Hi all. I don't post often, but thought this may be worth sharing. I recently found a mate in 69 in 4x4 chess: nN1b/2pB/B3/KBbk w - - 0 1. You can explore it in the online interface: https://calc.biokirr.com/4x4c/query?metric=DTM&pos=nN1b/2pB/B3/KBbk. (Let me know if you notice anything strange, or if you find an improvement for either side!).
This is 10 moves more than the longest mate in 9-piece endgames (59 moves), which by itself is interesting. The maxDTM values for 6 to 9 pieces were 52, 54, 56 and 59, so I did not expect this large jump with 10 pieces. Not yet 100% sure it's correct, as always can't rule out both software bugs and hardware glitches. Also, this is from partial 10-piece tables, so it's possible that an even longer mate can be found when all 10-piece endgames are solved (although I doubt it).
The DTM-optimal line has 46 moves without captures or pawn moves, which gets really close to 50 moves. I think it will be amazing if 50 move rule turns out to be relevant on 4x4 board. I still doubt that it will, but hopefully will have more DTZ data soon to check it.
More details: https://kirill-kryukov.com/chess/4x4-chess/ (The page is far from complete).
Mate in 69 on 4x4 board
Moderator: Ras
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jkominek
- Posts: 70
- Joined: Tue Sep 04, 2018 5:33 am
- Full name: John Kominek
Re: Mate in 69 on 4x4 board
Hi Kirill, nice to hear from you again.
Don't be such a doubter of your own work! Keep looking another three ply. I believe it's waiting to be found with just the right mix of bishops, knights, and pawns.
Don't be such a doubter of your own work! Keep looking another three ply. I believe it's waiting to be found with just the right mix of bishops, knights, and pawns.
Code: Select all
=========== kbbnppkbbp ===========
Win in 1: 16428113 ( 11.96%)
Win in 2: 11387814 ( 8.29%)
Win in 3: 11835956 ( 8.62%)
Win in 4: 13409515 ( 9.76%)
Win in 5: 13847391 ( 10.08%)
Win in 6: 13893253 ( 10.12%)
Win in 7: 13675750 ( 9.96%)
Win in 8: 11708065 ( 8.53%)
Win in 9: 8447551 ( 6.15%)
Win in 10: 5470314 ( 3.98%)
Win in 11: 3478380 ( 2.53%)
Win in 12: 2279980 ( 1.66%)
Win in 13: 1508048 ( 1.10%)
Win in 14: 1014727 ( 0.74%)
Win in 15: 687231 ( 0.50%)
Win in 16: 468901 ( 0.34%)
Win in 17: 334086 ( 0.24%)
Win in 18: 246970 ( 0.18%)
Win in 19: 198510 ( 0.14%)
Win in 20: 160762 ( 0.12%)
Win in 21: 131634 ( 0.10%)
Win in 22: 105935 ( 0.08%)
Win in 23: 83925 ( 0.06%)
Win in 24: 65546 ( 0.05%)
Win in 25: 50879 ( 0.04%)
Win in 26: 38144 ( 0.03%)
Win in 27: 28431 ( 0.02%)
Win in 28: 20313 ( 0.01%)
Win in 29: 15071 ( 0.01%)
Win in 30: 11379 ( 0.01%)
Win in 31: 8721 ( 0.01%)
