An article in this latest book gives some statistics on bank robbery in the United States. It's not as lucrative a business as I thought. Bank robbers get away with it 65% of the time. Chances are, the average bank robber gets away with it, but there is a pretty solid chance he doesn't. Another drawback is that they don't get nearly as much money as I thought. The average haul is only $4,120. That is quite a bit of money I suppose, but it isn't going to make you rich. You would have to rob a bank a month to get yourself to a middle class income. And a lot more than that to get rich.
When I read this, I wondered what the expected value would be? Expected value is the average value you expect to gain in an experiment with a large number of trials. In this case, you have a 65% chance of making $4,120. But how do you put a value on getting caught? You would be going to jail, I'm guessing for roughly 5 to 10 years. How much would you pay to have your freedom instead? In other words - How much would you pay for a get out of jail free card? I'm guessing conservatively that has to be worth at least $10,000 to you.
Expected Value = 0.65(4,120) + 0.35(-10,000) = -$822
We've established mathematically that crime doesn't pay.
What if we didn't just rob one bank. Let's try robbing two. Basically three things could happen.
1. You successfully rob both banks. Probability = (0.65)(0.65) = 42.25%. Payoff = $8,240.
2. You rob one and then get caught trying to rob the second. Probability = (0.65)(0.35) = 22.75%. Payoff = -$10,000. We're assuming they won't let you keep the money from the first bank and you still are going to jail for 5 to 10.
3. Probability you are caught the first time. Probability = 0.35. Payoff = -$1,000.
Expected Value = 0.425(8,240)+0.2275(-10,000)+0.35(-10,000) = -$2,293.60
Crime doesn't pay.
