Last man standing strategy Let's imagine a last man standing scenario in a video-game. A last man standing situation is one where each player is for himself and has to eliminate all other players to win. For analyzing the situation, consider the game mechanics of a simple shooter game like CSGO.
There are 3 people in this last man standing type of game, they all have the same level of skill and luckily, you aren't in combat. Yet.
Let's assign each player a letter, you are A and the other two are labelled B and C. B and C are in close combat, while you, on the other hand, have a sniper and have the choice to shoot at number B or C. Number B has a health of 30 and number C has 80 health. A shot from the sniper will do damage of fifty.
Considering you don't miss shots, Who would you shoot? My brother said ''Well I would shoot at B to eliminate him out of the equation.'' But think about it this way: If you shoot at C, he is down to 30 health and when either of them is done with his enemy (I am talking about B and C) he will have 30 health, even in the best scenario. So, when it comes to 1v1, you will have a much better advantage.
I think that the best strategy for last man standing scenarios are to feed and assist the weaker (but not too much) so that they will eat each other to the point where it's a Pyrrhic victory.
Which strategy has the best outcome for Last Man Standing scenarios? Should they 'level' the playing field by reducing the opponent's health or should he go for eliminating whole players out of the game?
 A: What you might be looking for in game theory the games are called Truels (three people) or N-uels (n people) or the simplified version Duals (two people). There are three kinds to consider

*

*Sequential (fixed order): The players fire one at a time in a fixed, repeating sequence, such as A, B, C, A, B, C, A...


*Sequential (random order): The first player to fire, and each subsequent player, is chosen at random among the survivors.


*Simultaneous: All surviving players fire simultaneously in every round.
If needed a firing order is chosen the when it is the players turn to fire (or they all fire at once) each may fire at either of their co-players. A player's marksmanship is the probability that he hits his chosen target. Throughout the game each player has no information as to the previous strategy choices of his co-players, except through their successful shots. There can also be variants of the rules in that each player will have only $n$ shots available or giving the players the ability to abstain from shooting in a round. All players share the same goal: to be the one survivor. In order to maximize their payoff, players have to chose strategies that maximize their survival probability.
As you get to fire first it looks like a sequential fixed order game without the possibility of abstaining from shots is the closest to what you are describing. A player who is about to fire, whether their turn comes up in a fixed order or is chosen at random, has a choice whom to fire. To make this choice optimally, we assume that a player considers only their own survival probability. Regardless of what the other players do, a player in a sequential truel maximizes their survival probability by firing at the opponent against whom it would less prefer to fight a duel. If a player's shot misses, then it makes no difference who was the target; but if a shot hits the target, the shooter is better off, because their opponent in the next duel is weaker. Thus, a player who follows this stronger opponent strategy fires at the opponent whose marksmanship is highest, trying to eliminate this player so as to set up a duel with the lower marksmanship player.
In you case you give health so you should target the player with the most health as you would prefer to try and set up a dual the weaker player.
