Every year the Ridgefield Volunteer Firemen host a fair at ERMS. They try to raise money to fund their department. Good cause. How can we help?
Well, what if they did this, what if they introduced a new gambling game where they flip a coin. If it lands on heads, the firemen pay you $1. If it lands on tails, you must pay the firemen $1. Sounds fair. But therein lies the problem, how can the firemen make money on this game? It’s not really possible exactly because it is a fair game.
So what can we do to mix things up a bit?
What if we changed the game slightly. What if there were two coins. You get to flip one coin and the firemen get to flip the other coin. If both coins are heads, you get paid $3. If both coins are tails, you get paid $1. If the coins turn out to be a heads and tails, or a tails and heads, then you must pay the firemen $2. That sounds fair again right? There are four options, you can earn $3 or $1, the firemen can earn $2 or $2.
And let’s add one little catch. Instead of flipping the coins. You and the firemen get to choose your coin, meaning you can look at your coin and set it to either heads or tails and on the count of three you lay the coin down on the table. Still sounds fair doesn’t it, each side gets to choose what they want on their coin.
So the puzzle is this, how can this game make money for the firemen?