How many chess moves?

Factual Questions
1

OK, so I couldn’t sleep last night, so I did a nerd-version of counting sheep: I tried to figure out how many possible combinations there are for white’s first two moves (assuming black stays the hell outta the way and there are no blocks or captures, or perhaps that black is confident enough in his/her superiority that white is allowed to make two initial moves). I got 433 possible first-two-moves. Of course, most of 'em are dumb ones like moving a pawn a single square and moving it again, or moving a knight out and then back, but i got 433 of them. Anyone else get the same answer? Anyone want to try to calculate the number of possibilities if you untie black’s hands? How about taking it farther and figuring out how many combinations are possible farther into the game?

Oh, and incase you’re wondering, it worked: I fell right asleep. :slight_smile:

-b

2

There are 20 possible first moves. The number of second moves varies according to the first move played:

If 1. a3, then 2. a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Ne3, Nf3, Nh3 (18 second moves)

If 1. a4, then you can’t play 2. a4, but you can play 2. Na3 (18 second moves)

If 1. b3, then 2. a3, a4, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Na3, Nc3, Nf3, Nh3, Bb2, Ba3 (21 second moves)

If 1. b4, then you can’t play 2. b4, and nothing else changes (20 second moves)

If 1. c3, then 2. a3, a4, b3, b4, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Na3, Nf3, Nh3, Qc2, Qb3, Qa4 (21 second moves)

If 1. c4, then you can’t play 2. c4, but you can play 2. Nc3 (21 second moves)

If 1. d3, then 2. a3, a4, b3, b4, c3, c4, d4, e3, e4, f3, f4, g3, g4, h3, h4, Na3, Nc3, Nd2, Nf3, Nh3, Bd2, Be3, Bf4, Bg5, Bh6, Qd2, Kd2 (27 second moves)

If 1. d4, then you can’t play 2. d4, but you can play 2. Qd3 (27 second moves)

If 1. e3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e4, f3, f4, g3, g4, h3, h4, Na3, Nc3, Ne2, Nf3, Nh3, Be2, Bd3, Bc4, Bb5, Ba6, Qe2, Qf3, Qg4, Qh5, Ke2 (30 second moves)

If 1. e4, then you can’t play 2. e4, and nothing else changes (29 second moves)

If 1. f3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f4, g3, g4, h3, h4, Na3, Nc3, Nh3, Kf2 (19 second moves)

If 1. f4, then you can’t play 2. f4, but you can play 2. Nf3 (19 second moves)

If 1. g3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g4, h3, h4, Na3, Nc3, Nf3, Nh3, Bg2, Bh3 (21 second moves)

If 1. g4, then you can’t play 2. g4, and nothing else changes (20 second moves)

If 1. h3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h4, Na3, Nc3, Nf3 (18 second moves)

If 1. h4, then you can’t play 2. h4, but you can play 2. Nh3 (18 second moves)

If 1. Na3, then 2. b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Nf3, Nh3, Nb5, Nc4, Nb1 (19 second moves)

If 1. Nc3, then 2. a3, a4, b3, b4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Nf3, Nh3, Na4, Nb5, Nd5, Ne4, Nb1 (21 second moves)

If 1. Nf3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, g3, g4, h3, h4, Na3, Nc3, Nd4, Ne5, Ng5, Nh4, Ng1 (21 second moves)

If 1. Nh3, then a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, Na3, Nc3, Nf4, Ng5, Ng1 (19 second moves)

So, there are 20 + 18 + 18 + 21 + 20 + 21 + 21 + 27 + 27 + 30 + 29 + 19 + 19 + 21 + 20 + 18 + 18 + 19 + 21 + 21 + 19 = 447 possible first two moves for White if Black does not move.

3

Libertarian:

You are correct, there are 20 initial moves. However:

If 1. a3, then for 2. there are 15 possible pawn moves, three knight moves, and you forgot Ra2 (19 second moves). This will be the same if 1. h3.

If 1. a4, there are still 15 possible pawn moves (you forgot 2. a5), four knight moves, Ra2, and Ra3. (21 second moves). Same for 1. h4.

If 1. b3, there are 21 possible second moves as you listed. Same for 1. g3.

If 1. b4, there are still 21 possible second moves (you forgot 2. b5). Same for 1. g4.

If 1. c3, there are 21 second moves as you stated.

If 1. c4, there are 22 second moves (you forgot 2. c5).

If 1. d3, there are 27 second moves as you stated.

