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BigBen · 03-06-2006, 10:55 AM

I think I discussed this already in the Tilted Entertainment thread about the show, but here goes:

The formula is a summation of expected values. You take the value of the amount in the case, multiply it by the expected chance of it being chosen, and then sum across all cases.

Therefore,

E(p)=Sigma (i=1 to N) E(i)*V(i)

Wow, that was really bad notation, but I don't know how to do math notation on a computer.

You should take the deal whenever the Banker offers you more than E(p).

E(.01) = 0.01 *1/26 or just .01/26
E(1) = 1 * 1/26 = 1/26
E(1,000,000) = 1,000,000/26

But wait. Using that equation, the banker should offer you 131,477.50$ at the first turn of the game, before the first case is opened. You would both call it even, at the start.

But this is obviously not the case. There must be a weight applied to the earlier rounds, because it costs nothing for the bank to open a few cases. The expected value of the Penny or even the 5,000 case in round one (where everything is divided by the probability of 1 in 26), the payoff is 192.31$ for the 5,000$ case!

If you pick the 1,000,000$ case first, you just gave the bank 38,561.54$ !

Of course, The deals are weighted poorly in the early rounds, or else there would not be very much of a show.

Remember, my calculation needs to be run every round, with updated information, and N has changed...

Am I right? That's how my brain interpreted it, anyway.

03-06-2006, 10:55 AM	#14 (permalink)
BigBen Comedian Location: Use the search button	I think I discussed this already in the Tilted Entertainment thread about the show, but here goes: The formula is a summation of expected values. You take the value of the amount in the case, multiply it by the expected chance of it being chosen, and then sum across all cases. Therefore, E(p)=Sigma (i=1 to N) E(i)V(i) Wow, that was really bad notation, but I don't know how to do math notation on a computer. You should take the deal whenever the Banker offers you more than E(p). E(.01) = 0.01 1/26 or just .01/26 E(1) = 1 * 1/26 = 1/26 E(1,000,000) = 1,000,000/26 But wait. Using that equation, the banker should offer you 131,477.50$ at the first turn of the game, before the first case is opened. You would both call it even, at the start. But this is obviously not the case. There must be a weight applied to the earlier rounds, because it costs nothing for the bank to open a few cases. The expected value of the Penny or even the 5,000 case in round one (where everything is divided by the probability of 1 in 26), the payoff is 192.31$ for the 5,000$ case! If you pick the 1,000,000$ case first, you just gave the bank 38,561.54$ ! Of course, The deals are weighted poorly in the early rounds, or else there would not be very much of a show. Remember, my calculation needs to be run every round, with updated information, and N has changed... Am I right? That's how my brain interpreted it, anyway. __________________ 3.141592654 Hey, if you are impressed with my memorizing pi to 10 digits, you should see the size of my penis.