Have you ever tried climbing Nelson's column with a backpack full of cheese burgers? Do you have any idea how many fearless and desperately hungry pigeons there are at Trafalgar Square , you will never make it to the top.
how many different moves are there?
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Wait, pigeons? Nevermind, then! We'll eat them instead!
Feb 25, 2016
0
#24
teek0 wrote:
wow thanks for the in-depth post. I'll take your word for it, still a lot when you think of how small a board is. so if my question was positions.. still looking at billions?
Billions? Dream on! It's FAR more than that.
Billions would imply 10 to 12 digits.
If you do Permutations (NOT Combinations as combinations would just give the combinations of squares occupied, a King on f1 and a Rook on g2 is different than a King on g2 and a Rook on f1), then you get the following:
nPr (64, 32) is about 3.965 time 10 to the 87th power!
Now, many of those permutations are illegal (pawns on 1st or 8th ranks, impossible positions, both kings in check, etc.), and there is also a decrease due to 2 rooks or 2 knights or 8 pawns, doesn't matter which knight is on g5 and which one is on e4.
So therefore, the number is a lot lower, like maybe 10 to the 86th power. But also keep in mind this only accounts for cases where 32 pieces are on the board. What about all the different cases of 31 pieces? 30 pieces? 29 pieces? Etc. That can be with a White pawn missing, a Black pawn missing, a White knight missing, a Black knight missing, etc.
Billions? Pa-leez! It's probably somewhere between 150 and 250 DIGITS!
Feb 25, 2016
0
#25
BlargDragon wrote:
Wait, pigeons? Nevermind, then! We'll eat them instead!
my initial plan involved getting tazered and paying a fine, now it is turning into a scene from the Triplets of Bellevue or Delicatessen. I can't believe I just involved the French in this.
Even better if we include the French! I think a fundamental question that ought to be asked about any scenario is "how can we escalate this to barbarism, international scandal, or, ideally, both?"
Whether I include the French for the barbaric or international side of things is left to interpretation.
Feb 25, 2016
0
#29
I thought the British Royal family already covered barbarism and international scandal , the French is really just like adding accordion music to the background
ThrillerFan wrote:
thanks
teek0 wrote:
wow thanks for the in-depth post. I'll take your word for it, still a lot when you think of how small a board is. so if my question was positions.. still looking at billions?
Billions? Dream on! It's FAR more than that.
Billions would imply 10 to 12 digits.
If you do Permutations (NOT Combinations as combinations would just give the combinations of squares occupied, a King on f1 and a Rook on g2 is different than a King on g2 and a Rook on f1), then you get the following:
nPr (64, 32) is about 3.965 time 10 to the 87th power!
Now, many of those permutations are illegal (pawns on 1st or 8th ranks, impossible positions, both kings in check, etc.), and there is also a decrease due to 2 rooks or 2 knights or 8 pawns, doesn't matter which knight is on g5 and which one is on e4.
So therefore, the number is a lot lower, like maybe 10 to the 86th power. But also keep in mind this only accounts for cases where 32 pieces are on the board. What about all the different cases of 31 pieces? 30 pieces? 29 pieces? Etc. That can be with a White pawn missing, a Black pawn missing, a White knight missing, a Black knight missing, etc.
Billions? Pa-leez! It's probably somewhere between 150 and 250 DIGITS!
Feb 26, 2016
0
#31
Dodger111 wrote:
Trillions and zillions isn't even close.
According to the America’s Foundation for Chess, there are 169, 518, 829, 100, 544, 000, 000, 000, 000, 000 ways to play the first 10 moves of a game of Chess.
The number of moves possible in a chess game is larger than the number of electrons in the known universe. (That's what I keep reading but I still can't bring myself to accept it)
Exemplary post!!
Feb 26, 2016
0
#33
ThrillerFan wrote:
Lagomorph wrote:
teek0 wrote:
are we talking like 100k+ or 1mil+. how many variables are in a game of chess ?
Way way way more than that.Think in many many billions.
After just three moves (3 for white and 3 for black ) the number is in the tens of millions
He asked how many different moves, not positions. Read the header.
The answer is less than you think:
Will use long algebraic to differentiate, as the move Kc1-d1 is different than the move Ke1-d1.
Pawn moves: From the 2nd rank, there are 30 pawn moves, 8 of the a2-a3 format, 8 of the a2-a4 format, and 14 of the axb3 format.
From the third thru sixth ranks, take the 8 "2-square" moves away. That's 22 possible pawn moves per rank. From the 5th rank, I consider axb6(e.p.) the same as axb6. If you don't, add 28 moves to the pawn count, 14 for White, 14 for Black.