If 1. d4, there are 28 second moves (2. d5).

If 1. e3, there are 30 second moves.

If 1. e4, there are still 30 second moves (2. e5).

If 1. f3, there are 19 second moves.

If 1. f4, there are 20 second moves (2. f5).

Already covered g and h pawn moves, and you hit all the knight moves already.

For the total, don’t add the 20 initial moves. These moves are the 20 tems in the addition.

So, starting from the top of my list we have: 19 + 19 + 21 + 21 + 21 + 21 + 21 + 21 + 21 + 22 + 27 + 28 + 30 + 30 + 19 + 20 + 19 + 21 + 21 + 19 = 441

(I forgot the second knight could move when counting the knight moves last night, so I was off by 8. Whoops. :slight_smile: )

So, 441 possible two-move combinations, I think. Right? Unless there’s some reason against moving pawns to the fifth rank?

-b

4

Wow, let me think about something at work that put you to sleep. :rolleyes:

OK, I’m doing it now.

A pawn goes first
Each pawn has two possible opening moves
For second moves, there are:
[ul]
[li]15 possible moves by pawns.[/li][li]0 possible moves by rooks (exceptions to be noted)[/li][li]4 possible moves by knights[/li][li]0 moves by bishops (exceptions to be noted)[/li][li]0 moves by the king (exceptions to be noted)[/li][li]0 moves by the queen (exceptions to be noted)[/li][/ul]

2 pawn moves x 8 pawns x (15 second pawn moves + 4 knight moves) = 304
Exceptions:
minus 2 for each blocked knight if pa2a3, et al are first move, times 2 (-4 )
plus 7 for each bishop if the proper pawn is moved, times 2 bishops times 2 pawn moves (+28)
plus 3 for each king move if the proper pawn is moved, times 2 pawn moves (+6)
plus 7 diagonal queen moves if the proper pawn is moved, times 2 pawn moves (+14)
plus 2 straight queen moves if her pawn is moved (+2)
plus 2 straight rook moves if its pawn is moved, times 2 rooks (+4)
plus 1 “lateral” knight move if proper pawn is moved, times 2 knights (+2)
Total pawn-first two-move combinations: 356

A knight goes first
Each knight has two possible opening moves
For second moves, there are:
[ul]
[li]14 possible pawn moves (it blocks at least one pawn)[/li][li]1 possible rook move[/li][li]0 bishop moves[/li][li]0 king moves[/li][li]0 queen moves[/li][li]2 other knight moves[/li][li]same knight moves noted below[/li][/ul]

2 knight moves x 2 knights x (14 + 1 + 2) = 68

5 same knight moves again x 2 knights = 10

The other pieces cannot move first.

Grand total: 434 possible two-move combinations, not counting possible capturing by pawns on the 2nd move.

5

Wow, let me think about something at work that put you to sleep. :rolleyes:

OK, I’m doing it now.

A pawn goes first
Each pawn has two possible opening moves
For second moves, there are:
[ul]
[li]15 possible moves by pawns.[/li][li]0 possible moves by rooks (exceptions to be noted)[/li][li]4 possible moves by knights[/li][li]0 moves by bishops (exceptions to be noted)[/li][li]0 moves by the king (exceptions to be noted)[/li][li]0 moves by the queen (exceptions to be noted)[/li][/ul]

2 pawn moves x 8 pawns x (15 second pawn moves + 4 knight moves) = 304
Exceptions:
minus 2 for each blocked knight if pa2a3, et al are first move, times 2 (-4 )
plus 7 for each bishop if the proper pawn is moved, times 2 bishops times 2 pawn moves (+28)
plus 3 for each king move if the proper pawn is moved, times 2 pawn moves (+6)
plus 7 diagonal queen moves if the proper pawn is moved, times 2 pawn moves (+14)
plus 2 straight queen moves if her pawn is moved (+2)
plus 2 straight rook moves if its pawn is moved, times 2 rooks (+4)
plus 1 “lateral” knight move if proper pawn is moved, times 2 knights (+2)
Total pawn-first two-move combinations: 356

A knight goes first
Each knight has two possible opening moves
For second moves, there are:
[ul]
[li]14 possible pawn moves (it blocks at least one pawn)[/li][li]1 possible rook move[/li][li]0 bishop moves[/li][li]0 king moves[/li][li]0 queen moves[/li][li]2 other knight moves[/li][li]same knight moves noted below[/li][/ul]

2 knight moves x 2 knights x (14 + 1 + 2) = 68

5 same knight moves again x 2 knights = 10

The other pieces cannot move first.

