Aggregating risk

I'm sure this is common knowledge for finance majors, but it seemed like a surprising conclusion to me.

Suppose you have the opportunity to take a risk-- the price is $1000, and there is a 1 in 1000 chance of winning $2,000,000.  The "expected value" of this is $2000, but I would still argue that it would be a bad idea for most people to take this risk.  It's hard to come up with $1000, and chances are you would never hit the jackpot your whole life.

On the other hand, suppose you have the resources of a bank at your disposal: $100,000,000. If you played this game 100,000 times with that money, you would win around 100 times.  You would be virtually certain of approximately doubling your money. Your chance of not getting back more than you spent is tiny. It would be very foolish not to take this risk.

Isn't it odd that doing something once is a bad idea, but doing it 100,000 times is a good idea?

(Of course in the real world, risks aren't usually independent rolls of the dice like this but are correlated, which explains how the recent mortgage securities crash was possible.)


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