# Computer Chess Club Archives

## Messages

### Subject: Re: Maximum Number of Legal Moves

Author: Uri Blass

Date: 01:09:48 05/09/05

Go up one level in this thread

```On May 08, 2005 at 23:44:31, Andrew Shapira wrote:

>What's best known (the smallest) upper bound on the number of legal moves, taken
>over all chess positions?  An obvious bound is 9*7*4+2*14+2*14+2*8+8 = 332.
>This comes from 9 queens, 2 rooks, 2 bishops, 2 knights, and 1 king.  Is a
>better bound known?

Of course

bishops can have at most 13 moves and not 14 moves so you can have

9*27+2*14+2*13+2*8+8

More than it

If you have one queen that can play 27 moves that it is in the center and other
queens can get at most 25 moves

d3 have 14 for rook but only 11 for bishop and 2 queens in the centre are in the
same rank or the same diagnol so the situation is even worse so you have at most
27+8*25+2*14+2*13+2*8+8=305 moves

I am sure that it may be possible to reduce the maximal number of 9 queens and a
computer program can calculate the exact maximal number of squares that 9 queens
can control by trying all possibilities(replacing a queen by a rook or a bishop
certainly will not help and you only need to check the possibility of replacing
a queen by a knight but I think that the 9 additional queen give more than 8
squares so it is not relevant.

intuitively for 27 squares for the queen you need d4
You can add only 2 25 squares by f3 e6 and
I think that the rest of the queens can control at most 23 squares and it reduce
the upper bound by 12 to 293

Uri

```