Why is a home-team game more interesting? It's about you. An adventure movie is more exciting when you are emotionally invested in the hero. The perils and progress of a company like IBM or Microsoft matter more when you own the stock.
You'll notice the last situation is an example of excitement generated from a contest than can materially affect you. Let's consider another such contest. This one is unfortunate (We would say insane): racing a train to a railroad crossing. The wager is the driver's life. The winning payoff is strictly a bit of excitement. This is how it looks as a mathematical formula. Don't be put off by the equation. The math is simple. Any bet can be analyzed this way.
Wager = desired outcome/all possibilities x payoff Here is the same formula with the contest values in place. Driver's Life = 1/2 x excitement
There are two possibilities and one desired outcome. We are assuming that both possibilities have an equal chance of happening, so the foolish driver has a 50 percent (1/2) chance of getting across. Some people might express this formula differently, with additional fractions, or they might use other terms (like risk, reward, or odds), but I've written the formula this way to make a point. We set a value on a wager when we bet. We are purchasing an opportunity for a desired outcome. Wagering more than we can ever expect to receive is the same as devaluing our bet. This formula shows the driver's life as equal to twice the pleasure of beating a train. Is that a smart bet? Of course it isn't. The driver is throwing his wager (his life) away.
The decision is easy (for most of us) when the bet grossly outweighs the payoff, but it's tougher when the two sides are closer to being equal. Remember, payoff isn't just money. It's the pleasure of a contest, the satisfaction of making the correct choice, the enjoyment of tangible and intangible rewards.