Science > Physics > UPPER-BOUND FOR THE NUMBER OF POSITIONS IN CHESS!!!!!
| Topic: |
Science > Physics |
| User: |
"NILS BÖRJESSON" |
| Date: |
11 Feb 2006 07:25:15 PM |
| Object: |
UPPER-BOUND FOR THE NUMBER OF POSITIONS IN CHESS!!!!! |
ERROR! It is also possible to have a piece be *off* the board, except
for kings. That makes 65 possibilities for 30 of the 32 pieces. This
correction will increase you upper bound.
IF I PUT A WHITE PAWNS ON a CHESS-BOARD,
THE NUMBER OF WAYS ARE:
64/(64-A)!/A!
THIS IS TRUE ALSO IF A=0
LATER I SUM FOR ALL VALUES OF A.
Your 'calculation' also fails to account for the fact that no two
pieces can occupy the same square at the same time,
NO, WHEN I LATER PUT B WHITE BISHOPS ON THE SAME BOARD
I USE THIS FORMULA:
(64-A)!/(64-A-B)!/B!
nor can the bishops
occupy more than 32 possible squares.
THIS IS NOT RELEVANT FOR AN UPPER-BOUND.
You also do not seem to account
for the fact that pawn promotion *reduces* the number of pawns
available for placement on the board.
THIS IS NOT RELEVANT FOR AN UPPER-BOUND.
You seem to omit the fact that a
pawn cannot reach the eighth rank to be promoted without first removing
at least one other piece.
THIS IS NOT RELEVANT FOR AN UPPER-BOUND.
MY COMMENT TO YOUR PUT-DOWN STATEMENT:
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
***** YOUR *****!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
.
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| User: "tadchem" |
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| Title: Re: UPPER-BOUND FOR THE NUMBER OF POSITIONS IN CHESS!!!!! |
12 Feb 2006 07:28:14 AM |
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NILS B=D6RJESSON wrote:
IF I PUT A WHITE PAWNS ON a CHESS-BOARD,
THE NUMBER OF WAYS ARE:
64/(64-A)!/A!
Shouldn't that be "64!/(64-A)!/A!"?
The devil is in the details!
THIS IS NOT RELEVANT FOR AN UPPER-BOUND.
THIS IS NOT RELEVANT FOR AN UPPER-BOUND.
THIS IS NOT RELEVANT FOR AN UPPER-BOUND.
It most certainly is relevant. As I wrote in the part you elided from
your reply:
"Each of these 'refinements' will decrease the upper bound."
If a refinement can establish an even lower value for an upper bound,
the crude calculation has been improved.
Otherwise your so-called 'upper bound' is simply a number that we can
all be certain is much bigger than the upper bound.
The 'upper bound' is the *smallest* number that we can identify as
being at least as large as the total number of possible configurations.
MY COMMENT TO YOUR PUT-DOWN STATEMENT:
It was not a put-down statement. It was simply a personal assessment
of the value of your effort. Nevertheless, in light of your total
intellectual meltdown, I accept your concession. I also recommend you
try to get some professional help to deal with your obsession with
repetitious sodomy.
Tom Davidson
Richmond, VA
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| User: "" |
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| Title: Re: UPPER-BOUND FOR THE NUMBER OF POSITIONS IN CHESS!!!!! |
12 Feb 2006 07:55:05 AM |
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Since yall have nothing useful to do, go on to the next level -
calculate the number of distinct possible games. Excluding this one.
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