Sorry if I don't use the correct terminology, I'm by no means particularly educated in mathematics. I'm in the processing of designing a game but in order to pace it well so it's not over too soon or takes forever, I'm balancing the results of my dice rolls to be closer to equal loss and gain with a tilt to gains. Normally this would be easy with a fixed number of dice, but in all but one circumstance I'm using two die, with 1-12 chance of landing a combination which leads to a third die. There are only three options on each die, so the results look as such:
WW WW WW GW BW BW
WW WW WW GW BW BW
WW WW WW GW BW BW
WW WW WW GW BW BW
WG WG WG GG BG BG
WB WB WB GB BB BB
where W is white, G is gold and B is black. One die has 4W, 1B, 1G and another die has 2W, 2B, 2G, Hence the results not being square. When a player rolls G and B (3 in 36; 1 in 12 as mentioned) they have a third die to role which is also 2W, 2B, 2G. However, GBW = WW, GBG = WW + GW and GBB = GW + BB.
As such, WW isn't really 12 in 36 (1 in 3) but a slightly higher likelihood due to both GBW and GBG contributing to its chances of occurring however I'm not sure how to account for this. Can someone help?
WW WW WW GW BW BW
WW WW WW GW BW BW
WW WW WW GW BW BW
WW WW WW GW BW BW
WG WG WG GG BG BG
WB WB WB GB BB BB
where W is white, G is gold and B is black. One die has 4W, 1B, 1G and another die has 2W, 2B, 2G, Hence the results not being square. When a player rolls G and B (3 in 36; 1 in 12 as mentioned) they have a third die to role which is also 2W, 2B, 2G. However, GBW = WW, GBG = WW + GW and GBB = GW + BB.
As such, WW isn't really 12 in 36 (1 in 3) but a slightly higher likelihood due to both GBW and GBG contributing to its chances of occurring however I'm not sure how to account for this. Can someone help?