A Simple Bet … On Prime Numbers
Okay. So, Eve, The Magician has a new TV show with a new trick. She talks to the camera and announces:
“For one night only, I want you to stake $1 on a bet. For this, you will generate a random number, and I will do the same. If those numbers share a factor, I will give you your money back, and will pay you $1 more. Think about it, half of the numbers are even. And you can play this game as many times as you want. It’s a licence for you to print money!”
Bob is watching at home and believes it’s a good bet, as surely he will win, as both Eve and him could pick an even number, and he’d be a winner at least half the time. Then there are all the other numbers that are divisible by 3, 5, and so on. So, Bob goes to his bank and withdraws $100,000, and tries 100,000 times. In the first few attempts, Bob wins more than he loses, and so he continues. But, by the end of the night, Bob has lost $39,200, and Eve — after taking all her winnings from the other players — is a multi-billionaire. But, how could this happen?
Well, it’s obvious that if either Bob and Eve pick a prime number, then Bob will lose the bet. But, we also have co-prime numbers, and where we have two numbers that do not share a common factor. This could be 21 (3x7) and 44 (4x11 = 2x2x11).
