[ActivePattern]

I don't think that bidding system really works. If one side is strongly favored in the opening, the optimal bid would be essentially 0.4999999999... so that you can pick the color and win the game by a slim margin. Players then increase the bid with tiny steps ad infinitum.

The other idea works but is essentially just discarding all of the lopsided starting positions, in which case they might as well not be in the game.