Maybe I'm missing some subtlety. But I'm thinking that the next time I play 1,000 matches against a perfect player, I want to borrow your time machine. I'll travel to the future to see which 500 matches I have lost. Then I'll know I can go back to the present and make a 10% MWC error in each of them without affecting the outcome. While I'm there in the future, I might as well see which 500 matches I have won. Then, back in the present, I can make a 10% MWC error in each of them, too, knowing that I'll win them all anyway.
Seems to me that your 1,000 matches divided equally between 500 won and 500 lost are an illusion. The outcome of those matches can be predicted but is not known until they're played. Before the fact, they can only be predicted to divide equally by assuming they will all be played perfectly. After the fact, once they've been played perfectly, they're done. You can't go back and somehow insert error(s) in each match. If you play 1,000 matches making a 10% MWC error in each, they're not the same 1,000 perfectly played matches. They can't be, because in one set of 1,000 matches you make no error at all, and in the other you make a 10% MWC error in every match.
I think this position (or something very close to it):
The score White 1, Blue 3 (match to 5 points). White on roll, cube decision?
| White | 70 |
|---|---|
| |
| Blue | 70 |
Position ID: 2r0PAADavQ8AAA Match ID: AQGgABAAGAAA | |
• White doubles
can be reached with perfect play. It doesn't really matter. It happens to be a nice reference position, and White's GWC happens to be very close to 60% -- about 60.05%.
If I, as Blue, play this match perfectly, I drop the redouble and have 50% MWC.
But if I have played this match perfectly up to now, take the redouble, and play perfectly thereafter, bot analysis will tell me that this one error cost me 10% MWC. And I know how often I should expect to win this match: 40% of the time.