Game Theory

So I don’t know much about game theory, as a scientific or mathematical entity. That’s why I’m prepared for this entry to be shot full of holes by the people who read this and are much better at logic and math than me. Regardless:

When players come to a board or card game, they typically expect to compete against other players and, implicitly, the randomized elements of the rules. If the players are unable to effectively respond to those randomized elements, the game is perceived as an empty exercise by most people above the age of six. Candy Land and War are two good examples. Chance is king, unless you cheat.

I think it’s fascinating that people who would brush off Candy Land and War would still play slots, despite the fact that it’s exactly the same exercise, and the average reward for playing slots is negative. But that’s a different topic. Or is it?

Some board games, like chess, involve no elements of chance at all–they’re entirely driven by player choice. Chess is obviously a thrivingly popular game, so why introduce elements of chance to any board game?

I’m honestly curious about this. I’ve been trying to come up with good reasons, but they seem to fail under test. “It’s interesting to see something unexpected” fails, because you can certainly see unexpected things from the other player in a chess game. “I believe that the odds might favor me and help me win against a more experienced player” fails, because I’m smart enough to know that in the average case, they’re going to favor that other player just as much, and I’m going to lose just as often. But I like games that incorporate both skill and luck more than skill-based games.

Do you? Why?

IMO -

In some games, it is the best, or simplest, way of representing that which falls outside of the remit of the game. To take Risk as an example, it allows - forces - players to ignore the untold miriad of factors that would be neccessary in an accurate depiction of a battlefield, and instead directs their attention to the business at hand, the tactical control and defense of territory. It it conceivable to combine Risk and Chess - have one as a sub-section of the other - but that would be too complex a proposition for the game market, which must sell to the masses and thus needs a degree of simplicity.

On the other hand, we end up with the Total War series for the PC, which does just that - combine tactical territory control with simulated battle micro-management - but still there is a neccessity for randomised elements to battles, or the infinite minuate of full battle simulation would overwhelm the player. Chess, which removes the randomisation, is thus more tactical and skill based, but also far less accurate, and more of a simplification of actual battle.

Ultimately, I guess, it’s to do with versimilitude. Chess and Go are great games - two of my favorite games - but they are representative, or iconic, at best. They belong to a certain mindset, one -without wanting to be too bullshity - more contemplative or meditative than Risk or War or AD&D, and not just because they require more skill, but also because they offer an impressionistic interpretation of reality, rather than an attempt at recreation.

So, two sides to the coin - there has to be a random element to some games, as there is a randomness, or at least and unfathomable (and probably deeply boring, in game terms) order, to life itself; on the other hand, there is a need for instant gratification from games, and people can’t always be expected to deal with too much and still be entertained.

I would also add that I consider computer simulations, such as the Total War games, to be the worst of both worlds. One thing I like about Chess is the crisp definition of the tactics, the sense of clearly regulated cause and effect, and the ability to plan, all of the the TW games remove through their impossibly abstract number-crunchery, with the morale and weather conditions being calculated to the n’th decimal place… Whereas what I like about Risk is the ease and immediacy of play, which TW removes with micro-management and petty beaurocracy. I think there is a line of reality that games are not meant to cross.

I second Josh’s notion that games have randomness to simulate real life, and I will further answer your question with my book-learnin’. In my AI class (which had nothing to do with AI except in a dead-end 1980s sense, but which had a lot to do with the fun topics of Lisp and games) I learned that a random element is a really cheap way to blow up a decision tree. I think that games use randomness to shape the decision tree, and that’s why games aren’t neccessarily improved by randomness removal.

Consider Risk or another simple wargame. With randomness, even if you launch an attack with a superior force you must plan for the contigency that you will fail. Without randomness, you could always plan exactly how to deploy your units. This would let you go deeper down the decision tree, and you’d have a more chess-like game. And that’s fine, but there are all different sorts of games, and randomness is the easiest way to create a decision tree so complicated that you can’t go very deep. It’s not that you might win or lose despite the odds; it’s that you have to *plan* for losing despite the odds.

Second, and less important, there’s a thrill in gambling that’s an end in itself. That’s why RPGs have critical successes, and why people play slot machines instead of Candy Land. The negative payoff of slots is a fee you pay for having that gambling thrill. It’s like buying a ticket for a roller coaster.

Third, and least importantly, some games are just eye candy. I’ve hated Candy Land ever since I first realized that nothing you could do would affect the game, but I still have a fascination for The Game Of Life(tm), even though they’re the same game. I like the robotfindskitten-like variety of the TGOL squares; the cool, fundamentally useless props; and the idea that right next door to it in the universe of games is a really cool strategy game, better than Monopoly. Maybe I should post that idea as a story.

On the “in the average case, they’re going to favor that other player just as much, and I’m going to lose just as often” note: mm, okay, but the influence of chance still means that the odds might go your way in any particular game. Sure, they’ll go against you just as often, but in a lot of cases there’s got to be a fairly large window of “sufficiently worse at the game than your opponent that if there’s no element of chance then you’ll almost always lose, but not so much worse that you can’t win sometimes with the help of lucky draws/rolls/etc”. That your opponent will win by more than they otherwise would have, sometimes, when chance favours them, doesn’t mean that you mightn’t still be winning twenty percent of the time instead of the five percent you’d be winning without the influence of chance, which might be enough to stop the game from feeling like a foregone conclusion and thus not worth the effort.

Holly: The point you make occurred to me a couple hours after I posted this. You said it better than I would have, though.

Josh and Leonard: Thanks! Your comments are lucid and useful; I agree with you on every point. Josh, your sentence “there is a line of reality that games are not meant to cross” is pretty much the explanation for every bad RPG ever.

Leonard, your point about the negative reward of slots as a price (rather than the coin you actually put into the machine) is excellent. I share your affection for the existentialist eye candy of TGOL, and I hope you do post your mapping to a cool strategy game.

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