Author: Uri Blass
Date: 21:44:20 11/28/02
Go up one level in this thread
On November 29, 2002 at 00:26:31, Mike Byrne wrote: >On November 28, 2002 at 23:34:04, Uri Blass wrote: > >>On November 28, 2002 at 23:23:19, Mike Byrne wrote: >> >>>On November 28, 2002 at 22:52:45, Uri Blass wrote: >>> >>>>On November 28, 2002 at 22:40:42, Mike Byrne wrote: >>>> >>>>>On November 28, 2002 at 22:20:02, Tanya Deborah wrote: >>>>> >>>>>>On November 28, 2002 at 22:05:39, Mike Byrne wrote: >>>>>> >>>>>>>snip >>>>>>>>> >>>>>>>>>All your answers are welcome... >>>>>>>>> >>>>>>>>>My best Regards! >>>>>>>>> >>>>>>>>>Tanya. >>>>>>>> >>>>>>>>6.5104179521361946395624758693608e+308 >>>>>>>> >>>>>>>>I know this is the exact number of chess positions, because I counted them one >>>>>>>>day using my Palm and Chess genius. >>>>>>>> >>>>>>>>But how do you count all the atoms in the universe? I might need a newer Palm >>>>>>>>for that one ...hmmmm ....yea, I could that on of those new palms. >>>>>>>> >>>>>>>>Hold on - let me go talk to my wife and explain to her why I need a new palm. >>>>>>>> >>>>>>>>THANKS - You gave me the perfect reason for a new Palm - to count all the atoms >>>>>>>>in the universe. >>>>>>>> >>>>>>>>eh ...Does anybody want to help? >>>>>>> >>>>>>> >>>>>>>got the answer for atoms - it's right here >>>>>>> >>>>>>>" >>>>>>>It seems, then, that the number of atoms in the Universe is at least about 4e78, >>>>>>>but perhaps as many as 6e79. I would suggest 1e79 as a reasonable estimate. That >>>>>>>is, 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >>>>>>>000 000 000 000 000 000 000 000 atoms. >>>>>>>" >>>>>>> >>>>>> >>>>>> >>>>>>Thanks Mike, very nice page. But how about the total number of chess >>>>>>positions??? >>>>>> >>>>>> , >>>>>>>http://www.sunspot.noao.edu/sunspot/pr/answerbook/universe.html >>>>>>> >>>>>>>looks like "positions in chess" beats "atoms in the universe" by a fair amount >>>>>>>.... >>>>>>> >>>>>>>...now about the 32 man EGTB that I was thinking about - how many drives would I >>>>>>>need?? >>>>>>> >>>>>>> >>>>>>>;>) >>>>> >>>>> >>>>>I gave you the number 6.5104179521361946395624758693608e+308 that is 6.5 x10 to >>>>>the 308 or just add 308 zeroes ... >>>>> >>>>>6,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 >>>> >>>>Your number is wrong >>>> >>>>The number of positions is clearly smaller. >>> >>>Yes you are correct -- clearly a big difference - I was counting games but after >>>second thought my second estimate is much close I believe. 1e154 or so. >> >>I know that the number of positions(not games) is less than 1e48 >>> >>> >>> >>>> >>>>You gave an estimate for the number of games >>>>and this number is also wrong. >>> >>>Show me. >> >>No problem >> >>The number of possible games is clearly bigger because the sides can play >>even 1000 moves when every side have 10 possibility not to capture,not to move a >>pawn and not to give checkmate. >> >>imagine that the sides always move with their knights in the first 50 moves >>and only in move 50 black plays 50...a7a6 >> >>they continue with 99 quiet plies and black plays 100...a6a5 >> >>If I assume that they have 10 possibility to move with the knight in every move >>they can continue without captures for more than 1000 plies. >> >>a7a6 a6a5 a2a3 a3a4 are 4 moves in the a file. >> >>4*8=32 moves so the side can play 32 pawn moves and more than 98*32 quiet moves. >> >>total number of moves is more than 32+98*32=3168 moves. >> >>If in every move every side has 10 not to move with a pawn and not to capture >>then you can get more than 10^3000 games without captures. >> >>The number of quiet legal moves in the first ply is 4 but even if you assume >>4^3000 it is clearly more than 10^1000 games. >> >>My estimate for 10 is follow from the fat that the side have more moves after >>they move the knights and the pawns. >> >>Uri > >Uri, > >I know there are lot more games than positions. That is obvious > >The "show me" was in reference to my number of 1e154 (my second estimate) games >is wrong. You might have my read first estimate of ~6e308 which is of course is >too high. I don't think you can prove 1e154 is wrong - but if you can, show me. > >Thanks, > >Mike I believe that I can prove that there are more than 1e154 games and even more than 1e308 games. First I need to calculate the number of possibilities when both sides play with the knight and the rooks in the first 99 plies without 3 time repetition. The main problem is not having 3 time repetition but I believe that I can prove that it is more than 1e50 later I need to prove the number of possibilities to do the same after e7e6 Again I believe that it is more than 1e50 I can continue in this way for every pawn moves and there are more than 20 pawn moves so I can prove that it is more than 1e1000(I am too lazy to try to prove it mathematically). Here is one possible game I was too lazy to continue the game but I believe that the number of possibilities in the first 99 plies is more than 10^50 and it should be more easy to prove it for the next plies(it is not a mathematical proof but if you assume that every side has only 4 possibilities in every move you get 4^99>10^50 If you push a pawn every 99 or 98 plies to avoid the 50 move rule you can get games of more than 3000 plies and the number of possibilities is clearly more than 1e1000 [Event "Edited game"] [Site "F3K9V7"] [Date "2002.11.29"] [Round "-"] [White "-"] [Black "-"] [Result "*"] 1. Na3 Na6 2. Nc4 Nc5 3. Ne3 Ne6 4. Ng4 Ng5 5. Ne3 Ne4 6. Nc4 Ng5 7. Na3 Nh3 8. Nf3 Nf4 9. Nc4 Nd5 10. Ne3 Ndf6 11. Nf5 Nd5 12. Nh6 Ngf6 13. Nf5 Nh5 14. N5d4 Nb6 15. Nb3 Nf6 16. Nh4 Nh5 17. Na5 Na4 18. Rg1 Nb6 19. Nc4 Nd5 20. Na3 Nhf6 21. Nf3 Rg8 22. Nd4 Nh5 23. Nf3 Nhf6 24. Rh1 Nf4 25. Nc4 N6h5 26. Na5 Ng3 27. Nc6 Ng6 28. Ng5 Nh4 29. Ne4 Nhf5 30. Nc3 Nd4 31. Nd5 Nb3 32. Nb6 Rh8 33. Ne5 Ne4 34. Ng4 Nf6 35. Ne3 Nc5 36. Nbc4 Ne6 37. Na3 Nh5 38. Nec4 Nc5 39. Ne3 Ne6 40. Rb1 Nc5 41. Ng4 Na6 42. Nc4 Nc5 43. Na3 Na6 44. Ra1 Nf6 45. Ne3 Nb8 46. Nb1 Nd5 47. Nc4 Nb6 48. Nca3 Na4 49. Nb5 Nc3 50. Nd4 e6 51. Nf3 Be7 52. Nd4 Bd6 53. Nf3 Bc5 54. Nd4 Bb4 55. Nf3 Ba3 56. Nd4 Qe7 57. Nf3 Qf6 58. Nd4 Qg5 59. Nf3 Qh4 60. Nd4 Qg5 61. Nb3 Qd8 * Uri
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.