There is a game called 21, played orally by n players and the rules are following:
First player starts by randomly saying an integer form [1,3] for his turn, then the next player randomly adds to the previous number an integer also from [1,3] an so on by circle, until someone will be forced to say 21 and lose (the sum can't exceed 21, so if the previous number was 20, player is forced to say 21(his range is{1}). Likewise, if the previous number was 19, the his range is [1,2]). Then the next player starts a new round. The game continues until there is only 1 player left.
The question is somehow similar to the Josephus problem, but the "random" part is where I got lost. I found that if a player says "$X$", where X = 21-(n-1) then he definitely won't lose, so I was trying to think of an algorithm that leads players to "$X$", but I am stuck.
My question is: Let one player to be "strategic" and use a certain algorithm in order to win, and the other players will choose entirely randomly, can it be such an algorithm for n players?
I recommend looking at the game "Nim" like Sean Xie suggested. https://www.archimedes-lab.org/How_to_Solve/Win_at_Nim.html or https://boardgamestrategy.blog/2017/02/13/counting-to-21-strategy/
As the number of players increase, however, there less of a strategy (except in extreme cases) because the other players can cooperate against you; they have a wider range of options, collectively, than you do, so you can't use the sort of strategy that you can use in the two-player version.