## Monday, December 28, 2009

### Some Finer Points on Skill and Luck

Let's say that a game gives me two opportunities: I can try to pick a black card from 2 red cards and 1 black card, or I can try to pick a black card from 99 red cards and 1 black card.

I have a 100% chance of successfully choosing the opportunity that I want [1]. There is no waiting for the results, no possibility of error, and nothing my opponent can do to prevent or overturn my choice.

Nevertheless, the game doesn't end after that choice. Once I have chosen, I must still pick the card and await the result. Between the time that I chose my opportunity and the moment that the card is revealed to me, I contribute nothing to the game. There is no skill I can exercise, no feat I can accomplish. All I can do is await the outcome. [2]

In a game of Chess, when I choose to make a legal move on my turn, there is a 100% chance of my move occurring. Between that move and my next move, my opponent may respond in many different ways. There is no skill I can exercise, no feat I can accomplish [3]. All I can do is await the outcome.

The difference between these two games is that in the former case, I await pure chance to determine the results, while in the latter case, I await the skills of my opponent to determine the results. In either case, I can be lucky or unlucky. Luck in picking cards is obvious. In playing Chess, luck may have to do with my opponent's mental state, somehow having hit a blind spot in his evaluation or knowledge, his having a weakness to which I played [4], and so on.

Here's a third game: I'm shown the location of the black card in a set of three cards, and then I go read a book. Now I come back and have to remember where the black card is. I remember that it's not the right card, but I can't remember if it is the middle or the left card. I decide to pick one of those two cards.

My choice is partially skill and partially luck [5]. My skill has reduced the amount of luck. After my decision, I must again await the result of my choice.

If I play the game a dozen more times, I will win every time - no luck involved. The first time I played, I didn't realize how hard it would be to remember. Or, perhaps, I hadn't yet come up with a workable mnemonic system.

If the first game is luck, and the twelfth game is not luck, when does the game change from being one of luck to one of skill? After all, some people will win every game, even the first one; they have a natural skill. Some will always rely on luck.

I determine from these questions that a) my skill can reduce the amount of luck, or eliminate it entirely, and b) beyond the reach of my skill there is still luck. A wild guess. Or an educated guess. A wild swing. The hope that my opponent will under- or over-estimate my play.

If a game relies entirely on skill, it is a puzzle, or it is a foregone conclusion (e.g. tug-of-war with a baby).

Yehuda

[1] Assuming that I can evaluate the situation correctly, and assuming that my opponent can't cheat or otherwise manipulate the odds as I understood them.

[2] Roman's comment on my last post noted that, though my choice of a card is in fact irrelevant, human nature ascribes importance to the selection of the card; if the card is simply flipped at random, it doesn't feel the same as my "picking" a card. This is true, and a fact of human nature that good games exploit.

[3] Assuming that I cannot influence the decision through meta-game actions, such as trying to make him nervous. I could, however, use the opportunity to plan my next move.

[4] That can also be skill on my part, and not only luck; for instance, I may play moves quickly, thereby rattling him.

[5] Of course, it may actually be the right card, and I remembered incorrectly.