Grand total: 434 possible two-move combinations, not counting possible capturing by pawns on the 2nd move.

6

Brian:

Ay, the rooks! They can also make one move if the knight moves out, so you need to add four more moves. And yes, of course, the pawns can move again.

Now, can we reconcile this 445 with AWB’s 434?

7

Forgive the above double post:

P.S. - I forgot about a knight moving back to its starting square, so my total is now 438.

8

Crap! Right, forgot those four rook moves. OK, I concur with 445 (so far).

AWB, couple problems I noticed:

There are three straight queen moves: pawn moves one, queen moves one; pawn moves two, queen moves one; and pawn moves two, queen moves two. Accounts for one move.

Likewise, there are three straight rook moves for the same reason. Since there are two rooks, this accounts for two more moves.

Also, I get six possible “same knight” second moves (excluding the move back to the original square which you already accounted for) where you had five, which accounts for two more moves (one for each knight).

So there’re five of the seven missing moves between our two totals. Haven’t found the other two yet, but I’m sticking with 445. :slight_smile:

-b

9

As per bryanmcc’s points, I add 5 more moves: 2 same-knight moves that I somehow missed shrug, and 1 straight move for each rook and the queen if their pawn is moved 2 to open.

So now my total is 443.

[talking-to-self]And no, AWB, I don’t have time to write a computer simulation to figure this all out![/talking-to-self]

10

Well, this is unacceptable. A reconciliation is necessary.

11

From ‘The Complete Chess Addict’ by James and Fox ISBN 0-571-14901-4

‘After 2 moves by each side, there are 72,084 possible positions.
This includes en passant captures.’

They mean 1. e4 a6 2. e5 d5 is a different position from 1. e4 d5 2. e5 a6 , since White can only play 3. exd6 in the first sequence.

The book also claims that the number of different 40 move games (approx 25 x 10 to the 115th power) is larger than the estimated number of electrons in the Universe (approx 10 to the 79th power)

Just thought you’d like to know that…

12

I believe I have resolved the discrepancy–AWB left out 2 “lateral” knight moves in “pawn goes first/exceptions”, since each knight can make that move whether the blocking pawn moves ahead 1or 2 spaces. Thus, I get 4 instead of 2 lateral knight moves. Recaping my understanding of the two approaches with the posted corrections:

Libertarian:

There are 20 possible first moves. The number of second moves varies according to the first move played:

  1. a3, then 2. a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Ne3, Nf3, Nh3, Ra2 (19)
  2. a4, then idential to previous, except a5 instead of a4, plus Na3 and Ra3 (21)
  3. b3, then 2. a3, a4, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Na3, Nc3, Nf3, Nh3, Bb2, Ba3 (21)
  4. b4, then identical to previous, except b5 instead of b4 (21)
  5. c3, then 2. a3, a4, b3, b4, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Na3, Nf3, Nh3, Qc2, Qb3, Qa4 (21)
  6. c4, then identical to previous, except c5 instead of c4, plus Nc3 (22)
  7. d3, then 2. a3, a4, b3, b4, c3, c4, d4, e3, e4, f3, f4, g3, g4, h3, h4, Na3, Nc3, Nd2, Nf3, Nh3, Bd2, Be3, Bf4, Bg5, Bh6, Qd2, Kd2 (27)
  8. d4, then identical to previous, except d5 instead of d4, plus Qd3 (28)
  9. e3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e4, f3, f4, g3, g4, h3, h4, Na3, Nc3, Ne2, Nf3, Nh3, Be2, Bd3, Bc4, Bb5, Ba6, Qe2, Qf3, Qg4, Qh5, Ke2 (30)
  10. e4, then identical to previous, except e5 instead of e4 (30)
  11. f3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f4, g3, g4, h3, h4, Na3, Nc3, Nh3, Kf2 (19)
  12. f4, then identical to previous, except f5 instead of f4, plus Nf3 (20)
  13. g3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g4, h3, h4, Na3, Nc3, Nf3, Nh3, Bg2, Bh3 (21)
  14. g4, then identical to previous, except g5 instead of g4 (21)
  15. h3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h4, Na3, Nc3, Nf3, Rh2 (19)
  16. h4, then identical to previous, except h5 instead of h4, plus Nh3 and Rh3 (21)

