3
2.4.1 -2
2.4.3 -2
3.1.2 -1
3.1.4 -3
3.2.1 -1
3.2.4 -3
3.4.1 -2
3.4.2 -2
4.1.2 -1
4.1.3 -1
4.2.1 -1
4.2.3 -1
4.3.1 -1
4.3.2 -1

24 scenarios

first roller wins 8 times
second roller wins 8 times
third roller wins 8 times


No.

I'm sure it's was obvious and considered, but being me, I had to satisfy myself that in fact it doesn't matter when you roll. And I did. But I still roll as fast as I can, particularly at the end of dungeons... but just as a common courtesy to resolve the pool as quick as possible.