[quote name=\'Ian Wallis\' date=\'Mar 26 2006, 12:35 PM\']In that senario you'd think the bank offer would be close to the half-way mark, but I wonder if they'd purposely low-ball it to
make the contestant go for it. It's been said they have a pre-set range for every possibility, but I'd love to know what the low figure would be on that particular range.
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It's an interesting mathematical exercise, so let's make some really basic assumptions and look at it.
Let's take ten contestants. Let's also make the (entirely hypothetical and non-scientific) assumption that the likelihood of a player to deal is exactly the same as the percentage of the top prize the bank offer is.
So, with a .01 / $1,000,000 situation, the average amount the players who elect to play on are going to win is $500,000, right? 'Cuz half of the time they will have the Big One, and the other half of the time they will have the monkey.
Which means, using this (again, entirely unscientific and basic) system, we get:
$500,000 bank offer: Five players Deal (for a total of $2,500,000), and five play on (also winning an average total of $2,500,000). Total payout over the long run: $5,000,000.
$300,000 bank offer: Three players Deal (for a total of $900,000), and seven play on (for an average total of $3,500,000). Total: $4,400,000.
So, yeah, doesn't make sense financially. That said, there is a psychological factor that comes into play, too: In the $500K offer scenario, on average 7.5 of the 10 contestants go home happy. In the $300K one, it's only 6.5. And happy contestants make for good television, especially on a show where the producers have already played the heartstrings card several times. So that might enter into it too.
(Also note that this is assuming contestants who are playing the game entirely mathematically. And we know the contestant selection process is skewing towards people who play at least somewhat recklessly. So the gap between expected payout on bank offers is probably a LITTLE larger than we think, as is the gap between "happy endings".)