Theoretical lottery question

[f97tosc]

If the other player(s) are strategic and rational and can buy multiple tickets, then they are in the same situation as you, and so by symmetry, you can't beat the game.

If the other players only get to buy one ticket each without coordination then you can still come out ahead if you are allowed to buy multiple tickets (you should buy different ones). This is true even if you don't know which tickets the other players picked. You have an edge in this game because you can coordinate your purchases in a way which they cannot.

To give a trivial example, if the game was only to pick one out of two numbers, there was one other player who got one random ticket, and you bought two different tickets, now your EV is -2 +0.5*3+0.5*0.5*3 = 0.25

[WhiteWolf]

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...but what if you have no reliable information about which combinations may have been picked already?

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I think you can prove the strategy of buying one of every possible combination is EV neutral in the very worst case, and +EV in every other case. However, I'm far from certain that is the optimal strategy.