Wednesday, April 22, 2015

Movement and Game theory

This is really Corvus' and Havoc's game

Hello there everyone!  I'm here to talk about something I don't know much about and something I hope to God I know more about, those being X-wing  and game theory.  Now I don't mean "game theory" as in a theory of how you best design board games or how to make the most money off them.  No, I mean the branch of economics that talks about how people make choices in different defined settings and how the structure of those settings ("games") influences how individuals choose, how they "play the game."  If you've ever heard of "The Prisoners' Dilemma," you've heard of game theory and have a bit of a leg up.  I'm going to start out with a short discussion of the Prisoners' Dilemma to illustrate some principles of game theory and then show how it applies to board gaming and makes me rather interested in X-wing, though I've only watched part of one game.

First things first, let's walk through some elementary game theory for you with the prisoners' dilemma.  You have two prisoners who have been caught committing some minor crime in the process of a larger crime.  The police can't pin the larger crime on either of them without them confessing.  The picture at the right shows us the sentences each prisoner will receive based on how they and their partner-in-crime behave.  How the game is played has major implications in which one of the cells will occur.

Can you solve for the simultaneous NE?
If both prisoners make their choices simultaneously, they can't know what the other will do and must make a guess based on what they think the other will do.  If A has to lock in their choice before B, B can make the best choice for himself based on what A is committed to doing.  These are called Simultaneous and Sequential games, based on when each player makes their choices.  Because of how the choices are made, we can say that in the Simultaneous version of this game, the players have Imperfect information, meaning that neither prisoner A nor B can be entirely sure of what the other will do.  In the Sequential version, A has imperfect information, but B has perfect information on what A will do before he makes his choice.  The Prisoners' Dilemma is a good framework to understand these terms, but we can move on and leave them in their cells.

Looking at 40k and WM/H when it comes to movement we have games where we have sequential decision making where your opponent has perfect information on what you have done as soon as you decide to do it.  There are some instances in WM where you can move out of sequence, e.g. countercharge, but for the most part, when you decide to move your models you know exactly where your opponent's models will be and whether they will be able to move out of sequence in a way you can or can't anticipate.  There's still some very important imperfect information that makes your choices exciting (dice variance), but as far as movement goes, the game is rather dull, which may be why so few people stress how much of the outcome can depend on your movement choices.

X-Wing, from what I've seen is quite different.  There's a much lower model count than even the most beast/jack heavy list in WM/H and extremely little terrain, but the movement in that game has me a bit fascinated.  First off, models can't move freely up to a certain distance as they can in 40k or WM/H.  Models can move a certain "distance" up to their movement stat during a turn and can only move in certain increments based on their front arc.  They don't have to move it all at once and players alternate moving models during the turn, but must commit to some movement with each model simultaneously and in secret.  For instance, I could have a tie fighter with move 3 and I'm not sure how you're wanting to move your x-wing, but I'm in position to shoot you, so I can choose to only go 1 directly forward and later do what I need to do so I can follow your moves and shoot you down.  You can see where my model is, but you can't know where I'm going to move to  when you make your decision to move your x-wing.  Once we've made our choices we go to move our models and I reveal my choice and move, then you reveal and make your move.  Once we've done this for all our models we begin using up the rest of our movement on each model, alternating our choices until they're all exhausted.  Then comes the flashy bits of shooting, but that's less interesting.

So while movement in 40k and WM/H is essentially a sequential game with perfect information, in X-wing it'snot just one game structure.  It's a two stage game: in the first we have simultaneous choices and imperfect information, in the second we have sequential choices and perfect information, but how we behave in the second stage depends on how we and our opponents behaved in the first stage.

Maybe I'm just a nerd, but I'm really excited to see game designers mixing up the structures of their games and making the choice structures more diverse.  If I can get time, I would love to see what I could dig up on some cooperative board games like Arkham Horror and how I could analyze them.  Really, I just want to play some Arkham Horror.  Any interesting game structures that sparked your interest?

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