Can we create a board game better than chess?
Оригинал взят у silly_sad в Can we create a board game better than chess?
With the recent release of a brand new abstract strategy board game game 37.6 (http://376.su) I dare answer: "Yes" -- and here is my "Why" below.
What was always depressing me about chess is that the game is determined. Completely. There is an optimal strategy that guarantees a victory to (allegedly) the white, and you can not change it. Isn't it a perfect mathematical model of doom? By the moment you start the clock, the winner is determined... unless players fail to play the optimal strategy. And they certainly do, because no one knows this strategy... YET. And this is the only reason they play at all! Give it a good deep thought. You can only enjoy a game of chess if you are sufficiently ignorant about the game. The thrill of the game is in the ignorance.
Which ignorance, by the way, is rapidly dissolving. Not among humans, among computers. The lack of computational capabilities is a quantitative issue. There is nothing supernatural about humans' ability to play mathematical games. Right before our eyes computers are getting progressively more skilled in playing finite determined games. In the light of the success of Deep Blue the idea of playing determined games seems a bit degrading for a human. Are we really going to compete with computers in performing computations and running algorithms? Seriously? Anyone wants to compete with a power-shovel in digging holes?
This is why I love games with a random component. At least for now humans are better at that than our deterministic computers. We are naturally born to assess risks, despite nurturing whole bunch of misconceptions about probability theory. Wait... Why "despite"? Precisely the mistakes in our brains' wiring (such as notorious "loss aversion" and "mutually exclusive paragraphs") testify for the problems they failed to solve! We have developed these issues because we needed to deal with unsolvable problems. We evolved in the world of incomplete information, hence we are hardwired in mysterious ways for indeterministic computations (mistakes included). Perhaps, this is why we enjoy games of chance, sometimes to a detrimental extent. And after all it is a pleasure in its own right to overcome your mental limitations.
But do not mistake a game of "37.6" for a game of chance, because it is not. "37.6" is a nondeterministic strategy game. First -- strategy, second -- nondeterministic. There are no "aces" nor "trumps" in the game, all random values that come into a game are nearly equally valuable. Sometimes a player needs 6-s, sometimes 1-s. Indeed it is a players responsibility to maintain a strategy that is capable of putting any die to a good use. This feature alone requires very subtle planning and constitutes a vast unexplored landscape of potential playing skill development.
Besides that, "37.6" is almost as large as chess in terms of possible different games and positions count, perhaps even larger. I estimate the amount of random distinct games to be at least 5*10^48 (only the first 12 turns are taken into account), and the "full board" positions count as 3*10^33 (the board's symmetry is taken into account). For comparison, chess is estimated to constitute as many as 10^40 to 10^50 different "sensible" games, while checkers -- merely 5*10^20. Of course, these numbers can not be compared directly, so that I am going to explain the meaning of my estimate, what sense does it make.
The question of the game's length is a huge uncertainty. Luckily a game of 37.6 is loosely divided in two major phases: players fill the board, and then players rearrange the dice on the board. While the latter phase hugely varies in length, the former gives us a fixed length of 12 turns, and this gives us a significant minimum estimate for the game's length (some insignificant fraction of games may end prematurely (theoretically a game may be as short as 6 turns) but by excluding those games from the scope we do not enlarge our estimate). Thus, players may have reach one of 3*10^33 "full board" positions via at least 5*10^48 paths (also we assumed the minimum or below minimum branching factor for each move while counting the number). After that a game may last for many turns with the branching factor 1008 (and in order to account those rare positions with any symmetry, we may divide it by 2, even though the factor 1/2 is a certain overkill, 504 is still an enormous branching factor).
Speaking of the game's length, it is difficult to estimate, because a random game (the only sensible model we have so far) is far from a real "heavily biased" game. Although, we have two bots, using their records would be even worse, because their playing style is naturally "biased" in an inhumane manner. Typically humans complete the "early" phase of the game, so that with high certainty we may assume that the minimum is 12 turns. Using the fact that among all late-game positions there are approximately 0.0086 satisfy a victory condition, we can roughly assess the odds for a random game to last "one more turn", as a result we may say: with 1/2 chance a game lasts longer than 25 turns. Also worth noticing that in a set of transitions originating in a random position the "best" possible move is worse by absolute value than the "worse" possible move (by "absolute value" we mean how many dice become locked/unlocked), in other words from any given position it is easier to deliberately unlock dice than to lock them. This might testify for a possibility of infinite games, however the answer is not known.
In conclusion, take a look at the random component, the dice rolling sequence alone gives us 36^25 different games (of average length). Even if "37.6" will be solved, and players will know their optimal strategies, they still have 36^25 games to play, using their skill to overcome random effects. ...So lifelike! ...but much better, because the game does really depend on your skills.
