As to the idea that if a repetition occurs, best play will lead to it occurring again: not necessarily. Best play (for on side or both sides), meaning trying to win, may necessitate avoiding the draw, and thus deliberately deviating to avoid the repetition.
The future of computer Chess
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May 26, 2009
0
#63
@Ricardo_Morro I don't follow why the first player would allow the repetition in the first place in a "perfect solution" world.
By the way, I have an algorithm that tests numbers for primality using only the operations of addition, subtraction, and comparison (equal or nonequal), without any use of multiplication or division. It also generates primes.
Ricardo_Morro wrote:
As to the idea that if a repetition occurs, best play will lead to it occurring again: not necessarily. Best play (for on side or both sides), meaning trying to win, may necessitate avoiding the draw, and thus deliberately deviating to avoid the repetition.
No, I'm afraid that making an inferior move to avoid the repetition (given that you played the best move on the previous iteration) is anything but best play.
Even if it were rational, it would just lengthen the iteration: eventually you'd find yourself back in the same position with all of your deviations exhausted and you'd have to start to repeat them. As I said before, playing a drawn position indefinitely is as drawn a game as one where you opt to end it.
May 26, 2009
0
#66
Ricardo_Morro wrote:
By the way, I have an algorithm that tests numbers for primality using only the operations of addition, subtraction, and comparison (equal or nonequal), without any use of multiplication or division. It also generates primes.
*Yawn*
Me too.
May 26, 2009
0
#67
Why do we really care if computers can outperform us. We use spell check because they spell better, we use CAD design because it has superior memory and integrated graphics, we use calculators because they are faster than us and more accurate. Why would anybody realistically think that they could out perform a computer in chess?
"A computer once beat me at chess, but it was no match for me at kick boxing" - Emo Phillips
May 26, 2009
0
#69
richie_and_oprah wrote:
bondiggity wrote:
richie_and_oprah wrote:
bondiggity wrote:
For a proof to be complete, you need to address every possible condition. For chess to be completely solved and declared draw, then every single possible line of play will have to be analyzed as ending in draw.
Incorrect.
Only best play needs be shown to draw, as in Tic-Tac-Toe and draughts.
Mistakes lead to decisive results.
Even a cursory look at large databases (40 million games+) gives more evidence than that evidence which is used to justify and accept biological evolution. I am puzzled by people that accept the one, with much less evidence, but continue to argue the other.
No it is you who is wrong.
The only way to determine best play is by proving that all other lines of play are inferior, thereby requiring you to address every possible condition. You agree with me yet say I'm wrong. I'm not arguing that chess is inheritantly won, but the only way to prove it beyond any doubt that that is true is to show that every possible line of play is indeed drawn.
If you call this wrong, you have no background in mathematics or proofs.
I am familiar with all the proofs, although I prefer 151.
My burden of proof is not so cumbersome to me as the one you choose for yourself.
"a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single exception. An unproved proposition that is believed to be true is known as a conjecture."
You wish to conjecture, I wish to prove.
May 26, 2009
0
#70
The accordion beat him at chess and he smashed it?
That's some accordion. Or was.
ozzie-c-cobblepot: I'm just saying that even if there is one repetition, that still does not prove the case for "chess is a draw." The chess-is-finite crowd are relying on the idea that repetition is inevitable, given that: 1) the number of pieces is finite; 2) the number of squares is finite; and 3) therefore the number of arrangements of the pieces on the squares is finite. If the moves are indefinitely many, then eventually all the possible arrangements are exhausted, and so one must be repeated.
Yet we may turn this logic on its head against its perpetrators. Take an even position at random involving a few men for each side. Is it always possible to determine if that position could have been reached by reasonable or even by legal moves? The difficulties of such a retrograde analysis must give us pause. For if that question cannot be answered in the affirmative, then we have an undecidable proposition that suggests the unsolvability of chess.
May 26, 2009
0
#72
richie_and_oprah wrote:
boondiggity: Then get off the intrawebs.
Only fools or mental patients really seek to prove things here on forums like this and I suspect you are neither.
Yes, I proved you wrong so how do you respond.
1) Incorrectly type my name: indication of a fool
2) Try to change the argument/completely forget what was being discussed: the sign of a mental patient. We were discussing (at least I was, maybe you weren't in full comprehension) that if formal proof of the result of chess is to be found, then it will have to include all variation because if it doesn't it isn't a proof but a conjecture. If you can't understand this, you aren't worth my time and good day.
Ricardo_Morro wrote:
ozzie-c-cobblepot: I'm just saying that even if there is one repetition, that still does not prove the case for "chess is a draw." The chess-is-finite crowd are relying on the idea that repetition is inevitable, given that: 1) the number of pieces is finite; 2) the number of squares is finite; and 3) therefore the number of arrangements of the pieces on the squares is finite. If the moves are indefinitely many, then eventually all the possible arrangements are exhausted, and so one must be repeated.
Yet we may turn this logic on its head against its perpetrators. Take an even position at random involving a few men for each side. Is it always possible to determine if that position could have been reached by reasonable or even by legal moves? The difficulties of such a retrograde analysis must give us pause. For if that question cannot be answered in the affirmative, then we have an undecidable proposition that suggests the unsolvability of chess.
Difficult = impossible?
May 26, 2009
0
#74
Time is a matter of perception. Since you responded indicates that you don't perceive the time it took you to respond as time at all. Indeed time has a name much similar to the concept of "nothing". If nothing is really nothing then it couldn't possibly have a name. If time can be measured and replicated, it must be real. I find that the replication of time is impractical and unachievable. Therefore, I must conclude that you did in fact use time (waste) to prepare a response.
TheGrobe: the issue is whether or not it is always possible. Can we know?
May 26, 2009
0
#76
TheGrobe wrote:
Ricardo_Morro wrote:
ozzie-c-cobblepot: I'm just saying that even if there is one repetition, that still does not prove the case for "chess is a draw." The chess-is-finite crowd are relying on the idea that repetition is inevitable, given that: 1) the number of pieces is finite; 2) the number of squares is finite; and 3) therefore the number of arrangements of the pieces on the squares is finite. If the moves are indefinitely many, then eventually all the possible arrangements are exhausted, and so one must be repeated.
Yet we may turn this logic on its head against its perpetrators. Take an even position at random involving a few men for each side. Is it always possible to determine if that position could have been reached by reasonable or even by legal moves? The difficulties of such a retrograde analysis must give us pause. For if that question cannot be answered in the affirmative, then we have an undecidable proposition that suggests the unsolvability of chess.
Difficult = impossible?
TheGrobe, thanks for reading and responding - I think my mind glazed over after the 2nd line and I stopped reading after the 3rd.
May 26, 2009
0
#77
Just so I know what I'm dealing with here, where did y'all get your computer science degrees?
May 26, 2009
0
#78
if there are more chess moves than atoms in the universe, wouldnt we have to discover several other universes first to store the data on??....and if we did find other universes that could be lived in, i think maybe the powers that be 'might' find a slightly more serious need for them than solving our precious game :-)
May 26, 2009
0
#79
You might think that my alma mater is the University of Gotham, but it's snot.
This is the difference between a strong solution and a weak solution.
In other words, solving chess does not require looking at all moves, it only requires defining a strategy which will win against all possible replies. For example, if it decides that 1.d4 wins against all moves, it does not need to examine 1.e4 or any other opening move.