the game is a k shot roulette such that k>=3.

The min bet is 1 points.

There's 1 guy who bet 10000 points

There's n other players such that 1<=n<=11, who bet 100 points each.

Assume everyone are cowards who only pulls the gun once.

Assume the gun never jams.

Assume your max bet is 11100 points.

Chapter 1

Q1. Assume k=12 and n=2, how many points should you bet for maximum profit?

(Hint: derive the equation once and find it's root!)