[RocketManJames]

As Bozeman said, maybe a Normal distribution is a better random variable for your bowling scores. Again, as Bozeman said, you will need to have the SD's of the bowlers involved.

I'm no expert on this stuff, I can barely remember a probability class I took long, long ago. I believe what you're looking for is a new probability function resulting from the sum of two random variables, namely Normal RV #1 for Bowler A and #2 for Bowler B. Normal RVs being defined by mean and variance.

Now, when you get the new RV as a result of (RV #1 - RV #2) you have some probability distribution with which you can produce fair odds, I think. Ultimately, you're looking for the area under the curve that is greater than 0 and area under the curve that is less than 0. With this, you have a fair way (I think) to set up the proper odds for your bet w/o having to add/subtract pins.

Now, I said I haven't thought about this in years, but from what I remember, you can come up with a new random variable resulting from the difference of two RV's using something called a convolution. It's some funky star symbol and is defined by some whacked integral that I really want to have no part of. Perhaps the more mathematically educated could elaborate. Or, perhaps they'd like to tell me that my proposed method is wrong altogether. Either way, I'm all ears.

-RMJ