Author: Andrew Dados
Date: 15:31:43 07/12/99
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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...) > > 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; >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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