So a quick rule of thumb might be to continue picking, as long as picks were available, until one of the top five prizes was obtained. The EV of a pick would rise as subsequent picks were made, because after the initial low-value picks, the average of the remaining picks would rise.

The above notwithstanding, I would expect most contestants to stop and take the prize if they got $1,000, and maybe even $500.

(64,000 + 4x) / 50 = x,

Where x is the expected value of the first pick (the 4x represents the 4 second chances.)

This gives EV=x=$1,391.

Since there are only a maximum of 4 picks, I know you should never settle for a prize less than $5,000.

This is illustrated by this simple example:

Suppose on your first punch you hit $1,000. Do you keep it or punch again? If you keep it you get $1,000. If you punch again, your next pick has an EV of (63,000 + 4x)/49 = x, and we get an EV = x = $1,431 which is greater than the $1,000. So you should punch again.

Quote:cardsharkmkl, you're mistaken in your calculation of the expected value of the first pick. This is the correct formula:

(64,000 + 4x) / 50 = x,

Where x is the expected value of the first pick (the 4x represents the 4 second chances.)

This gives EV=x=$1,391.

Since there are only a maximum of 4 picks, I know you should never settle for a prize less than $5,000.

This is illustrated by this simple example:

Suppose on your first punch you hit $1,000. Do you keep it or punch again? If you keep it you get $1,000. If you punch again, your next pick has an EV of (63,000 + 4x)/49 = x, and we get an EV = x = $1,431 which is greater than the $1,000. So you should punch again.

You reached the same basic conclusion as I did--I think the difference between my calculation and yours is a slight disagreement over the effect of the second chance rule.

Of course someone might want to keep $1000 if that money means alot to them.

Say you only get 2 punches because you sucked at the higher/lower portion of the game. You then punch 2 compartments (#1 and #2). Drew will then pull out the #1. if it is one of the 4 second chance cards, you will then pick 1 more compartment(#3). Drew will then add #1 and #3 to get your first offer. You can then reject or accept this offer.

Quote:mipletFor those who are confused by "second chance" cards:

Say you only get 2 punches because you sucked at the higher/lower portion of the game. You then punch 2 compartments (#1 and #2). Drew will then pull out the #1. if it is one of the 4 second chance cards, you will then pick 1 more compartment(#3). Drew will then add #1 and #3 to get your first offer. You can then reject or accept this offer.

AIEEEEEEE! Drew Carey!!! You just ruined my mental image of the game, which still had Smiling Bob Barker in it!!

I find the strategy of the game is to always trade with less than $5,000, regardless of how many rounds you have left.