Posted December 20th, 2005 @ 11:53am by Erik J. Barzeski
Carey and I watched the first episode of "Deal or No Deal" last night. We watched a dumb woman pass up $171,000 for a 1-in-3 (2-in-6) chance of winning either $300k or $500k. The other four choices were $50k, $7500, $500, and $100 or something like that. The lady, who had never owned a house, ended up with $25,000 (her briefcase had something small; $500 I think).
Anyway, towards the end of the game, the banker's offer (I'm not gonna explain the show - look it up or something eh?) was pretty close to the average of the remaining choices. In fact, when only two cases were left, they were $50,000 and $1,000 (I think), and the banker's offer was the $25k the woman took. At the beginning of the game, with 10 "small" numbers (<$1000) and 10 "big" numbers, on average, remaining, the banker's offer is relatively small compared to the average to urge contestants onward. Last night's first offer was $17,000 - not bad money for five minutes of work.
I'm wondering if "the banker" is simply following some algorithm that weights the number of possible payouts remaining, and I'm wondering when an observer of the show will figure out what that algorithm is. Is there an algorithm? How much do the intangibles - namely, the psychology of greed and gambling - play into it? Is the algorithm (again, if it exists) flexible or is it simply mathematically based to attempt to minimize the payout based on the odds each stage of the game presents?
I've never had any mathematical training in such an area or I'd look into this myself. As such, I can only sit back and hope to read about someone else cracking the algorithm, if there is an algorithm to be broken, that is.