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The Magic Cafe Forum Index » » Magical equations » » Mathematics in Chess. (0 Likes) Printer Friendly Version

drkptrs1975
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The way I figured, there has to be mathmatics involved, or how else can you program a computer to play chess and not even the best in the world can win. I would think there are a few things that come into facture, the value of the pieces, tempo, spaces you can attack, and finally king safety, with king satety the most important. That is what I came up with.


There is no way you program every situation and board position, there is at least a few thousand positions. There is no way you can be able to do that. So what are your thoughts on this. Another related question, is this considered to be artificial intelligence.
rgranville
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There are many books on computer chess programming. Amazon has a slew. Your public library probably has or can get some.

The "standard" chess program quantifies positions, assigning a numerical value to each one based on the value of pieces, what's attacked/defended, etc. Then game tree search techniques such as minimax and alpha-beta pruning are applied. The world-class programs are more sophisticated, but I'm not up on that literature.

Quote:
Another related question, is this considered to be artifical intelligence.


Yup.

:banana:
bigdw1
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There are billions and billions of potential positions in chess that's what makes it so facinating when a human plays and beats a computer that can search faster and through more info. But, human's play creative whereas computers are not as creative.
tiberius magus
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Artificial intelligence is a non-magic interest of mine, so I though I'd pop in and comment. People are usually unclear on what they mean by 'artificial intelligence.' Commonly, this is just used to mean that a computer is doing some 'figuring out' instead of just trying every possible combination or following some predetermined list of what to do in a given situation. In that sense, a computer playing chess is a form of artificial intelligence because the computer does not store information about what to do in every possible situation.

However, the term 'artificial intelligence' is also used to refer to the idea that a computer might be able to learn, interact, solve poorly defined problems, etc in all the same ways that a human might. In this sense, chess playing is a poor example of artificial intelligence.

sincerely,
Tiberius Magus
kerpa
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Before I expound, there is one writer who was written beautifully about mathematics in chess, and even mor so about magic - that would be Martin Gardner.

As I understand it, the sheer computational power available has enabled the best chest programs ever (e.g. Deep Thought) to overcome world class grandmasters, by combining an exhaustive opening book, database of played games (we're talking about several hundred thousand), and weighted criteria, together with calculations of tens of thousands of positions in several seconds. This yields a computer program able to play at a 2400 ELO level available to everyone with a PC. The special supercomputer programs can go up beyond 2500 easily and reach world class.
By the way, my late father, himself a superb chess player, pointed out to me that Garry Kasparov, then world champion, made the typical, egotistical mistake of not insisting on a rematch before his losing match to Deep Thought. This was the same mistake Capablanca made 70 years before, when his human opponent Alekhine defeated him. Both Capa and Garry were so sure they would win, they did not bother on insisting on a rematch!! So, Alekhine refused for 15 years on a rematch,a nd IBM, to secure its publicity boost, promptly dismantled Deep Thought.
(or maybe it was Deep Blue, I can't recall).
kerpa
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rgranville
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Quote:
Artificial intelligence is a non-magic interest of mine, so I though I'd pop in and comment. People are usually unclear on what they mean by 'artificial intelligence.' Commonly, this is just used to mean that a computer is doing some 'figuring out' instead of just trying every possible combination or following some predetermined list of what to do in a given situation. In that sense, a computer playing chess is a form of artificial intelligence because the computer does not store information about what to do in every possible situation.

However, the term 'artificial intelligence' is also used to refer to the idea that a computer might be able to learn, interact, solve poorly defined problems, etc in all the same ways that a human might. In this sense, chess playing is a poor example of artificial intelligence.


As someone who has spent his entire career in artificial intelligence of one sort or another (expert systems, intelligent tutoring systems, text generation, text processing, speech processing), I can tell you a "standard" definition of artificial intelligence is any system that addresses problems or tasks that people generally agree require some intelligence.

:banana:
dr chutney
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Fascinating documentary the other night on the Kasparov v Deep Blue contest. Game Two was obviously the turning point with Kasparov convinced there was human intervention. His game didn't really recover for the remaining encounters. I love TV like this. Makes a nice change from Celebrity Airline Wife Swap On Love Island.
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drkptrs1975
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Kasparov vs Deep Blue, that was like playing against yourself. I remember it though, hearing about it on the news.
tiberius magus
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Quote:
On 2005-06-03 09:59, rgranville wrote:
Quote:
Artificial intelligence is a non-magic interest of mine, so I though I'd pop in and comment. People are usually unclear on what they mean by 'artificial intelligence.' Commonly, this is just used to mean that a computer is doing some 'figuring out' instead of just trying every possible combination or following some predetermined list of what to do in a given situation. In that sense, a computer playing chess is a form of artificial intelligence because the computer does not store information about what to do in every possible situation.

However, the term 'artificial intelligence' is also used to refer to the idea that a computer might be able to learn, interact, solve poorly defined problems, etc in all the same ways that a human might. In this sense, chess playing is a poor example of artificial intelligence.


As someone who has spent his entire career in artificial intelligence of one sort or another (expert systems, intelligent tutoring systems, text generation, text processing, speech processing), I can tell you a "standard" definition of artificial intelligence is any system that addresses problems or tasks that people generally agree require some intelligence.

:banana:



Nice to run into someone who actually has skills in an area where I have interests. I've come at ai almost entirely from the philosophical sense (Turing, Searle, etc.) so the first thing that comes to mind is the strict definition in the sense of perfect simulation of conscious behaviour, or actual conciousness, ie weak and strong ai, respectively. In spite of my head-in-the-clouds history with it, I do have a project set to come out that involves some wonderful twists on combining various ai algorithms with neural nets and genetic algorithms. One might say, from a pragmatic perspective instead of a pilosophical one, that the problem with being clear on what artificial intelligence is is not the artificial part but the intelligence part. For years many people considered chess-playing a measure of intelligence. With computers having beat humans at that now(even if it was without rematch) many people are changing their standards.

sincerely,
Tiberius Magus
Scott Cram
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If you would like to see how a computer analyzes potential moves in chess, checkout Thinking Machine 4.

On that site, you can play chess, and visually see the computer's analysis, too!
rgranville
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Quote:
One might say, from a pragmatic perspective instead of a pilosophical one, that the problem with being clear on what artificial intelligence is is not the artificial part but the intelligence part. For years many people considered chess-playing a measure of intelligence. With computers having beat humans at that now(even if it was without rematch) many people are changing their standards.


Indeed. One (seemingly never ending) frustration from being in this field is that as soon as one demonstrates that a problem can be solved (for some definition of "solved") by algorithmic means, many people then claim that this fact alone proves that the problem didn't really require intelligence in the first place. "If it works, it's not AI." After all, a hundred years ago, people would have agreed that performing arithmetic required intelligence. But while computers perform arithmetic computations faster and more accurately than humans, no one ever considered this a form of artificial intelligence.

:pepper:
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