Can you tell me how you start those games?

I just started a bot game on my own table (no option changed) and the first game had me as the starting player.

Then I started a bot game via automatching and the 3rd game on that table had me going first.

Then I started a bot game again via automatching, and after each game started anew with automatching, and then the 4th game had me going first.

So while this took 2 more games than the mathematical expected value would predict, I guess it's still just random noice over an unbiased selection.