To explain for neil: Take a coin. Give yourself five 'points', and then flip the coin. If the coin lands as heads, give yourself a point. If it lands tails, take one away. The goal of the game is to stop while you have the most points possible, and the game is over when you hit zero.

This is how the gambler's dillema works: It is possible to win (by quitting while you're ahead) but because you lose instantly when you run out, there is a greater chance of having to stop at that point.