That’s a horrible offer from the banker. I would have turned it down too.
Wrong choice: -42,000.
Correct choice: + 205,000.
This is not even a close decision. She played it correctly.
I’m surprised the offers are so low on the UK show. On the U.S. show, the offers are slightly under whatever the current mathematically expected value of your choice is (slightly under, to encourage contestants to keep going).
For example, with a set of values like this:
500
1000
50000
750,000
1,000,000
The expected value is 360,300. That would be a ‘fair’ offer - if you played out the game 1 million times from this point, choosing randomly, the average value of the player’s earnings would be that amount. But the bank will offer slightly under that, so there’s slightly more value in continuing the game. In the early rounds, the offer is WAY under. But in the later rounds, it’s almost exactly the expectation.
In your case, the real value of the player’s position was 147,500. In the U.S, the banker would probably have offered something like 145,000. I can’t believe they’d make an offer as low as 45,000 on the U.K. version. Did you leave a one off at the beginning of that number?
BTW, all the claims that Deal or No Deal is a simple show are dead wrong. It’s just that the decision-making and knowledge required are very different than most other game shows. The key elements in that show are expected value, variance, and utility. It’s a show economists love.