A Fair Game?

Probability Level 3

Mursalin and Trevor decide to play a game where Trevor gets to pick any positive integer n<1000n<1000.

After that the game begins.

First Mursalin names an integer xx from 11 to nn [both inclusive]. Then Trevor has to name an integer from 11 to nn [both inclusive] that does not divide xx. Then it's Mursalin's turn again and so on. On each turn the player has to select an integer from 11 through nn [both inclusive] that doesn't divide all the numbers selected so far. The first person unable to name an integer under these constraints loses. Assuming that both players play optimally, for how many nn's does Mursalin have a winning strategy?

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