The Bias of Odds & Evens
Recently on National Public Radio (NPR) there was a story of how nonrandom a coin flip can be. For example, with a simple device which flips a coin with the same force every time, the coin always turns up the same way! Also, it can be an illusion that a coin actually flips in mid-air - depending on how the coin is tossed into the air, the coin might simply wobble and rotate. And finally, the coin itself can have a built-in bias, for example turning up "heads" 51% of the time instead of the expected 50%.
Like the idea of "no two snowflakes are ever alike," a truism sometimes falls apart under actual observation. (And yes, scientists have actually found two identical snowflakes.)
So if a coin flip is a biased means of decision-making, what works? Odds & Evens?
Well, no.
Let's review how to play. One person picks Odds, the other Evens. On a count of three ("One two three shoot!") each person simultaneously puts out some fingers on one hand, usually 1, 2 or 3, or even 4 or 5. The sum of the fingers results in either an odd or even number, and that person gets a point. Both sides play until one side gets the number of required points, say 3 or 5 points.
In practice, nobody ever puts out 0 fingers. This means the sum of fingers can never be 0 nor 1, only 2 through 10. How fair is that? Let's count.
| Sum | Even wins | Odd wins |
| 2 | Y | |
| 3 | Y | |
| 4 | Y | |
| 5 | Y | |
| 6 | Y | |
| 7 | Y | |
| 8 | Y | |
| 9 | Y | |
| 10 | Y | |
| Total | 5 | 4 |
- The Odds player wins 4 times out of the possible 9 combinations.
- The Evens player wins 5 times out of the possible 9 combinations.
Perhaps Rock, Paper, Scissors would be fairer.