Author: Timothy J. Frohlick
Date: 00:06:12 01/24/01
Go up one level in this thread
Tania, With one checker piece there are only 32 possible positions each for both the king and regular man. That is 64 positions. In the case of 24 pieces, there are only 7 possible moves on each side with one of those being stupid. I am not sure where you got your data from but one thing is certain...you didn't get it from Marion Tinsley. I doubt that there has ever been a game in the history of checkers with 12 kings on each side. Fairy checkers, in which positions are invented, is a different matter. Checkers is actually a much harder game than chess when it comes to doing look-ahead sequences of 60 to 90 ply. Most people don't even look 5 ply ahead. Jump sequence and minor positional errors will usually lose against most of the better programs and players. The same is true in chess. In chess, the complexity is higher because of more pieces and more variety in their moves. Tim Frohlick On January 24, 2001 at 02:14:20, Tania Devora wrote: > > >Here are the total number of checker positions sorted according to the number of >pieces on the board. > > # PIECES # POSITIONS > 1 120 > 2 6,972 > 3 261,224 > 4 7,092,774 > 5 148,688,232 > 6 2,503,611,964 > 7 34,779,531,480 > 8 406,309,208,481 > 9 4,048,627,642,976 > 10 34,778,882,769,216 > 11 259,669,578,902,016 > 12 1,695,618,078,654,976 > 13 9,726,900,031,328,256 > 14 49,134,911,067,979,776 > 15 218,511,510,918,189,056 > 16 852,888,183,557,922,816 > 17 2,905,162,728,973,680,640 > 18 8,568,043,414,939,516,928 > 19 21,661,954,506,100,113,408 > 20 46,352,957,062,510,379,008 > 21 82,459,728,874,435,248,128 > 22 118,435,747,136,817,856,512 > 23 129,406,908,049,181,900,800 > 24 90,072,726,844,888,186,880 > > Total: 500,995,484,682,338,672,639 > > >Seems to be a smaller number compared to all chess positions. > >There are any formula like this to know how many position exist in chess? > > > > >Of particular interest are those positions where either the material is even if >there is an even number of pieces on the board, or the difference is no more >than one when there are an odd number of pieces present (for example, 4 vs 3 and >3 vs 4 for 7 pieces). > 1 vs 0: 60 (x 2) > 1 vs 1: 3,488 > 2 vs 1: 98,016 (x 2) > 2 vs 2: 2,662,932 > 3 vs 3: 46,520,744 (x 2) > 3 vs 3: 783,806,128 > 4 vs 3: 9,527,629,380 (x 2) > 4 vs 4: 111,378,534,401 > 5 vs 4: 998,874,699,888 (x 2) > 5 vs 5: 8,586,481,972,128 > 6 vs 5: 58,769,595,279,296 (x 2) > 6 vs 6: 384,033,878,250,176 > 7 vs 6: 2,046,244,120,757,760 (x 2) > 7 vs 7: 10,359,927,057,187,840 > 8 vs 7: 43,428,742,062,013,440 (x 2) > 8 vs 8: 171,975,762,422,069,760 > 9 vs 8: 569,058,493,921,640,448 (x 2) > 9 vs 9: 1,765,698,358,650,175,488 > A vs 9: 4,596,454,069,579,874,304 (x 2) > A vs A: 11,113,460,838,901,284,864 > B vs A: 22,520,313,165,772,750,848 (x 2) > B vs B: 41,842,926,176,229,654,528 > C vs B: 64,703,454,024,590,950,400 (x 2) > C vs C: 90,072,726,844,888,186,880 > > Total number of positions: 329,847,169,676,858,217,781 > > >Thanks! >Tanya,D.
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.