Win in 32: 6283 ( 0.00%)
Win in 33: 4687 ( 0.00%)
Win in 34: 3473 ( 0.00%)
Win in 35: 2780 ( 0.00%)
Win in 36: 1999 ( 0.00%)
Win in 37: 1415 ( 0.00%)
Win in 38: 790 ( 0.00%)
Win in 39: 505 ( 0.00%)
Win in 40: 358 ( 0.00%)
Win in 41: 241 ( 0.00%)
Win in 42: 263 ( 0.00%)
Win in 43: 216 ( 0.00%)
Win in 44: 141 ( 0.00%)
Win in 45: 63 ( 0.00%)
Win in 46: 36 ( 0.00%)
Win in 47: 13 ( 0.00%)
Win in 48: 5 ( 0.00%)
Win in 49: 6 ( 0.00%)
Win in 50: 9 ( 0.00%)
Win in 51: 11 ( 0.00%)
Win in 52: 16 ( 0.00%)
Win in 53: 10 ( 0.00%)
Win in 54: 9 ( 0.00%)
Win in 55: 17 ( 0.00%)
Win in 56: 21 ( 0.00%)
Win in 57: 35 ( 0.00%)
Win in 58: 66 ( 0.00%)
Win in 59: 79 ( 0.00%)
Win in 60: 41 ( 0.00%)
Win in 61: 34 ( 0.00%)
Win in 62: 25 ( 0.00%)
Win in 63: 6 ( 0.00%)
Win in 64: 9 ( 0.00%)
Win in 65: 13 ( 0.00%)
Win in 66: 19 ( 0.00%)
Win in 67: 15 ( 0.00%)
Win in 68: 16 ( 0.00%)
Win in 69: 12 ( 0.00%)
Win in 70: 10 ( 0.00%)
Win in 71: 22 ( 0.00%)
Win in 72: 11 ( 0.00%)
Draw: 5892264 ( 4.29%)
Loss in 37: 4 ( 0.00%)
Loss in 36: 5 ( 0.00%)
Loss in 35: 7 ( 0.00%)
Loss in 34: 2 ( 0.00%)
Loss in 33: 8 ( 0.00%)
Loss in 32: 6 ( 0.00%)
Loss in 31: 3 ( 0.00%)
Loss in 30: 14 ( 0.00%)
Loss in 29: 22 ( 0.00%)
Loss in 28: 20 ( 0.00%)
Loss in 27: 43 ( 0.00%)
Loss in 26: 88 ( 0.00%)
Loss in 25: 132 ( 0.00%)
Loss in 24: 232 ( 0.00%)
Loss in 23: 365 ( 0.00%)
Loss in 22: 507 ( 0.00%)
Loss in 21: 599 ( 0.00%)
Loss in 20: 859 ( 0.00%)
Loss in 19: 1153 ( 0.00%)
Loss in 18: 1477 ( 0.00%)
Loss in 17: 2085 ( 0.00%)
Loss in 16: 2967 ( 0.00%)
Loss in 15: 3950 ( 0.00%)
Loss in 14: 5250 ( 0.00%)
Loss in 13: 7059 ( 0.01%)
Loss in 12: 8957 ( 0.01%)
Loss in 11: 11280 ( 0.01%)
Loss in 10: 13881 ( 0.01%)
Loss in 9: 16694 ( 0.01%)
Loss in 8: 19958 ( 0.01%)
Loss in 7: 21439 ( 0.02%)
Loss in 6: 23706 ( 0.02%)
Loss in 5: 28319 ( 0.02%)
Loss in 4: 35250 ( 0.03%)
Loss in 3: 52978 ( 0.04%)
Loss in 2: 71115 ( 0.05%)
Loss in 1: 49097 ( 0.04%)-
jkominek
- Posts: 70
- Joined: Tue Sep 04, 2018 5:33 am
- Full name: John Kominek
Re: Mate in 69 on 4x4 board
Adding together, in total...
Code: Select all
=========== Total for 3042 tables ===========
Win in 1: 36816976071 ( 18.71%)
Win in 2: 19337546490 ( 9.83%)
Win in 3: 13561140552 ( 6.89%)
Win in 4: 10607652946 ( 5.39%)
Win in 5: 8490299010 ( 4.31%)
Win in 6: 6735848719 ( 3.42%)
Win in 7: 5227614316 ( 2.66%)
Win in 8: 3986891673 ( 2.03%)
Win in 9: 2978808571 ( 1.51%)
Win in 10: 2189137988 ( 1.11%)
Win in 11: 1590929800 ( 0.81%)
Win in 12: 1142662790 ( 0.58%)
Win in 13: 815664489 ( 0.41%)
Win in 14: 581864046 ( 0.30%)
Win in 15: 414453930 ( 0.21%)
Win in 16: 293185859 ( 0.15%)
Win in 17: 204711003 ( 0.10%)
Win in 18: 142537665 ( 0.07%)
