Author: Mike Byrne
Date: 21:50:28 11/28/02
Go up one level in this thread
On November 29, 2002 at 00:44:20, Uri Blass wrote: >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 Oh ...you thought I too light - I can accept that -- I thought when you said I was wrong that you were implying I was too high - I knew I was not too high. I was just submitting a point that there are possibilites for a chess game than atoms in the universe. What I did took 2 minutes - I have no intention in trying to work out any numbers at this point. Mike
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