Talk:The Tournament of Lilies/@comment-76.11.71.146-20150831205605/@comment-50.174.211.129-20160926015955

I ran a simulation and got a different result than the gentleman who said it took 24, assuming you have 50% chance of winning at each level the median number of tries it takes is 32. (The mean is 42 ish... there's a chance toget very unucky which brings up the mean.)

The math seems complicated to me, I didn't see an easy way to just write down the answer. It has to take into account that if you lose at the lowest level, you don't get set back in the tourney, but if you lose at higher levels you do.

Fun facts from my simulation:

From the lowest level, it takes a median of 32 fights to win. Once you're at a contest of cunning, it takes a median of 30. So getting that first win barely means anything. Once you're at the contest of blood, it takes a median of 26 actions to win. Once you're at Mysteries, 19. Once you're at Voices, 8. Once you're at Beauty, a median of 3 actions to get a win!

But it's never certain - in my 1-million-run simulation, there was one poor virtual sap who took 609 actions to get a win when starting from the contest of beauty! So no matter what your progression in the tournament, you can always lose it all and be back where you started, many times over.