Author: Andrew Dados
Date: 15:56:43 07/12/99
Go up one level in this thread
On July 12, 1999 at 18:50:31, KarinsDad wrote: >On July 12, 1999 at 18:31:43, Andrew Dados wrote: > >>On July 12, 1999 at 18:23:45, Andrew Dados wrote: >> >>>On July 12, 1999 at 12:41:18, blass uri wrote: >>> >>>[snipped] >>> >>>>some numbers: >>>>The upper bound: >>>>3.70106301212072366*10^46 >>>>29 pieces on the board:2.18...*10^46 >>>>28 pieces on the board 9.45...*10^45 >>>>30 pieces on the board 4.58...*10^45 >>>> >>>>Uri >>> >>> (Note that those 3 figures above add up to 3.9*10^46, which is somehow more >>>then your total...) > >oops. > >This adds up to 3.583^46 which is less than Uri's 3.7^46. So far, so good. > >>> >>> I will try to put my idea into small program as soon as I get some time, but >>>for now let me describe it: >>> Let's take into account possible pawn configurations. >>>For each file if no capture was done (32 pieces on board) we have 15 distinct >>>positions for one white and one black pawn... which gives us 15^8 pawn >>>configurations (2,526,890,625). This is many orders less then your bound there. >>> Now lets consider one capture. I'll mark P=pawn; O=other piece. >>>We have 4 possibilities: >>> >>>1. OxO (piece captures piece) - no pawnstructure changes; still 15^8 pawn >>>configurations; no promotions possible; >>>2. PxP: up to 2 promotions can be done here: >>> 2a) no promotions; pawn structure number can be estimated at 15^7*6*4; >>> 2b) 1 prom; psn<=15^7*(6+4); >>> 2c) 2 proms; psn<=15^6*6*6; > >Double oops. > >PxP allows for up to 3 promotions, 2 for the taking side and 1 for the taken >side. > >KarinsDad :) > >>>3. OxP: a) 15^7*6 with no proms and >>> b) 15^7 with one promotion >> >>oops... this below should be PxO case... >> >>>4. PxP a) 15^7*6*4 with no proms; >>> b) 15^7*(6+4) and one prom >>> c) 15^6*6*6 and 2 proms... >>> For second capture each of cases above breaks down further etc.... looks like >>>mundane work, but smart program can surely be written. >>> I think one should give it a try.... >>> >>>One more thought: positions with, say, 0-0 castling availible are less then >>>(1/48)*(1/48) of all positions (K is positioned on e1 in 1/48 of all >>>positions), so neglible. EP can be available way more often, but still below 1/8 >>>of all positions. >>>-Andrew- KarinsDad you're of course right... sometimes one has 3 minutes to put not-well-thought idea on paper, and that's what it is...:). -regards- -Andrew-
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.