I have a fascination with tabletop sports games, and through that, I've developed an interest in probability. That said, it's not my strong suit, so I wanted to pose this question because I think involves a few different probability principles to solve it.
Here's the premise...the game uses a roll of 3d6 to determine the result of a play. The dice are read from lowest to highest, as in:
a roll of 3, 6, 2 would be 2-3-6 a roll of 1, 4, 1 would be 1-1-4 etc.
That roll is then looked up on a chart to determine the result.
I was curious about the probability of different results coming up so that if I wanted to make a house rule, I would know which result would be the best place to modify.
So, what I do know is that for probability, you multiply chances together, correct? So without the low to high rule I discussed above, any number would have a 1/6 * 1/6 * 1/6 chance of occurring, correct?
How would I apply this principle to any result? My guess is something like:
1-1-4 = 1/6 * 1/6 * 5/6
only one chance for the first 2 die, and the last can be anything but 1, so 5 remaining numbers
2-3-6 = 1/6 * 4/6 * 4/6
first number can be 2 only = 1/6
second number can be any number but 2 or 6 = 4/6
second number can be any number but 2 or 3 = 4/6
Am I understanding this correctly?