Friday, January 18, 2008

Breaking the Game

To Solve the game is to determine all the possible endings from any given state
To Break the game is to determine a strategy from which there is no advantageous alternative.

I've heard lots of talk about solving games, but I've never heard anyone else discuss (or at least use the term) breaking them. Is the concept out there but just known known by a different term?

To elaborate on the definition above, I understand breaking a game as finding a strategy (or trick, or technique) that any player must adopt or, to the degree that they do not adopt it, they lose. The idea of games being breakable first occurred to me when reading Ender's Game by Orson Scott Card. In brief, a tactical prodigy in a military school breaks the zero-g combat simulator by realizing that a combatant can use his disabled legs, doubled up underneath him, as a shield. This technique gives such an advantage to the team employing it that all other strategic variation is, at a stroke, ironed out of the equation.

As I think about this, I'm getting echoes of summer afternoons playing Super Nintendo fighting games. The relative lack of variety in possible moves in those early games often led to complaints that one of the players was being "cheap" in ceaselessly exploiting a particularly effective move or combination. Other players then had to either keep getting beaten, adopt the tactic, or stop playing. (Find a counter would be a 4th option, but if a strategy is counterable then it's not longer a "breaking" strategy. In fact, wouldn't the counter now in a sense be the game's breaking strategy?)

Going somewhat further afield, I can see that if the idea of "game" is expanded to encompass all competitive scenarios, then breaking strategies could be anything that forces players to adopt it or cede the field. Ranged weapons is perhaps one example. (See Agincourt, Battle of) I can conceive of other candidates (Fosbury flop, baseball steroids) but in the real world it's easier to think of counterexamples or edge cases which would allow survival despite the strategy.

So, returning to the world of games meaning something more akin to its casual usage, has anyone else thought about this? In computer games, broken games, especially when broken by betas, usually lead to play balancing. After all, when a game is broken it ceases being fun because there's no strategy. Or rather, there's only one strategy. But now I wonder how it's possible to draw a meaningful line between a breaking strategy and...I don't know, a game goal? "Don't screw up" sounds like it fits the definition of a breaking strategy, but it doesn't make the game feel broken. Maybe it's that constraint of choice that's at the heart of the idea that the effect of "breaking" is to undo the essence of a game.

By way of example I propose Tic-Tac-Toe and Ghost.

Tic-Tac-Toe has been Solved. It's a few hours worth of work, days at the most, to brute force through every possible outcome from every possible game state. The end result is essentially a table listing the implications of any given move. If the players were truly playing to win there would be essentially no "strategy" any more complex than looking up the possible moves in a table and picking the one that forced the game into the ply containing the most advantageous outcomes for the player. It's not really "playing", anymore. If you proposed a casual game of tic tac toe to someone and they pulled out a Tic Tac Toe table you would be very unlikely indeed to stick around.

The nice thing is, though, that most people don't walk around with phonebook-sized outcome tables for tic tac toe. So the breaking strategy, if employed, does retire the game, but its not generally feasible. Therefore, despite being Solved and thereby Broken, it seems that Tic Tac Toe is still a viable game.

Ghost is a similar game to Tic Tac Toe in that it has very simple rules and a large but finite universe of outcomes and moves. In Ghost, players alternate proposing a letter, trying to avoid being the first to propose a letter that completes a word. Because all moves must contribute to a valid word, the apparently open game is in fact very determinative and can thus be both Solved and, to a greater degree than tic tac toe, Broken. As pointed out most recently by xkcd's Randall Munroe, Ghost can be won by any player who can memorize a short list of words. This means Ghost is more susceptible to breaking than Tic Tac Toe because the strategy is easier to deploy. Essentially, if you want to win at Ghost, you can.

So, what of it? This proposes to me a few insights and a few questions. First, Tic Tac Toe and Ghost are still fun, that is, people still play them. This suggests even in simple games there are really two goals, not one: Playing and winning. In broken games, it becomes clear that players often mutually subordinate the goal of winning to the goal of playing. (Or, perhaps, tacitly rewrite the rules to excise the breaking strategy while vigorously pursuing victory under the modified rules.)

This also gives insight into the idea of a strategy being "cheap". It seems that breaking strategies have the effect of deflating the gameplay experience by removing the "play" from it. Therefore, the social distaste, the sense of "cheapness" that other players feel when having a breaking strategy deployed against them, is not so much a response to being foiled at the "winning" goal, but in being foiled at the "playing" goal.

Lastly, I'm curious if anyone can come up with other examples to flesh out my list below. The brief survey I came up with suggests that there is partial overlap between Solvable and Breakable games, and that not all games are Solvable or Breakable. Are there any Solved games which haven't been Broken? These are just ideas from off the top of my head; I haven't done any deliberate research. Is there more to this?

  • Checkers has been Solved
  • The Battle Room has been Broken
  • Tic-Tac-Toe has been Solved and Broken
  • Prisoner's Dilemma has been Solved and Broken
  • Ghost has been Solved and Broken
  • Nim has been solved and broken
It occurs to me that another possible definition of breaking the game would be simply "Taking the skill out of it" or "Rendering it meaningless as an indicator of the tested attribute". A propos that latter definition I append an idea that I've been kicking around for awhile which is: On the SAT, wouldn't it be ballsy-awesome to prove you're damn smart *and* show contempt for the whole process by getting them all wrong? On a multiple choice test with 4 possible responses, you'd get 75% wrong by pure chance, but to get 100% wrong on a, say, 160 question test you would only have a 0.00001005658% chance of getting them all wrong. That is to say, the powers that be must either deny statistics or admit that they have no empirical grounds for preferring your score over another candidates. (Or, lets be honest, for ranking it below anyone's, which they would do anyway. No one ever said being an iconoclast was a bed of roses.)

Parts of this article are a rebuttal in spirit to a rather nasty piece of work I stumbled across at a "game design" site. It argues (in the strongest language) essentially that winning is the only goal of play and that playing to win is the only acceptable form of play. Choosing not to employ and exploit or breaking strategy is the mark of a "scrub" and grounds for ridicule. See if it sticks in your craw, as it apparently did mine. Link defaced so as to not provide Google ranking.

Edit: TV Tropes has a some good examples, including how certain cards are banned in Magic the Gathering tournaments and certain characters are disallowed in Street Fighter tournaments.


Fidus Aelius said...

Five paragraphs into the article you mentioned and already I'm fuming. I find his arguments poorly constructed and his reasoning grossly fallacious.

We call this one a "Donut" fallacy or a false dichotomy. He insists that there are only two kinds of donut, plain ("scrub") and chocolate ("player"). How about all those other flavors of people who play for various degrees of fun and skill?

Urge to kill...rising!

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