From the 7th rank, multiply those 22 moves by 4, 22 cases of =Q, 22 of =R, 22 of =B, and 22 of =N.
That's 30 + 22 + 22 + 22 + 22 + 88, or 206 possible pawn moves. Double that for Black since he goes in the opposite direction, so d4-d5 is a White pawn move, d5-d4 is a Black pawn move. Different moves though.
TOTAL PAWN MOVES: 412 (440 if you consider axb6 and axb6(e.p.) different moves.
Other pieces, color doesn't count. Nb4-d5 is Nb4-d5 whether the Knight is White or Black.
Therefore:
Knights: 16 squares with 8 moves, 16 squares with 6 moves, 20 squares with 4 moves, 8 squares with 3 moves, and 4 squares with 2 moves.
(16*8)+(16*6)+(20*4)+(8*3)+(4*2) = 128 + 96 + 80 + 24 + 8 = 336 Knight Moves
Bishops: The outer ring, every square the Bishop has 7 moves. From the next ring in, 9 moves. Next ring in 11 moves. Middle 4, 13 moves.
(13*4) + (11*12) + (9*20) + (7*28) = 560 Bishop Moves
Rooks: Each square a Rook has 14 legal moves. 14*64 = 896 Rook Moves
Queens: Queens have the total legal moves of a Rook or Bishop. 896+560 = 1456 Queen Moves
Kings: Kings have 8 moves from the center 36 squares. 3 moves from the corners. 5 moves from the rest.
(36*8) + (24*5) + (4*3) = 420 King Moves
Then you have 4 more moves, White castles Kingside, Black castles Kingside, White Castles Queenside, Black castles Queenside. Notation may look the same, but e1-g1 is not the same as e8-g8, just like pawn moves.
So in all:
412 (Pawns) + 336 (Knights) + 560 (Bishops) + 896 (Rooks) + 1456 (Queens) + 420 (Kings) + 4 (Castling) = 4084 Legal Moves, though only 3878 of them are available to each player (206 moves are impossible for White, 206 others are impossible for Black).
So depending on your definition of whether axb6 and axb6(e.p.) are the same or different, there are 4084 or 4112 different moves in the game of chess!
You are a genius.
In fairness, accordion music adds that bit of levity that always seems to be missing in any atrocity.
ThrillerFan wrote:
Lagomorph wrote:
teek0 wrote:
are we talking like 100k+ or 1mil+. how many variables are in a game of chess ?
Way way way more than that.Think in many many billions.
After just three moves (3 for white and 3 for black ) the number is in the tens of millions
He asked how many different moves, not positions. Read the header.
The answer is less than you think:
Will use long algebraic to differentiate, as the move Kc1-d1 is different than the move Ke1-d1.
Pawn moves: From the 2nd rank, there are 30 pawn moves, 8 of the a2-a3 format, 8 of the a2-a4 format, and 14 of the axb3 format.
From the third thru sixth ranks, take the 8 "2-square" moves away. That's 22 possible pawn moves per rank. From the 5th rank, I consider axb6(e.p.) the same as axb6. If you don't, add 28 moves to the pawn count, 14 for White, 14 for Black.
From the 7th rank, multiply those 22 moves by 4, 22 cases of =Q, 22 of =R, 22 of =B, and 22 of =N.
That's 30 + 22 + 22 + 22 + 22 + 88, or 206 possible pawn moves. Double that for Black since he goes in the opposite direction, so d4-d5 is a White pawn move, d5-d4 is a Black pawn move. Different moves though.
TOTAL PAWN MOVES: 412 (440 if you consider axb6 and axb6(e.p.) different moves.
Other pieces, color doesn't count. Nb4-d5 is Nb4-d5 whether the Knight is White or Black.
Therefore:
Knights: 16 squares with 8 moves, 16 squares with 6 moves, 20 squares with 4 moves, 8 squares with 3 moves, and 4 squares with 2 moves.
(16*8)+(16*6)+(20*4)+(8*3)+(4*2) = 128 + 96 + 80 + 24 + 8 = 336 Knight Moves
Bishops: The outer ring, every square the Bishop has 7 moves. From the next ring in, 9 moves. Next ring in 11 moves. Middle 4, 13 moves.
(13*4) + (11*12) + (9*20) + (7*28) = 560 Bishop Moves
Rooks: Each square a Rook has 14 legal moves. 14*64 = 896 Rook Moves
Queens: Queens have the total legal moves of a Rook or Bishop. 896+560 = 1456 Queen Moves
Kings: Kings have 8 moves from the center 36 squares. 3 moves from the corners. 5 moves from the rest.
