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I assume you are aware about the game PUBG (see the Wikipedia entry), where 100 players are dropped on island, and last team/individual to survive wins.

I was thinking about a mathematical model/framework for determining the probability of finding players at a particular location on the map by considering all parameters: flight path, RP of top players, numbers of players, offline players, and the map itself.

I am just brainstorming something like this. Could any body help in mathematical brainstorming of this idea?

I suppose the question is really: why shouldn't the distribution of players in the play area be uniform? That is, each possible location is as probable as any other when looking for players.

In the initial stage players choose where to jump out of a plane that flies over the island, and they parachute down, so there is a small amount of control over where they land. The path of the plane usually covers the centre of the island, so players can jump out anywhere and aim to land (almost) anywhere, so it would be reasonable to treat the distribution as uniform over the island, or perhaps as uniform over all but the sides it is hardest to parachute to.

However, if the loot (weapons mostly) is in fixed locations, then regular players may have strategies on where to parachute down to to maximise their chances of getting a favoured item of loot. In this scenario you get clumping as players compete for loot, which rapidly disperses as players kill one another with the loot they've claimed. As they must kill everyone else (except team members in team play) they then move out hunting for their next victim -- with no knowledge of where they may be -- so they must move randomly. So the initial non-uniform distribution will rapidly become uniform again.

In the next stage, the play area shrinks to a circle of specific radius. Any player outside that circle takes damage and quickly dies, so the probability of finding a player outside that circle falls quickly to zero, and inside the circle -- well, there's a brief period where the circle boundary has a high probability of having players, but as they disperse into the circle and kill each other, it smooths out again. Subsequent rounds shrink the circle more and more in order to force players to find each other and reach a resolution.

So for modelling, this is essentially a uniform distribution except at the start of each stage where (briefly) there is a peak at the boundaries. Overall, I'd suggest that for the inital phase the heat equation $Delta u = u_t$ will give a reasonable model with an initial distribution $u_0$ that is where players land from the plane; for the later stages the heat equation with a boundary condition $u(x,y,0) = c$ on $partial B(x_0,y_0,r) $ will work. $u$ will be the density of players. This fails to model the race to the new area when the play area shrinks though, but this can be handled by a term that 'attracts' -- when players see each other they tend to move towards each other in order to obtain a kill. This will need an $f(x)$ or maybe $u_x cdot f(x)$ term to model.

It's worth noting that a model is built to answer a question and at the moment you haven't really told us what the question you want to answer is, which makes it hard to refine the model. The probably location of a player on the map at any time feels like data for answering a different question.