MC Banhammer Posted:

I’m basically trying to determine if someone can use a roll of two dice to determine fairly between outcomes, by bumigning the result of odd to one choice, and even to another choice.

Yes you can. Here’s another way to think about it:

Chances one dice even: 0.5

Chances one dice odd: 0.5

So there are four possible outcomes:

Both dices even (adds to even): 0.5 x 0.5 = 0.25

Both dices odd (adds to even): 0.5 x 0.5 = 0.25

First dice even, second odd (adds to odd): 0.5 x 0.5 = 0.25

First dice odd, first even (adds to odd): 0.5 x 0.5 = 0.25

So adding up the probabilities:

even: 0.25 + 0.25 = 0.5

odd: 0.25 + 0.25 = 0.5

I think everyone is already clear on this, but the reason 2&1 and 1&2 are counted as “different” is because, compared to a value like 1&1, it happens twice as often. Therefore you must count is as two separate values, even though they add up to the same value.