by hollis
FileAccess wrote:
Hm. Differing by up to 6% seems like more than a slight difference to me.
Yup. That seems like alot. I threw in a few random numbers, and only ever saw differences of less than 1%. Obviously, I wasn't thorough enough in my checking!
FileAccess wrote:
Maybe your formula is correct and mine is the one that's wrong, but the two definitely don't line up.
Well, I am inclined to trust your formula over mine. All I did was muck around with different multiplications until I had a formula where the chance of p1 winning on side A, plus the chance of p1 winning on side B, divided by 2, equaled p1's chance of winning. I have no justification other than "the numbers it gives me look plausible". That's not the best justification.
That said... can you verify something for me?
In the case where X = 2/3 and Y = 2/3, my spreadsheet is telling me:
p1 should win on Side A 80% of the time
p1 should win on Side B 50% of the time
However, this means that p1 should win 65% of the time. But we already know that p1 should win 66.6... (2/3)% of the time.
The discrepancy between (p1's overall winrate as determined by combining side A and side B wins) and (p1's win rate as set by X) gets larger as X or Y get further from 0.5.
Could just be I screwed up the formula when I put it in my spreadsheet, but I don't think so. Can you verify you're getting the same numbers as me?
Here are some others:
Case 1: X = 2/3, Y = 2/3
p1 wins on side A: 80%
p1 wins on side B: 50%
(win on A + win on B) / 2 = 0.65 (should be 0.66...)
Case 2: X = 0.60, Y = 0.70
p1 wins on side A: 77.77%
p1 wins on side B: 39.13%
(win on A + win on B) / 2 = 0.58 (should be 0.60)
Case 3: X = 0.55, Y = 0.90
p1 wins on side A: 91.66%
p1 wins on side B: 11.96%
(win on A + win on B) / 2 = 0.52 (should be 0.55)