Originally posted by: ProfJohn
umm you need to redo the math.
With the example I gave the chances of you taking home the $100,000 are 1 in 24 (1/4 * 1/3 * 1/2)
You would be stupid to not take the $25,000 they will offer at that point and walk away.
YOU need to redo the math, ProfJohn. You even contracticted yourself a bit in my quote above. If you truely had a 1 in 24 chance of winning $100k, why would they offer 25% of $100k?
The correct math is this:
1) You have a 3 in 4 chance of picking a low number the first time (picking low is a good thing).
2) You have a 2 in 3 chance of picking a low number the second time.
3) You have a 1 in 2 chance of picking a low number the third time you pick.
Thus, your overall chance of picking three low numbers in a row (ie winning the $100k) is 3/4 * 2/3 * 1/2 = 1/4. You have a 1 in 4 chance of getting $100k, not 1 in 24.
But, here is the crux. They don't offer $25,000 in that situation. If you were offered $25,000 (the expected value), then on average the contestant should take the $25,000 and walk away (as you mentioned). But, the game plays on the psychology of the audience. More people will watch tomorrow (ie more ad revenue) if the person doesn't take the deal. Thus, the TV station makes more money if the person doesn't take the deal. Thus, they don't offer $25,000. They offer something like $16,000. In which case, it is on average a far better deal to turn down the $16,000 and try for $100,000. If they offered $25,000, then Skoorb would be correct that this show isn't worth watching.
