Games, Game Theory, and Puzzles

The difference between games and puzzles is that puzzles are static; games have an opponent or an element of randomness. Both have a goal; you can solve a puzzle or win a game.

The difference between toys and puzzles are that puzzles have a goal.

The difference between games and toys is that games have goals. With a toy, you have to think up your own goal. Building toys like Lego blocks and Tinkertoys are a bit puzzle-like in the way they respond to your actions; they don't really 'behave' different. If you built a tower out of them, though, it creates a new context. You can build a fort, or a car. But a toy like that isn't a game unless there's a goal.

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Game Theory is, well, the study of games. It's the attempt to capture, in mathematics, game-like behavior. It's typically mentioned in discussion of economics, ethics, and politics. You might built a tree of "if I do this, then my opponent might do one of these three things, and for each of his responses, here are my possible reactions...", and then weight each action by some probability and/or 'strength', eg how close you are to 'winning'.

If you play a game against a rule-bound opponent, one whose response to your actions is dictated by a formula that doesn't involve randomness, then what you have is really a puzzle. Puzzles are generally amenable to solving through logic, although some puzzles are grossly difficult to solve without tools. Simple tools would be pen & paper; maybe add a calculator. A more complex tool would be a computer program.

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To some extent, the goal of the meta-game of poker is to figure out how to turn it into a puzzle. It's not really a puzzle due to randomness, but then, I'm not talking about poker proper. You can sit down and play one hand of poker; that's a game. But if you play against the same opponent over and over again, you can start to analyze your opponent's behavior. Assign each of their actions a percentage, due to randomness. Once you've done that, game theory will tell you how to act.

Likewise, from session to session over the course of a year, you'll face many similar opponents. If you can put your opponents into buckets -- rock, fish, shark -- then you can again apply game theory to the problem.

This is what happens in many video game communities, most especially in RPGs and Sims. Players want to figure out the rules, and then from there figure out how best to beat the game. WoW players figure out where their best items drop and go farm; Sim and RTS players calculate their optimum build orders.

Game designers can do the same thing, of course. It's a great way to find the holes in your design; possible exploits; build strategies that can make the game too easy or too hard.

I guess I don't have a lot to say here. :) I thought it interesting to think that game theory reduces games to puzzles.