Hypothetical Heads Up Gambling Situation

[joeg]

Thats wrong jay, for purposes of notation I'm gonna define R as the percentage rank of a hand, i.e. aces has R=100%, and then define W as the win percentage of that hand against a random hand, so in this case aces have W=~80%

The method you show is mathematically correct if for every hand R=W (or if they were linearly related), it could still be correct if this was not the case but it would be a coincidence, I doubt this will be 'correct' for holdem hands, its probably close, but not correct.

I dont really have the skills to prove this, but I'm sure its the case, I'll post a link & question on the probability forum tomorrow.