Fictional Prop Bet

[djames]

Please settle an argument. I believe this is a straight-forward application of EV, but I'm having trouble convincing others to accept this game.

Game:
10 player tournament, top 3 get paid, 1st > 2nd > 3rd.

Assume:
1) you have an unlimited bankroll
2) this game will be offered to you forever
3) you have a positive ROI for this game, and always will, where ROI = prize / buyin - 1 as usual.

Bet:
Someone offers to bet $X that you'll be negative after 10 tourneys.

I claim you should take this every day. I have a positive ROI, so I'm expected to be ahead after 10. I say screw variance because I have an unlimited bankroll and can always just play again.

Why can't I convince people of this? Can you?