261–270 of 285 posts
Related, here is one that plays 6x6 perfectly: https://mame.github.io/6x6-reversi-oracle/ via: https://twitter.com/mametter/status/1476379841004183556 I didn't know 8x8 was unsolved until now.
I can't get one single black... it's this what perfectly means?
This is cool. I solved a simpler game about 15 years ago that my brother and I used to play: an African game with about 10 pits on each side of the board that hold stones. I coded up an alpha-beta engine for it, and discovered crazy always win strategies to match how my brother and I played. Suddenly I would win all the games, and then he never wanted to play again. This was a classic match up of a computer scientist…
I can't remember the source for it (help me out if you know it), but people only like to play games when they're in the band of 30-70% winrate. Win too much or too little, and they'll stop enjoying playing the game.
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Does this paper render the championship moot? Is any software based on the paper entered? Is Othello like checkers, where there were mostly draws in high level games?
This paper "weakly solves" Othello. That means that we know for the initial board state both 1) the final win/lose/draw outcome (it's a draw), and 2) the sequence of moves that should be taken by perfect players to get there (Figure 1, right). In particular, the paper does not "strongly solve" Othello. If you have an arbitrary board state, 1) and 2) are are not necessarily known for it. That means it's still possible…
This part is not correct. If the arbitrary board state you start from is reachable from the fixed opening state given that the other player plays perfectly, then weak-solvedness means the other player can force whatever (a draw, in this case). If not, then the question is open. I don't know Othello, but an example of a chess position that is not reachable from the standard opening position is one where White has 8 pawns (so none have been promoted) but two bishops on white squares -- such a position can never arise through a legal sequence of moves. If we pretend for a moment that chess has been weakly solved as a draw, another example would be a position where White has only its king left, while Black has two rooks -- in this situation, Black can force a win, which implies that this is not a position that could ever arise under perfect play from the standard opening position, since that has already been proven to always result in a draw.
I found it helpful to (re-)derive what "forcing a draw" actually means, maybe you will too: Player 1 can force a draw from board position B in k moves or less iff, on their turn, (1) it is already a draw or a win for them, or (2) k >= 1 and they can play a move that draws or wins immediately, or (3, the inductive case) k >= 2 and they can play a move such that, for every legal move that player 2 could then play, player 1 can force a draw or win from the resulting board position in k-2 moves or less.
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Implementing these rules can give you a fairly decent opponent and it's interesting to see how quickly people will ascribe "intelligence" to something that is very simple. Who is actually "ascribing intelligence" to this? Othello has been on $10 LCD games that take double AA batteries.
People see something behaving based on some very simple rules and assume that it is “thinking”.
Someone had to come up with the heuristics and then baked it into rigid rules. For the outside observer it's impossible to tell if it's baked or if it's being intelligently decided on the fly.
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Does the board size matter here? Wouldn't the strategy from 8x8 board somehow generalize to bigger boards? The one issue that I can possibly see is even vs odd board sizes, e.g. play on 9x9 board can be a bit different than 8x8 or 10x10.
Solve a 2x2 Rubik's cube and see if that helps solving a 4x4 ^^ From the computer point of view, it's more possible states to explore, so I think it makes things much harder
I would love a Wikipedia list article of games that have been solved computationally and but also games where humans can still beat computers / AI, discussing the challenges and context behinds wins / losses.
Are there any board games left where humans beat the best computers? On a related note, are there any Wikipedia list articles which are empty lists?
One of the first games I've coded as a kid was Othello. "Othello is now solved, computationally proved that perfect play by both players lead to a draw." I could never win against my creation :-)
Othello is a great game to demonstrate how powerful some basic heuristics can be. There are certain squares that you should avoid placing pebble on as the game develops - equally there are squares that you should definitely try and place a pebble on if you can. Implementing these rules can give you a fairly decent opponent and it's interesting to see how quickly people will ascribe "intelligence" to something that is…
Implementing these rules can give you a fairly decent opponent and it's interesting to see how quickly people will ascribe "intelligence" to something that is very simple. Who is actually "ascribing intelligence" to this? Othello has been on $10 LCD games that take double AA batteries.
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And in Scrabble it's fine to use a nonsense word if nobody challenges it.
And in American Football it's fine to deflate the ball if no one measures it.