deal or no deal

[Chip Turner]

On 2005-12-26 15:05:21 -0500, james.moughan at sunderland.ac.uk said:

> I believe not; the Monty Hall problem is biased by the fact that the
> presenter knows where the prize is, and eliminates one box accordingly.
>  Where boxes are eliminated at random, it's impossible for any given
> box to have a higher probability of containing any given amount of
> money than another.  And for the contestants box to be worth more or
> less than the mean, it must have a higher probability of containing a
> certain amount.

Agreed -- unless the presenter takes away a case based on knowledge he 
has about the contents, then Monty Hall doesn't enter into it.  Deal or 
No Deal seems to be a purely chance based game.  However, that doesn't 
mean there aren't strategies beyond strictly expecting the average 
payout.

> Like another member of the group, I've seen them offer more than the
> average on the UK version, which puzzled me quite a lot.

I imagine it is about risks.  Many gameshows take out insurance 
policies against the larger payoffs to protect the show and network 
from big winners.  I believe Who Wants to be a Millionaire actually had 
some difficulty with their insurance when they were paying out too 
often, or something.  Perhaps the UK Deal or No Deal didn't want to 
risk increasing their premium :)

But even the contestant has a reason to not just play the average, 
thereby bringing psychology into the game.  It comes down to the odd 
phenomenon that the value of money isn't linear to the amount of money 
in question.  If you're playing the game, and only two briefcases are 
left -- 1,000,000 and 0.01, and the house offers you 400,000... take 
it!  On average you'll win around 500,000, but half the time, you'll 
get a penny.  Averages break down when you try to apply them to a 
single instance.  On the flip side, if you think about how much 
difference 500,000 will make in your life vs, say, 750,000, then taking 
a risk to get 750,000 is probably worth it; sure, you might lose 
250,000 but on top of 500,000, the impact of the loss you would suffer 
is significantly lessened.  In the end, it comes down to what the money 
on the table means to *you* and how willing you are to lose the 
guaranteed amount to take risks.

It's similar to the old game of coin flipping to double your money.  
Put a dollar on the table.  Flip a coin.  Heads, you double your bet, 
tails you lose it all.  You can stop any time you want.  The expected 
outcome is infinite money (1 * 1/2 + 2 * 1/4 + 4 * 1/8 ...), but a 
human playing it would do well to stop before the inevitable tails 
comes along, even though mathematically the house pays out an expected 
infinite number of dollars over time.  Exponential growth in winnings 
doesn't offset exponential risk in taking a loss because, once you hit 
a certain point, the money on the table is worth more than the 50% 
chance of having twice as much.

Chip

-- 
Chip Turner                   cturner at pattern.net