Author: KarinsDad
Date: 15:50:31 07/12/99
Go up one level in this thread
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-
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