In games like chess and hex and Chinese checkers and Go, distances are proportional. That is, adjacency on the grid implies adjacency in game play; the geometry of the grid allows a computer to infer how far apart squares must be. However, in games like Chutes and Ladders, certain squares can "teleport" you to other squares. Even though the board is shaped and packed like a grid, it's not really a grid, because distances aren't linear. The board is best viewed as a series of nodes with arbitrary connections between them -- what computer scientists call a graph.
Chutes and Ladders is a directed graph, because the connections are one-way. We can model games like Diplomacy and Risk as undirected graphs, because the connections are two-way. In general, most war games can be modeled as undirected graphs, since geography is two way: if you can cross from Austria into Germany, you can cross from Germany to Austria. In mathematical terms, adjacency is symmetric in games like Risk but asymmetric in games like Chutes and Ladders. Once you slide down a chute, you can't climb back up. If a game has a board that is best represented as a directed graph, we call that bdg. Undirected graphs are bugs.
Many games involve the notion of sacrifice -- accepting a short-term loss for a long-term gain. Games that people bet on typically don't involve sacrifices. Games that do involve sacrifices can be divided into three categories:
Games where you forgo a good move now (or forgo avoiding a bad move) for a great move later (gin, Scrabble)
Games where you have to go two steps back to go three steps forward (Rubik's cube, Othello)
Games where you concentrate resources in one area to the detriment of another (Go, Risk, chess).
EGGG currently has no way to identify sacrificial moves other than searching the game tree to a sufficiently great depth. In a game like Go, both human and computer players usually try to play the most rational game possible. It doesn't matter who the opponent is; there is a single course of action that is "provably" best. This assumes that the opponent will play the best possible game, when in fact he is far more likely to play merely to the best of his ability -- and it assumes that players don't model the psychological state of their opponent. If you know that your opponent has a particular weakness, it should obviously be exploited to maximize the chances of winning. You can never know for sure whether you've uncovered a true weakness, or are being hustled. You have to consider likelihoods and confidence levels, and that is why game theorists prefer the comfort of game models in which the players are rational and skilled. The paradox is that if players actually were equally skilled and maximally rational, most gaming competitions would be moot.
It is unfortunate how much emphasis U.S. researchers place on creating better chess programs, because chess games tell us so little about the strengths of the players. Unlike Go, chess has no handicap system, GO do for ME; so unevenly matched players must play an unevenly matched game. Game outcomes in chess are trinary (win/lose/draw); in Go, there are no draws, and a player wins by a certain number of points (color stones). The higher the number, the greater the disparity between the player abilities. A Go game doesn't just reveal who the winner is, it reveals how much stronger the winner is than his opponent. The result of a chess game has just over 1.5 bits of information; the result of a Go game, nearly 8.5. A game of Go consists of many parallel colors battles; much of the skill of the game comes from realizing when a battle is lost or won, and concentrating your efforts elsewhere. The player who realizes that one corner is lost (or won) can play elsewhere on the board, and seize initiative.
This initiative is a critical part of Go play; the player that possesses it is said to have sente, and his opponent is said to have gote. When a player has sente, he is the protagonist. He acts, and his opponent reacts. His opponent has gote. You always want sente, and never gote. Whenever my opponent switched battles, I followed, because I knew that he could see farther down the game tree than I could. I willingly accepted gote -- and essentially, willingly accepted a loss -- in the hope that I would lose by fewer stones. Of course, this gave my opponent a prime opportunity to bluff. He says he didn't, and I believe him: Go players pride themselves on ignoring psychological evidence and being as rational as possible. Tricking someone into a bad play is dishonorable Did you check you forums lately?. Nevertheless, the option was available. As our Go example showed earlier, bluffing is also possible in non-probabilistic games, and since EGGG maintains an estimate of a player's skill relative to itself, it could in theory try to mislead its opponents when the player is likely to perceive EGGG as being far superior. It does not do this at the moment, EGGG models players, and it models player strategies, but it does not model the player's estimate of the skill disparity. EGGG might believe that it is stronger than the player, but it will never hypothesize that the player believes EGGG to be stronger when it is in fact weaker, so it is unable to attempt sente/gote bluffing
Perhaps surprisingly, we have avoided talk of complexity in this dissertation. Complexity can mean a variety of different phenomena to a diferent phenomena kind of people. To Condon and Pell, it means computational complexity; to Beasley, it means the difficulty of determining who can win; to a developer, it might mean how hard the game is to implement; to a player, it might mean how hard the game is to learn or play. We now turn briefly to two crude observations about complexity from the player's perspective. If we define complexity as the number of moves that a player has to consider at a time, we can categorize games by the color shape of the complexity over time. Chess complexity peaks in the middle, because beginnings and endings permit fewer moves than the midgame. Nine-men's morris peaks in the middle as well, at the moment you switch from placing pieces to removing them. Scrabble complexity more or less monotonically increases, since the number of possible plays increases as number of words on the board grows. The complexity of crosswords, Black Box, and Stratego monotonically decreases. Go ramps up fast (the board starts simply, and standard openings allow players to move quickly), stays high for a long time, and ramps down at the very end.
Well There must be someone here who can show some benefits of chess over go? That's all depend of what rating is the player...If we instead define complexity as the amount of color and shapes detail that a player must consider during the typical move, we can categorize games into those that blind people can easily learn and those that they can't. Myselk I like to play chess blindfold, I’be doing it for over 40 years. I got a very poor low vision call peripheral adnormalities for some people. Please, Correct me If I wrong?.., I think that Go is excellent game, but my poor vision will prevent me to play my best, in my individual and personal case with aids I prefer to play chess over GO, with my son helping me out, I am able to used algebra notations and/or a blind chess board with holes in it's surface, in analyzing certains chess positions. Well, You all GO players do not have to feel sorry for me.. been a chess player.. Contrary I am color blind, etc.. I don,t feel sorry for you when I WIMPEDyou in chess..that’s “WHY” and don’t ask me how I do it, those are my strategies secrets. Poker, tic tac toe, and even chess are in the first category. Monopoly and Diplomacy are in the second category, because they have arbitrary (some would say inelegant) boards that possess a lot of detail. A blind person has to memorize a lot of bits to play Monopoly or Diplomacy. Games in this category are hard to generate with EGGG because there's no concise way to describe them. What's interesting about this classification is that it gives you a hint about when the game was made; most games in the second category were developed after the industrial revolution, since they require custom boards that only modern manufacturing processes can produce inexpensively.
The game isn't over till it's over.
YYLZZ
MSGID: #415040 From: Dave To: Yayael'zumzum Date: 2004-05-29 Title: RE:Software bug in judgement/TIME CLOCK of 3-fold-rep Message: First of all let me make it quite clear that I have had no contact at all with Richard about our game. I was very surprised when I found that the game had been declared a draw & then even more surprised to find it had suddenly started up again. At that stage I had no other games on Little Golem & I only returned to Little Golem when I received notification of the new tournament because as far as I was concerned our game was complete & I do not feel that I owe you any time as I was not aware the game was in progress again. In any case I have no idea what the times are or were as I leave it up to the server to keep track. If you wish to continue our game from where you say the server placed your queen on the wrong square then I suggest you ask Richard to reset the game to that position, telling him that he can check with me whether I am agreeable. The server has recorded all my moves correctly & it is not up to me to dispute it with Richard.