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Pig Redux
We first examined the game Pig in Games as Systems of Uncertainty. In Pig, the goal of the game is to score points by rolling a die and adding to your score until you reach 100 points. If you roll a 1, then you lose the points you earned that turn and pass the die. Otherwise, you keep rolling to try to increase your score. You can always decide to stop rolling, at which point you add your current total to your overall score and pass the die to the next player. The game is very simple. But is it truly fair? Does the first player have an advantage? Because Pig is about accumulating a score, turn after turn, it does favor the first player: that person has an added chance of reaching 100 first. If there are five players and on the tenth turn the player that went first scores 100 points or more, that player wins. But some of the other players, who only got to play nine rounds, might have reached 100 if they had been allowed a tenth turn as well.
Pig embodies the classic game design problem of creating a level playing field. Ideally, every player should have an equal chance of winning. So what is the solution? There are a few possible game design adjustments. One solution is that the winner of the previous game gets to go first, as an added reward. But this does not solve the problem of deciding who goes first in the very first game. Should the winner be rewarded in this way? Doing so creates a positive feedback loop, which might unbalance the game. Should the player with the lowest score go first? Neither of these solutions create fairness for all players. Another solution is using a random die roll to determine player order. The player that rolled the highest number goes first. Even though a great many games use this method, it is not necessarily the best solution to the problem. Will it feel fair to all of the players? For example, because play proceeds around the circle of players, the player that rolled the lowest number may end up as the second player, if that player is sitting next to the person that rolled the highest number. In any case, even if the order of players is randomly determined, the player moving first still has an advantage over the other players, and the inequality remains. Yet another solution would be to play the game a number of times equal to the number of players at the table, rotating which player goes first. If there were ten players, they would play the game ten times. Each time, a different player would go first. Players would either add up their scores for a grand total or the player who won the most times would be named the overall winner. This solution works mathematically to equalize the game, but it suddenly transforms the casual experience of Pig into a structured tournament. What if you only want to play a game or two and not an entire series of games?[7]
We borrowed the game of Pig from Reiner Knizia's book Dice Games Properly Explained. Knizia notes this very inequality and suggests the following as a variation: when a player reaches 100, all of the rest of the players get to roll once more and finish the round. If more than one player ends up exceeding 100, the player with the highest score wins.This is better than any of the previously proposed adjustments, but even this well-designed solution is flawed. In Knizia's solution, it is best not to be the first player to reach 100, because all of the other players know exactly the score that they need to win, and they will push their luck in order to beat the player that is about to win. It is actually best if you roll last during the final round. Because the player that went first at the beginning of the game is mathematically more likely to be the first to reach 100, it ends up being a slight disadvantage to be the first player. Even in a very simple game such as Pig, there is no perfect solution that offers absolute equality for all players. But luckily, players are not perfectly rational beings. They are human, and the best solution is not necessarily the best mathematical answer to the question of equality, but the one that feels right within the context of a game. Absolute equality, like pure randomness in a computer algorithm, may be a myth. But as long as the feeling of equality persists within the game, players will keep the faith and enter into the magic circles you design for them. As a final thought, is fairness itself something that can be put at play in a game? We have suggested that other components of game conflict, such as competition and cooperation, or achieving game goals, could be challenged through innovative game designs such as Catch the Dragon's Tail. Does this extend to the level playing field of a game as well? Perhaps. But it is a very complicated question. In the next schema, Breaking the Rules, we do our best to answer it. [7]Reiner Knizia, Dice Games Properly Explained (Tadworth, Surrey: Right Way Books, 1992), p. 128-30.
