Monday, May 07, 2007

Skill vs Luck

I like games. I enjoy playing them with other people, or just using them as an excuse to unwind. I also have a compulsive need to understand and categorize everything in my life, so to that end, here's a little classification I came up with for classifying games on a spectrum of skill vs luck.

On the one hand you have games that are Pure Luck. No strategic choices are made at any point, and an expert should win no more often than a complete newbie. Candy Land, Snakes and Ladders, and War are all "pure luck" games, where unless you cheat you're really just sitting back and watching the game unfold randomly. Playing War is low pressure since there's really nothing to be competitive about or strategies to worry over, and anyone can pick it up, follow the rules, and do equally well.

At the other end of the spectrum you have games that are Pure Skill. No random chance is involved, no dice rolling or drawing cards from a deck, and there's no uncertainty. Both players have an equal awareness of all the specifics of the game and a better player will almost always beat a worse one. Chess, Checkers, Go, and Othello are all examples of this type of game, and a lot of A.I. research has been invested in teaching computers to play them since they tend to map out the most logically, a fast enough computer could play any of these games perfectly, there's no unpredictable social aspects.

Coming from the other side of things, I'd think of Go Fish as a game that's about 10% Skill, 90% Luck. Most of how the game turns out comes down to the luck of the draw, although there is some memorization involved and you do have a choice of what cards to reveal to the other players. I'd say that's enough for a better player to win more often than average, but not by much.

Sorry! would be a game I'd think of as being closer to 20% Skill. The only choice you get to make is which piece to move when you have more than one out, and most of the time your options are pretty obvious, although not completely trivial. Similarly, Uno/Crazy Eight's and Masterpiece all take some basic strategy, but most of the game is in the luck of the draw and it's not at all unusual for a beginning player to master the game or win on their first try.

Above that, I'd put Monopoly, Careers, and Clue in the 30% Skill range. Most of your gameplay in Monopoly comes down to where you roll, the rest of it is about your tolerance for risk in where you put your money. There's some strategic trading in that game as in Careers. Clue is another game where you can play mostly on autopilot with a basic strategy, although it's possible to infer some of the evidence based upon what clues other people are shown.

I think of the basic trick-taking card games like Hearts, Spades, and Pitch as being in the 40% Skill range. A lot of the time your play is constrained by what suit is being led and you don't spend a lot of the time in control of where the game is going. There are some significant strategic choices however and while it's certainly possible to get lucky, skilled/experienced players would tend to win more often over the long run

Right smack dab in the middle of the spectrum I'd put Liar's Dice, Half Skill and Half Luck. With a large enough group of people there's some complex probabilities to keep track of as the game goes through its rounds, and it involves a lot of the same bluffing and social aspects as a good poker game. Anyone CAN win, but the better players tend to make it to the end pretty reliably.

Above Liar's Dice I'd place the class of board strategy games like Risk or Axis and Allies, with an arbitrary figure of 60% Skill. There's clearly a lot of strategic choices being made, even though a lot of it does come down to your tolerance for "risk". But so much of the game is social and depends upon the other player's willingness to avoid ganging up on you that it's hard to imagine it being used for serious tournament/competitive play.

Poker I'd place below the board strategy games, so I'll call it 70% Skill for now. It's clearly a game in which expert players can dominate weaker ones over the long run, but it's not a game in which the same players win the tournaments every year. After a certain level of play it seems to come down to the luck of the cards.

Bridge I think of in the 80% Skill range. It's the most heavily analyzed out of any of the games of chance, to the point where there are bridge columns in the newspaper. All of the players are aware of half of the cards during gameplay, meaning you're only guessing on a few variables as to how the cards are divided up. There's a fair amount of depth to the strategy in bidding too, and it seems to be quite complex for all its unpredictability.

