Bhaduri sets up the "balls in the hat game":
The game consists of a hat that contains 6 black balls and 4 white balls.
The player picks balls from the hat and gains $1 for each white ball, and
loses $1 for each black ball. The selection is done without replacement. At
the end of each pick, the player may choose to stop or continue. The player
has the right to refuse to play (i.e. not pick any balls at all). Given these
rules, and a hat containing 6 black balls and 4 white balls, would you play?
No, I wouldn’t play, even knowing that mathematically speaking there’s a positive
expected value to playing the game. One reason I wouldn’t play is that the positive
EV comes only if you know exactly what you’re doing – and I don’t.
I picked a random easy-to-calculate strategy: keep on picking balls out of
the hat until you reach a black ball, or four white balls, and then stop. With
that strategy, you’ll lose about 13 cents on average. Meanwhile, the optimum
strategy apparently generates a positive yield of less than 7 cents, on average.
I don’t know what it is, but it hardly seems worth it.