In order to mitigate the large advantage of the first player, we used ZeusAI to test several variants of the rules. In the end we devised the following variant, that requires only minimal changes to the initial wonder draft:
In both phases of the wonder draft, the 2nd player is allowed to choose who picks the first wonder — the remaining three are selected according to the normal pattern A-B-B-A. After all wonders have been drafted, the game proceeds as usual.
When playing with this variant, ZeusAI predicts a win rate of 55% for the first player, approximately the same as in chess.
To test the rebalanced rules, we organized several tournaments on Board Game Arena, inviting strong players and agreeing to use our rebalanced rules.
Across more than 10 tournaments with a total of over 300 games played, the win rate for the first player is around 52%. This is quite close to ZeusAI's estimate.