(36*8) + (24*5) + (4*3) = 420 King Moves
Then you have 4 more moves, White castles Kingside, Black castles Kingside, White Castles Queenside, Black castles Queenside. Notation may look the same, but e1-g1 is not the same as e8-g8, just like pawn moves.
So in all:
412 (Pawns) + 336 (Knights) + 560 (Bishops) + 896 (Rooks) + 1456 (Queens) + 420 (Kings) + 4 (Castling) = 4084 Legal Moves, though only 3878 of them are available to each player (206 moves are impossible for White, 206 others are impossible for Black).
So depending on your definition of whether axb6 and axb6(e.p.) are the same or different, there are 4084 or 4112 different moves in the game of chess!
Is this counting moves like Nbd2 or N1e2 as separate to Nd2 and Ne2? If not how many moves would that make it?
Haha, the number of possible chess games is so fun.
Imagine two computers are playing a complete 40 moves chess game every second. They never repeat and will eventually play every 40 move chess game possible. This means every day they play 86400 games, and every year they complete about 31.5 million unique 40 move chess games. How long will it take for them to finish?
Well let's see what you can do while you wait. You build a death star, except instead of destroy planets, it destroys stars. It takes a billion years to warm up. So after a billion years, the two comuters are still playing chess, and you blow up a star. A billion years later, the computers are still playing chess. That's another star.
Okay, you continue destroying stars visible to the naked eye of Earth. After 9.096 trillion years, you have destroyed every star visible in the night sky. Because of your efforts, those looking up from Earth (that are somehow still alive...) see nothing but blackness with the naked eye.
You check on the two chess playing computers. They are still playing chess.
Okay, well you have galaxies to destroy. So you destroy all
250 billion stars in the milky way. It takes you 2.5 quintillion years. You check on the computers, they are still playing chess.
Your death star is getting old, but you decide to repair it and keep going. Your ambitious are limitless, and you are waiting for the two computers to finish play all possible games of chess within 40 moves.
There are probably about 7 * 10^22 stars in the known universe. Well that number means nothing to your ambitious. After 7 * 10^31 years, you have taken a billion years each to destroy ever star in the universe. You check back on your chess playing computers- they still have not played every possible chess game within 40 moves.
Well this aggravates you, you are super bored. Luckily, in your eons long intergalactic rampage, you learned the secret to the reversal of entropy, so that's good. You create a new universe. Everything is the same, except the sun has one less atom. Yep, just one single atom is missing from the son. It could be helium, hydrogen, whatever. But it's just a single atom, nobody is going to miss it.
Well over this entropy revearsal you have preserved the chess playing computers, and they are still playing chess. You decide to destroy the universe again, taking another 7 * 10^31 years. You are starting to get immune to boredom now. This time, when you rebuilt the universe, the sun is missing TWO atoms. TWO WHOLE ATOMS.
You repeat this for while... it's pretty fun to destroy all the stars in the universe a billion years a piece, then take away one atom from the sun.
Well, you continue this process for a while, checking on the chess playing computers ever 7 * 10^31 years. "Have you finished playing every possible chess game for the first 40 moves? Nope."
Then, something astonishes you. The sun runs out of atoms. After about 1.39 * 10^88 years, you remove the last atom from the sun. Well now what will you do? You check on the chess computers. They still haven't finished. You are furious now.
Well you start the universe over, but repeat the process you have done with the sun. Now you skip the star destroying stuff. You simply remove on atom from ever star in the universe ever 7 * 10^31 years. In fact, why stop there? Every 7 * 10^31 years, the universe starts over with one less atom than it had before. You have been alive so long, you are pretty much omnipotent.
So you destroy the universe by speaking one atom out of existence every 7 * 10^31 years.
Well SURE ENOUGH, YOU DESTROY THE ENTIRE UNIVERSE.
You are furious now. You go to the chess computers. THEY ARE STILL PLAYING CHESS.
However, they have good news for you.
"So you're still playing chess?"
"Yes"
"But we can tell you when we will finish."
"really"
"Yep, we have a progress bar. When it's full, we're done."
"Awesome, where is it?"
"Where's the progress"
"You just have to look closer."
"Still Nothing."
"Just look closer."
"Okay, seriously, have you guys been doing anything? I have been waiting for a practically uncountable amount of time."
"We have completed a chess game every second. We still play now."
"Okay, I guess I just have to look close enough."
11111111111111111111112354789*4566666842719000000000000000000
(more than all the grains of and in the universe)