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Subject: Is it possible to have a pure abstract strategy game where no side is favored and it doesn't draw? rss

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dale walton
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First, The basic question of this thread answers itself: If a game is an advantage for a player, it means he has a better chance of winning, but the idea of a prefect strategy game is there is no chance i.e winning is all or nothing. So if one side is favored it means on side wins. and so if neither side is favored it means exactly that it is a draw. No need to discuss how.

If The issue is to design a game in which it is unknowable who wins or who loses or whether it is a draw; this is possible if the game is not finite, which is why the theorem applies only to finite games. Many games in real life are not finite (eg have infinite loops) but if the loops are detectable rules are often added to break the loops or define them as a draw, making the game finite in states.

If one has a finite number of moves, but an infinite decision process, eg outcome depends on whether the turing machine defined by the current player stops or not, the game still has infinite states, as the rule set has infinite states, so the theorem is not applicable. But in practice, you could start playing the game with all going well for X turns, and then one player would take a turn, but after a month still not know the outcome of his move, and might never know. So is that a game? I think I won, but no one will ever know for sure
 
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dale walton
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Assuming the intent is "appears to be favored", in other words the game is still being investigated and insufficient states have been analysed to determine its actual nature -- can such a state yield surprises? - Yes.

Will a player eventually stumble on a situation whose outcome they can determine - This is normal. Will a player therefore always win? No, sometimes the best move for a player is to force a draw. This is seen in real life games.

A bad attribute for a game would be if players typically will reach a level of play that is challenging to their opponent but insufficient to recognize they are in a situation that loops or loses, and thus cannot bring the game to a conclusion as a draw. Or similarly but worse, neither perceives the winning move choices, and end up preferring looping moves.

Another thing a game should avoid is giving a perception that it is more easily solved, than it is, or that one player or another has a strong advantage, when the game is far more difficult to solve than that. This results in players avoiding the game unfairly.

And of course a game should not be so easy to investigate that one player should be able to select winning moves with a high rate of assurance, without a long period of practice.
 
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Tony Chen
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Depends on your definition of "favored." All abstract strategy games start with one player being able to force a win or a draw, with perfect play. In fact this stays true at any point in the game, though the player in the position to force a win/draw may change when one player makes a mistake.
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christian freeling
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It's the difference between looking at it in terms of Zermelo's Theorem or in terms of the limitations of the human mind. Because of recent developments in AI, every game in this category can in principle have a superhuman program alongside. Not 'all-seeing according to Zermelo' but superhuman nonetheless. Chess and Go a case in point. This may have various consequences, none of them lethal. One of them is that imo. things get more interesting rather than less.
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Maurizio De Leo
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russ wrote:
christianF wrote:
russ wrote:
I guess that in reality, such strange positions never really happen in "real life".

I'm an alien to magic but isn't the very point of abstract games that it's never really like real life? It's boxed conflict that can easily be put aside (well, by most players anyway).

I meant that such a situation won't appear in a real life game played by ordinary players who are simply playing to win as usual, instead of playing to intentionally create the weird situation.

(Similar to e.g. saying a triple ko rarely appears in "real life" games of Go, even though it's easy to artificially construct a triple ko if you want to.)


(Also, FWIW Magic is not an abstract game.)


Not to "necro" the thread (pun intended), but infinite loops happen relatively frequently in MtG. So much so that they are actually forbidden by the rules if one player has the option to stop the infinite loop (e.g. by not activating a "may" triggered ability).

Even the unconditional infinite loops are not outside the realm of possibilities in competitive play. A famous example is the pro Louis Scott Vargas drawing a game with 3 Oblivion Ring on the battlefield.

I have not read this article on complexity, but it doesn't surprise me. Magic has close to 20'000 different cards, many of which are basically algorithmic modifications of the rules.

Already many years ago they had devised a board state (totally ludicrous I must say) that behaved like a Turing tape machine.
Already some time ago they had
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Nick Reymann
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I feel like the closest one could get to this ideal are "complicated" impartial games, where any non-optimal move gives your opponent the ability to force a win. "Complicated" just means ones whose nim-values aren't easily calculated.
 
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