You look at a carnival game. The person running it says, "Just reach your hand into this bag. There are 9 yellow balls and 1 red ball in the bag. You get 4 chances to pull out the red ball. (You have to put the ball you drew back before you draw another ball.) You only have to pay one dollar to play, and you get 3 dollars if you pull out the red ball!"

Assuming the person running the game is telling the truth, and the balls only differ in color, would you expect to make a net profit or a net loss on this game?

(In reply to Solution by fwaff)

I would expect to lose money on this proposition, and you should, too.

I agree with fwaff's math on this, which showed that the player has a slight mathematical advantage over the house, winning an average of $0.0309 per game over the long haul. Statistically speaking, however, winning and losing comes in streaks, and for the player to win overall, she needs to bring a big enough bankroll to outlast a losing streak of potentially infinite length. Generally, players don't bring a big enough bankroll to do this, or in any case their bankroll is substantially smaller than the house's, so it is the house that has the advantage.

Sure, some players will make some dough, but most will leave a losing streak when their bankroll (or nerves) runs out, and the house should still turn a profit.

Posted by Bryan on 2003-09-18 11:24:18