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With the recent release of a brand new abstract strategy board game game 37.6 (http://376.su) I dare answer: "Yes" -- and here is my "Why" below.
What was always depressing me about chess is that the game is determined. Completely. There is an optimal strategy that guarantees a victory to (allegedly) the white, and you can not change it. Isn't it a perfect mathematical model of doom? By the moment you start the clock, the winner is determined... unless players fail to play the optimal strategy. And they certainly do, because no one knows this strategy... YET. And this is the only reason they play at all! Give it a good deep thought. You can only enjoy a game of chess if you are sufficiently ignorant about the game. The thrill of the game is in the ignorance.
Which ignorance, by the way, is rapidly dissolving. Not among humans, among computers. The lack of computational capabilities is a quantitative issue. There is nothing supernatural about humans' ability to play mathematical games. Right before our eyes computers are getting progressively more skilled in playing finite determined games. In the light of the success of Deep Blue the idea of playing determined games seems a bit degrading for a human. Are we really going to compete with computers in performing computations and running algorithms? Seriously? Anyone wants to compete with a power-shovel in digging holes?
This is why I love games with a random component. At least for now humans are better at that than our deterministic computers. We are naturally born to assess risks, despite nurturing whole bunch of misconceptions about probability theory. Wait... Why "despite"? Precisely the mistakes in our brains' wiring (such as notorious "loss aversion" and "mutually exclusive paragraphs") testify for the problems they failed to solve! We have developed these issues because we needed to deal with unsolvable problems. We evolved in the world of incomplete information, hence we are hardwired in mysterious ways for indeterministic computations (mistakes included). Perhaps, this is why we enjoy games of chance, sometimes to a detrimental extent. And after all it is a pleasure in its own right to overcome your mental limitations.
But do not mistake a game of "37.6" for a game of chance, because it is not. "37.6" is a nondeterministic strategy game. First -- strategy, second -- nondeterministic. There are no "aces" nor "trumps" in the game, all random values that come into a game are nearly equally valuable. Sometimes a player needs 6-s, sometimes 1-s. Indeed it is a players responsibility to maintain a strategy that is capable of putting any die to a good use. This feature alone requires very subtle planning and constitutes a vast unexplored landscape of potential playing skill development.
Besides that, "37.6" is almost as large as chess in terms of possible different games and positions count, perhaps even larger. I estimate the amount of random distinct games to be at least 5*10^48 (only the first 12 turns are taken into account), and the "full board" positions count as 3*10^33 (the board's symmetry is taken into account). For comparison, chess is estimated to constitute as many as 10^40 to 10^50 different "sensible" games, while checkers -- merely 5*10^20. Of course, these numbers can not be compared directly, so that I am going to explain the meaning of my estimate, what sense does it make.
The question of the game's length is a huge uncertainty. Luckily a game of 37.6 is loosely divided in two major phases: players fill the board, and then players rearrange the dice on the board. While the latter phase hugely varies in length, the former gives us a fixed length of 12 turns, and this gives us a significant minimum estimate for the game's length (some insignificant fraction of games may end prematurely (theoretically a game may be as short as 6 turns) but by excluding those games from the scope we do not enlarge our estimate). Thus, players may have reach one of 3*10^33 "full board" positions via at least 5*10^48 paths (also we assumed the minimum or below minimum branching factor for each move while counting the number). After that a game may last for many turns with the branching factor 1008 (and in order to account those rare positions with any symmetry, we may divide it by 2, even though the factor 1/2 is a certain overkill, 504 is still an enormous branching factor).
Speaking of the game's length, it is difficult to estimate, because a random game (the only sensible model we have so far) is far from a real "heavily biased" game. Although, we have two bots, using their records would be even worse, because their playing style is naturally "biased" in an inhumane manner. Typically humans complete the "early" phase of the game, so that with high certainty we may assume that the minimum is 12 turns. Using the fact that among all late-game positions there are approximately 0.0086 satisfy a victory condition, we can roughly assess the odds for a random game to last "one more turn", as a result we may say: with 1/2 chance a game lasts longer than 25 turns. Also worth noticing that in a set of transitions originating in a random position the "best" possible move is worse by absolute value than the "worse" possible move (by "absolute value" we mean how many dice become locked/unlocked), in other words from any given position it is easier to deliberately unlock dice than to lock them. This might testify for a possibility of infinite games, however the answer is not known.
In conclusion, take a look at the random component, the dice rolling sequence alone gives us 36^25 different games (of average length). Even if "37.6" will be solved, and players will know their optimal strategies, they still have 36^25 games to play, using their skill to overcome random effects. ...So lifelike! ...but much better, because the game does really depend on your skills.
(
Comments |Comment on this)