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GDC Austin: Raph Koster's Deceptively Simple Coin Toss

A coin toss is a simple little game, but an incredible amount of math happens between the flip and the results. Metaplace president Raph Koster used a penny as a jumping-off point for one of the "crunchier" GDC Austin sessions on Friday.
A coin toss seems like a simple little game, Metaplace president and industry veteran Raph Koster said in a GDC Austin presentation on Friday. But an astounding number of factors determine whether a coin toss lands heads or tails: the upwards force behind the flip, the lateral force, the weight distribution between each side of the coin, precession, surface irregularity, and so on. "This is a lot of math for a really stupid game," he said. So if a "stupid game" is so chock-full of math, imagine how complicated an MMORPG, or chess, is as a game. "We learn how games work, like flipping a coin, by using the scientific method as gamers" -- observation, hypothesis, experiment, and conclusion, Koster said. Unraveling a problem like flipping a coin, or designing an MMORPG quest, is where the challenge lies in the search for fun. Koster explained how breaking a game down to the molecular level can help game designers get closer to the core of "fun." He offered several examples of complex games broken down into abstract graphs. For instance, he took the strategy board game Blokus, in which four players use tiles of various shapes to try to block other players' ability to place a piece. Only corner-to-corner contact is allowed between pieces of the same color. No edges can touch, and the object is to use as many of your allotted tiles as possible. Koster plotted out a sample session of a Blokus game using dots representing the vertices of each playing tile where a new piece could be placed. By looking at the game from this perspective -- looking at just a group of dots instead of a cluster of tiles and squares -- it was clear, by counting the number of dots per each player, which color was winning. "Stop thinking about how a game looks," he said. blokus1.jpg blokus2.jpg In much the same way, he graphed out a game mechanic that MMORPGs closely follow: mmocombat.jpg Koster's session revolved primarily around what's known as Karp's 21 NP-complete problems ("NP" meaning non-deterministic polynomial time), which Berkeley professor Richard Karp wrote in a 1972 paper (PDF link). During a "bonus" section of his talk, Koster said, "A lot of game design is based on exploiting bugs" in peoples' brains. For example, there's the "scarcity principle," in which "we overvalue what we think is scarce." It makes the rare sword in an MMORPG so valued by players. There's the "commitment fallacy," in which we value things that were extremely difficult to attain, that required a large level of commitment. Koster said an MMO with a very hard first level is much like hazing in real life. "If it's hard to get, we value it more," he said. "Make some early stage [in an MMO] a massive pain in the ass, and if people make it through, it'll be like the secret club. 'I can't quit now! I got through level one!'" Koster said, "What we're doing when we flip a coin is solving that problem without knowing how we do it." We know when we press a button, we get a certain result. Removing the mystery and solving how we get to that result is what's hard about deciphering fun.

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