19 + 21 + 21 + 21 + 21 + 22 + 27 + 28 + 30 + 30 + 19 + 20 + 21 + 21 + 19 + 21 = 361 pawn first moves

  1. Na3, then 2. b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Nf3, Nh3, Nb5, Nc4, Nb1, Rb1 (20)
  2. Nc3, then 2. a3, a4, b3, b4, d3, d4, e3, e4, f3, f4, g3, g4, h3, h4, Nf3, Nh3, Na4, Nb5, Nd5, Ne4, Nb1, Rb1 (22)
  3. Nf3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, g3, g4, h3, h4, Na3, Nc3, Nd4, Ne5, Ng5, Nh4, Ng1, Rg1 (22)
  4. Nh3, then 2. a3, a4, b3, b4, c3, c4, d3, d4, e3, e4, f3, f4, g3, g4, Na3, Nc3, Nf4, Ng5, Ng1, Rg1 (20)

20 + 22 + 22 + 20 = 84 knight first moves

361+84 = 445 possible first two moves for White if Black does not move.
AWB:

A pawn goes first
Each pawn has two possible opening moves
For second moves, there are:
15 possible moves by pawns.
0 possible moves by rooks (exceptions to be noted)
4 possible moves by knights
0 moves by bishops (exceptions to be noted)
0 moves by the king (exceptions to be noted)
0 moves by the queen (exceptions to be noted)
2 pawn moves x 8 pawns x (15 second pawn moves + 4 knight moves) = 304

Exceptions:
minus 2 for each blocked knight if pa2a3, et al are first move, times 2 (-4 )
plus 7 for each bishop if the proper pawn is moved, times 2 bishops times 2 pawn moves (+28)
plus 3 for each king move if the proper pawn is moved, times 2 pawn moves (+6)
plus 7 diagonal queen moves if the proper pawn is moved, times 2 pawn moves (+14)
plus 3 straight queen moves if her pawn is moved (+3)
plus 3 straight rook moves if its pawn is moved, times 2 rooks (+6)
plus 1 “lateral” knight move if proper pawn is moved, times 2 knights, times 2 pawn moves (+4)
Total pawn-first two-move combinations: 304 - 4 + 28 +6 + 14 + 3 + 6 + 4 = 361

A knight goes first
Each knight has two possible opening moves
For second moves, there are:
14 possible pawn moves (it blocks at least one pawn)
1 possible rook move
0 bishop moves
0 king moves
0 queen moves
2 other knight moves
(same knight moves noted below)
2 knight moves x 2 knights x (14 + 1 + 2) = 68

8 same knight moves again x 2 knights = 16

68+16=84 knight-first moves

The other pieces cannot move first.

Grand total: 361+84=455 possible two-move combinations, not counting possible capturing by pawns on the 2nd move.

If you’ll excuse me, I’m going to go to Florida now to find Gore’s missing votes…

13

Whitetho, you are my new hero! One less quantum of ignorance. Very good work! You, sir or madam, are the Melancholy’s Melancholy.

Glee, how was the 40-move game calculated?

14

361+84=445, of course…

15

Sorry, I don’t know how they calculated it.

I do recommend the book though - a real mix of information!

16

Sorry for the hijack, but I figured anyone interested in a new problem is already reading this thread.

For years Bobby Fischer has advocated that to avoid lengthy home-cooked analysis and to force each player to start thinking at move 1 the pieces should be placed at random on the back rank, subject only to the condition that the bishops be on opposite colored squares.

How many different set-ups are possible under Fischer’s plan?

I make it 2,880. Right?

17

All of you are in possession of dangerous quantities of spare time.

18

42

19

jcgmoi you’re almost right. actually, there are a few rules for how the pieces should be set up in the back, because there are provisions for castling.

Look at this Fischer Random Chess web site.

There is an answer on another web page to how many legal starting positions there are, but I’m not going to ruin the fun. It is well under 2800.

As for the originally stated question, it’s a little tricky, as you have two each of rooks, knights and bishops, and one queen and king. So there’s quite a few duplicate positions possible. That said, I’ll let somebody else calculate. Hey, I’m just lazy. :slight_smile:

20

hmmm… my quick guess is 3696 positions, so, actually, more than you calculated.

8 ways to place the king … leaving
7 ways to place the queen … leaving
11 ways to place the two rooks … leaving
6 ways to place the bishops … leaving
1 way to place the knights

871161 = 3696