Pente is that way too. The advantage is not significant for novice players, but expert players rarely lose as Player 1.

In games like these, I think the BKRs should be calculated as follows:

Calculate BKRs separately for games in which the player moved first (Player 1) or second (Player 2). Calculate the percentage of the player's wins that come as Player 1 and as Player 2. Multiply each BKR by the player's winning percentage **of the other position**.

For example, if player has a BKR of 2000 as Player 1 but only 1800 as Player 2 and was Player 1 in 70% of his wins (meaning he was Player 2 in only 30%of his wins) then his BKR should be 2000 * .3 + 1800 * .7 = 1860.

This system usually produces better BKRs than the curent system. And it never produces worse BKRs than the curent system, at least not in any situations that I can think of. I can think of situations where this system wouldn't give a very good result, for example, when a player plays as P2 exclusively. but the system we have in place now doesn't give a good result in these situations either.