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 Corrected Simulation Results by Charlie)

"And when starting out with a measly $1, trying to leave with $100, she won not much more than 3% of the time (but of course gaining $100) and took an average of about 24 plays for a loss or 1400 plays for a win."

This is my point, and is why I would play. If there was a lottery that cost $1 to play, paid $100 and paid out 3% of the time, most rational people would play it. In the long run, it's quite obvious, as people have mentioned: If I play this lottery 100 times, I would expect to have paid $100 and won $300.
If I had a lottery that paid $1000000 for your buck, and paid out 33% of the time, would you play it? In the short term you might lose, but you should play it even if you had a single buck, because your expected returns are higher than your costs. In the carnival example, the expected returns are higher than the cost, so one should play (and the house is stupid because it is losing money).

Posted by Sam on 2003-09-18 19:51:03