In the Deal or no deal game, I often calculate the expected value as the game goes along. The amount that the banker offers to buy the player out is roughly proportional to the expected value, but the actual proportion changes. At times it is close to the EV, other times he offers as little as half the EV.

I cringe when I see somebody with, for example, $200K, $100K, $1, and $5 left. The EV here is about $75K. If the banker offers $70K and the guy doesn't take it, he's an idiot.

Here's why.

The offer is like money in his pocket. It's already his - he can walk away with it. So here we have a person who is essentially BETTING $70 THOUSAND DOLLARS of his own money. The next pick has a 1/4 chance of being the $200K. That would change his EV to $33K, and the dealer would probably offer $25K next time. So the player is accepting a 1/4 chance that he will lose $45 THOUSAND DOLLARS, while trying (hoping) for the maximum of 1/4 chance of to gain him $130K. (Because he already has $170K)

That's a stupid bet.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)