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New answers tagged game-theory

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essentially, it seems that in a more complex game, it is more likely that there will be a draw. Connect-Four is the most complex game we have solved so far, and although the first player wins, that is due to the mathematical nature of the game (i.e., it is impossible to go back to a previous position like for one side of chess). There is no proof that either ...

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One of the following is true: There is a dominant strategy for White. There is a dominant strategy for Black. There are strategies for both players that guarantee they don't lose, i.e. perfect play results in a draw (e.g. as in Tic-Tac-Toe). No one knows which is true. Most experts guess that perfect play leads to a draw, and a few believe White can ...

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Since chess is open-information deterministic game, it is bound to have some kind of optimal strategy for both players, which would result in same outcome every time, provided both players play perfectly. IMO this outcome would probably be a draw, but could be victory for either side.

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In a game where there is a scoring function, one can always rank players beyond the winner into 2nd, 3rd, etc. The real question is whether positions beyond first have any value. That question depends on many things, including player psychology, game design, and external incentives. Here are some examples of ways that this varies between games: Example 1:...

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It depends on what the goal is. Games like Scrabble or Yahtzee have scores on a fairly wide "continuum." So in games like these, it may be valid to use scores to measure "degrees of goodness." Games like Catan have scores on a narrower continuum (7 or 8, up to 10). Such games are more "binary." You either achieve, or don't achieve the victory condition. ...

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These answers seem to me to conflate two slightly different goals because of English usage considerations. Winner and "Best player" are not necessarily the same, In my Puerto Rico circle there is one player who is decidedly the "best", winning most of the time. When he loses he doesn't lose the assessment of being the "best" (most skillful) player, even ...

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Tl;dr: Players' meta-goals do affect gameplay. And unless all players have the same goals, the entire concept of "best player" isn't well defined, let alone "second best", etc. First a bit of game-theory framework. Let's say each player has a "utility function" which takes as input the game end-state and gives as output how much "utility" they get - an ...

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