Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can freely determine provided they're no less than 1%.
Each player takes turns to shoot in the order specified by Alice. In his/her turn, a player must shoot one shot at another player. This process continues until only one survives. Players are intelligent and rational. They correctly calculate which targets to shoot to maximize their own survival probabilities. (In case where different choices of target yield equally maximizing survival probability for a shooter, he/she just randomly shoot one of those targets.)
An example: when $N=2$, if Alice give herself a gun with hit probability 100%, and give both of her opponents guns with hit probability 1%, she can guarantee herself survival probability of 99% by specifying herself as the first one to shoot. The 99% survival rate is achieved by her randomly killing one of the opponent and dodging the other's bullet.
Question: Is there a strategy for Alice to achieve decent survival probability for a very large $N$? What are some good strategies?
If $N$ is large, say 100, it'll be a terrible idea for Alice to choose 100% gun for herself and give all her opponents 1% guns. She will become targets of many, and minnows do bring down a giant if they're a vast crowd.