The statistical world: Part 1

We live in a statistical world. What I mean is that for most of the decisions we face, there are some choices that are better than others, but they do not guarantee success or even that minimal level of success, breaking even.

Tic-tac-toe is part of the mathematical world. In the mathematical world we have proof, a guarantee of success or a guarantee of failure. If two player are at the maximum skill level in tic-tac-toe, every game is a draw, because the first player puts his or her mark in the center and the second player puts the opposite mark in one of the four corners.

Not every game in the mathematical world ends in a draw. In the simple number game "How much money does your dad make?", the first player names a number and the second player can always name a higher number. There are other simple games where going second is a forced win, like certain variations of Nim.
 

Yahtzee is the commercial name for a game that has been around for a long time. It is more involved than tic-tac-toe, but at the end of the 20th Century computer scientists "solved" the game, meaning they found the optimal play in every possible situation, meaning every possible roll with even possible combination of scores you have already achieved. If you were to match two computers perfectly programmed, you would not expect a draw in every game. In fact, actual tie scores should be extremely rare. What you would expect in the very long run is that both sides would win equal numbers of games, regardless of who played first or second. (Yahtzee is really a solitaire game, though usually played in groups. My dice rolls do not effect yours and vice versa, though some players might make decisions because they are ahead or behind late in a particular game that they would not make in a true solitaire game.

Even though we know the best way to play, it does not insure victory or even a draw every time. Randomness is so great in Yahtzee that the best possible strategy might lose to some other strategy if both players are promised to roll the same values in all cases until the game ends.

This is what I mean by the statistical world. Risks and rewards may or may not be completely understood, but even if we know the odds down to exact values, randomness can produce very strange results. Tomorrow, I will discuss the idea of assessing risk, something we do not always do very well.