Tuesday, January 03, 2006

Followup on an Old Thread: Luck

Follow up to an old thread on Gathering of Engineers:

1. Dave Wilson, like me, distinguished between "after" and "before" luck. This follow-up is meant to clarify this.

Consider the following two games:

A) Each player tosses a beanbag onto a rectangle with ten squares numbered 1-10. Then a card is drawn from cards numbered 1-10. If your beanbag is on the square picked, you win.

B) A card is drawn from cards numbered 1-10. Each player tosses a beanbag onto a rectangle with ten squares numbered 1-10. If your beanbag is on the square picked, you win.

Game A is entirely luck. Game B is entirely skill. What's the difference?

In Game A, players have no information on what card will be drawn, nor any control over what card will be drawn, nor any ability to plan probabilistically for the card draw. After the card is drawn, there is no opportunity to respond. The game is already decided. Your initial toss, therefore is not the result of any meaningful decision.

In Game B, the randomness only serves to vary the game each time, after which each player can react as they like; the randomness does not determine any hardship or boon for any player. The game is entirely about meaningful decision and skill.

Now consider the following games:

C) As in game A, but the deck contains 1 of each card numbered 1, 2 numbered 2, and so on.

D) As in game B, but the field is large enough so that some of the squares are closer to some people than to others.

In game C, the results are still luck, but enough probabilistic information is given that players can make a meaningful decision to try to hit areas 9 or 10. As a Eurogamer, I would then be happy to end the game after the bags are thrown and just say that the players who hit 10 are the winners. Nevertheless, many games then require you to flip the card to determine the results (e.g. Louis XIV).

In Game D, the random draw has hindered some people and has helped others, but each player still has the opportunity to win. It's just that some have an advantage. If the advantages and boons are slight, and the game were extended to a long series of such draws, and the determination of exactly who benefited and who didn't were more hazy, the game would still interesting to the players (e.g. Puerto Rico).

2. Greg Aleknevicus said about the possibilities for cards vs dice:

Much better are the games in which no single card can be said to be better than another. Consider Titan: The Arena. Is the 10-Titan better than the 5-Titan? Not absolutely; in some circumstances it will be better but in others it will be worse

Consider the following Game X: A player must draw one of ten cards. After drawing the first card, the cards are shuffled together and the player must again draw the same card in order to win.

In Game X, each card is of equal value, but the value of a card depends on the circumstances. Yet, Game X is entirely luck.

It makes no difference that some cards are better than others in certain circumstances. All that matters is that you do or don't get the cards you need when you need them due to luck of the draw, and whether you can do anything about it; either by planning to increase your odds of success, or by reacting to the draw without undue advantage or disadvantage.

To be fair, I know nothing about Titan: The Arena, but I assume a mitigating fact is that you can draw the cards and hold onto them until you need them, so that it is less a matter of which cards and more a matter of timing.

Yehuda

Previous post by me on this topic: Dice, Luck, Bah Humbug

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