Seems like a lot of fancy math or simulation to justify a conclusion, but that math might not fit the real world situation at all. I feel like I've seen a lot

Seems like a lot of fancy math or simulation to justify a conclusion, but that math might not fit the real world situation at all. I feel like I've seen a lot of variations on this theme on HN and it tends to be a pet peeve of mine- maybe showing a ton of math might your result seem more authentic, but I see no evidence that it would be if there's no data to justify the fit of the math. For one thing, the factor noted as "ignored for the sake of simplicity" where a player can carry his un-lost lives into the next round (and the opponent gets a chance to proactively choose who to go up next) seems to me like the far and away #1 most important factor in why order would matter or what the best possible order would be. If you have a lop-sided player who doesn't perform very well, but does really well in one specific matchup, you should probably try to save that player for when you can send them into that matchup. Without any of that that, in a series of perfectly randomized one off matches in a perfect mathematical frictionless vacuum, order might not matter... but that just isn't what a crew battle is.