Aletonomikon: The Truel (W1-2)
12 07 07 - 22:14
"Game Theory" as it pertains to economics and global thermonuclear war doesn't always offer a lot to game design. But there are quite a few interesting examples anyways that illustrate points that can be used while designing a game. One example is "The Truel". Picture a wild west town. Three men all want to kill each other, but in the most civilized way possible - they decide to have a 3-man duel. A Truel, if you will. Mister White, Mister Black and Mister Red. You're Mister White and you're the worst shot in town. How are you supposed to survive?
To further set the stage, Mister Red is a very good shot. Mister Black is a remarkable shot (why anyone wanted to piss-off Mister Black... history does not relay). A conservative estimate of everyone's skill breaks down like this.
Mister White hits 25% of his targets. Mister Red hits 50%. Mister Black has never missed a shot, he hits 100%. While our three Misters are cold-blooded killers, they're still not without a sense of fair play. It's decided that since Mister White (You) is the worst shooter, he can go first, followed by Mister Red and finally Mister Black. So, Mister White. What's the plan? Well... let's check out the options. You can aim at Mister Red. Yeah! Let's kill red! That one plays out a little like this:
You and your 1 in 4 chance of success, against Mister Red. Let's say you miss, as you're most likely to do. Your turn is over and then Mister Red is up. Now... Mister Red will almost certainly aim for Mister Black, because... you're not much of a threat. So Mister Red aims and misses. Uh-oh.
Mister Black would aim at Mister Red, too. So Mister Black aims and kills Mister Red. You're now in a duel with Mister Black. If you miss, you're dead. You have a 25% chance of survival
Stepping back a moment, if Mister Red HAD killed Mister Black, you'd now be in a duel with Mister Red. Your chances are better with Mister Red, you have a 25% chance of hitting Mister Red and a 50% chance of survival if you fail to hit him.
Let's move alllll the way back and say you get lucky with your first shot and kill Mister Red. Then, Mister Black kills you and presumably sleeps with your girlfriend. The way things played out, Mister Red might not have been the best target. If you get lucky, you actually wind up dying!
So, Mister Black it is. Again, assuming you miss (which is likely). Mister Red will aim for Mister Black and the same scenario replays itself, with you never really having a very good chance of survival. Hitting Mister Black means you have a 50% chance of taking ANOTHER shot, because Mister Red misses half of the time.
Aiming for Mister Red can turn into disaster if you hit him. Aiming for Mister Black puts you at a coin toss... 50/50, of even living to the next round! Then you have to try and hit him, so your chances of winning drop to about 12.5%.
Turns out, the best scenarios for you are the ones where you miss. In actuality, it's better for you to shoot at NO ONE. If you shoot at no one, then the scenario plays out the way we expect it. Mister Red and Mister Black will do what they need to to survive, which is try and kill each other. When that dust settles, you have the first shot in a duel - with at worst 25% chance of success. Any scenario which has you shooting second (which will happen if you hit either guy) drop your chances of winning to lower percentages. 25% isn't a lot, but it's at least a chance - certainly better than 0%, if you killed Mister Red. So let them two try and kill each other, you're better of trying to finish things.
It's an interesting type of morality - it's better not to fight sometimes. All possibilities should be explored because the optimal solution might not always be apparent.
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