Stratego is a game I'd consider to be about 90% Skill. While all the battles and movements are decided by non-randomly by the players themselves, neither player has full information about the pieces held by the other side. One player can certainly get lucky and strike down the correct path to find the flag early on or simply guess right about where his opponent is set up, but a skilled player still certainly has an edge almost all of the time. It ranks below the pure skill games just because the setup is unknown, but it still involves a heavy amount of strategy.

And there you have it. The more random a game is, the more your strategy becomes about weighing risk vs potential payoff rather than considering all possible outcomes, and the more you focus on anticipating and outguessing what other people will do. You can teach a computer to play Poker perfectly just by the numbers and going with the best odds, but you can't teach it to read people. Games of skill are predictable, just complex. Technically the outcome of a game of Chess can already be determined in advance if both players play perfectly. In Connect Four, for example, the first player can always win with a perfect strategy. It's just that most games of pure skill haven't been completely analyzed yet.

Oh, and just for fun, the graphic at the top is a classification of games by number of players, not sure what I'd want to do with it yet.

Movie Trilogies

Every movie trilogy can be classified into one of six types, depending upon how they all rank against each other in terms of quality.
  • Trilogies of declining quality ( 1 > 2 > 3)
    This is usually typical of a series where the first movie stands on its own and makes a lot of money, then a few sequels are tacked on to play off of that. I'd think of the Matrix "Trilogy" in this category, Pirates of the Caribbean, probably Back to the Future as well.
  • Trilogies with a strong first movie, and a weak middle movie(1 > 3 > 2)
    I think of the Mission Impossible movies in this category, the first movie was excellent, the second film was a Matrix/James Bond clone, and the third movie did a good job of getting the series back to its roots.
  • Trilogies of increasing quality (3 > 2 > 1)
    This is the case when the moviemaking or general quality gets better as you go. Typically in trilogies with tacked on sequels the story tends to wear thin as the special effects get better, so this may be more rare. The prequel star wars trilogy seems to fit this pattern, although that may be a special case since it took them three movies to get to the plot. The man with no name trilogy is another possible contender (the good, the bad, and the ugly series)
  • Trilogies with a strong third movie, and a weak second movie. (3 > 1 > 2)
    Another example of a weak middle chapter that made up for it later. The Indiana Jones trilogy (so far) fits this one for me, the temple of doom didn't have the same intrigue or significance as the other two, and the last crusade was simply great, you can't go wrong with both Sean Connery and Harrison Ford.
  • Trilogies with a strong second movie, and a weak third movie (2 > 1 > 3)
    The original star wars trilogy is the classic example of this one, the empire strikes back fared the best critically and a lot of people think the series jumped the shark with the ewok-a-thon in Return of the Jedi, even if it is warm and fuzzy when you're a kid.
  • Trilogies with a strong second movie, and a weak first movie (2 > 3 > 1)
    This one is even rarer, since it's not very often than the first title in a series is the weakest since that's usually the one to justify all the others. I think the x-men movies are a good candidate though, with adaptations from comic-books you have so much source material to draw from you can really make any number of movies before you get the right story, and the first film didn't do as good of a job with the characters as the other two.

I'm still somewhat undecided on how I'd rank the Lord of the Rings films or the Spiderman movies. My intuition is that for most trilogies the first movie is the best, although it may be different if the entire trilogy is conceived in advance, as in the case of Lord of the Rings, or if the trilogy is composed with a two part sequel, as in the case of Back to the Future, The Matrix, and Pirates of the Caribbean.

Update: Rottentomatoes (a site which aggregates ratings from actual critics) rates Spiderman, X-men, and the original Star Wars trilogy 2>1>3, LOTR and the Star Wars prequels 3>2>1, Back to the Future, Austin Powers and Indiana Jones 1>3>2, The Matrix and Pirates of the Caribbean and Spiderman 1>2>3, and Mission Impossible 3>1>2. Wasn't able to find any trilogies that were ranked 2>3>1.

Further Update: The Five Harry Potter movies so far are ranked 3>4>2>1>5, which is probably the order I would rank the first five books as well.