Consider the following game that costs $2 to play: You roll a fair, six-sided die. You are awarded a $6 prize if, and only if, you roll a six; otherwise, you get nothing. Should you play the game? Well, considering the odds, the average payout - or "expected utility" - is (1/6)x($6)=$1, which is *less* than the $2 cost of playing. Therefore, since over many trials you would lose out, you should not play this game.
That line of reasoning sounds OK. But let's say you are given a chance to play only once. What sort of bearing does this "average payout" argument have on this special "one shot" case? If you are in this for a single trial, it is not obviously irrelevant what the trend is "over many trials?"