Author: TEERAPONG TOVIRAT
Date: 00:19:15 01/24/01
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On January 24, 2001 at 02:53:55, Uri Blass wrote: >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. > >I think that these numbers are not correct and they are only upper bounds. > >It is clear that there are many illegal positions that cannot be reached from >the initial position and it seems that you counted them(otherwise the C vs V >number seems too big). I do agree with you. From one AI book, total positions in chess =10^40 for checkers=10^18. Teerapong
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