You are a member of a countably infinite population of which every member of the population has been assigned a natural number.

In sequential order, an AI will ask each member of the population if they would like to play a game.

Requiring just one player in the inaugural round, and doubling the number of required players in each subsequent round, once the AI has recruited the appropriate number of players the AI will roll a pair of fair six sided dice which are each truly uniformly random such that there is precisely a 1/36 chance that the roll result will be snake eyes. If the result is snake eyes, the game ends and each player in the final round loses one dollar. If the result is not snake eyes each player in that round wins 1 dollar, and the AI will continue the game and resume recruiting players for the subsequent round of the game.

Today the AI asks if you want to play the game, risk losing a dollar for the chance to win a dollar. Assuming that you are a rational player and will always/ONLY play if you have a positive expected return and will pass if your expected return is zero or negative, do you agree to play?

Is this a paradox?

If you play, you only observe a single dice roll, so you should have a 35/36 chance of winning and only a 1/36 chance of losing.

But wait, each round the number of players doubles and has 1 more player than all the prior rounds combined, the final round being the largest of all the rounds, so theoretically, more likely than not, you will play in the final round and therefore you might expect to lose more often than not if you were Paradox?

So do you Play or Pass when asked if you would like to play the game?