Win in 19: 99472274 ( 0.05%)
Win in 20: 70268683 ( 0.04%)
Win in 21: 50459890 ( 0.03%)
Win in 22: 37066619 ( 0.02%)
Win in 23: 28452687 ( 0.01%)
Win in 24: 22306982 ( 0.01%)
Win in 25: 17428324 ( 0.01%)
Win in 26: 13898737 ( 0.01%)
Win in 27: 10943191 ( 0.01%)
Win in 28: 8826106 ( 0.00%)
Win in 29: 6600688 ( 0.00%)
Win in 30: 4741130 ( 0.00%)
Win in 31: 3249106 ( 0.00%)
Win in 32: 2143079 ( 0.00%)
Win in 33: 1412092 ( 0.00%)
Win in 34: 976461 ( 0.00%)
Win in 35: 674189 ( 0.00%)
Win in 36: 447896 ( 0.00%)
Win in 37: 305654 ( 0.00%)
Win in 38: 232037 ( 0.00%)
Win in 39: 176727 ( 0.00%)
Win in 40: 147986 ( 0.00%)
Win in 41: 115119 ( 0.00%)
Win in 42: 83682 ( 0.00%)
Win in 43: 58118 ( 0.00%)
Win in 44: 47501 ( 0.00%)
Win in 45: 42092 ( 0.00%)
Win in 46: 36887 ( 0.00%)
Win in 47: 28704 ( 0.00%)
Win in 48: 18140 ( 0.00%)
Win in 49: 12780 ( 0.00%)
Win in 50: 7541 ( 0.00%)
Win in 51: 4271 ( 0.00%)
Win in 52: 2674 ( 0.00%)
Win in 53: 2488 ( 0.00%)
Win in 54: 1785 ( 0.00%)
Win in 55: 789 ( 0.00%)
Win in 56: 444 ( 0.00%)
Win in 57: 273 ( 0.00%)
Win in 58: 183 ( 0.00%)
Win in 59: 114 ( 0.00%)
Win in 60: 45 ( 0.00%)
Win in 61: 34 ( 0.00%)
Win in 62: 25 ( 0.00%)
Win in 63: 6 ( 0.00%)
Win in 64: 9 ( 0.00%)
Win in 65: 13 ( 0.00%)
Win in 66: 19 ( 0.00%)
Win in 67: 15 ( 0.00%)
Win in 68: 16 ( 0.00%)
Win in 69: 12 ( 0.00%)
Win in 70: 10 ( 0.00%)
Win in 71: 22 ( 0.00%)
Win in 72: 11 ( 0.00%)
Draw: 19487284124 ( 9.90%)
Loss in 73: 2 ( 0.00%)
Loss in 72: 2 ( 0.00%)
Loss in 71: 7 ( 0.00%)
Loss in 70: 11 ( 0.00%)
Loss in 69: 7 ( 0.00%)
Loss in 68: 8 ( 0.00%)
Loss in 67: 14 ( 0.00%)
Loss in 66: 5 ( 0.00%)
Loss in 65: 11 ( 0.00%)
Loss in 64: 5 ( 0.00%)
Loss in 63: 5 ( 0.00%)
Loss in 62: 3 ( 0.00%)
Loss in 61: 20 ( 0.00%)
Loss in 60: 23 ( 0.00%)
Loss in 59: 37 ( 0.00%)
Loss in 58: 82 ( 0.00%)
Loss in 57: 180 ( 0.00%)
Loss in 56: 312 ( 0.00%)
Loss in 55: 580 ( 0.00%)
Loss in 54: 1244 ( 0.00%)
Loss in 53: 2401 ( 0.00%)
Loss in 52: 2584 ( 0.00%)
Loss in 51: 3997 ( 0.00%)
Loss in 50: 6999 ( 0.00%)
Loss in 49: 12483 ( 0.00%)
Loss in 48: 19749 ( 0.00%)
Loss in 47: 26882 ( 0.00%)
Loss in 46: 38997 ( 0.00%)
Loss in 45: 47435 ( 0.00%)
Loss in 44: 50626 ( 0.00%)
Loss in 43: 55167 ( 0.00%)
Loss in 42: 76496 ( 0.00%)
Loss in 41: 108422 ( 0.00%)
Loss in 40: 143187 ( 0.00%)
Loss in 39: 176948 ( 0.00%)
Loss in 38: 207751 ( 0.00%)
Loss in 37: 265007 ( 0.00%)
Loss in 36: 337698 ( 0.00%)
Loss in 35: 477623 ( 0.00%)
Loss in 34: 676036 ( 0.00%)
Loss in 33: 966548 ( 0.00%)
Loss in 32: 1408569 ( 0.00%)
Loss in 31: 2168831 ( 0.00%)
Loss in 30: 3269503 ( 0.00%)
Loss in 29: 4822896 ( 0.00%)
Loss in 28: 6678675 ( 0.00%)
Loss in 27: 8726427 ( 0.00%)
Loss in 26: 10836236 ( 0.01%)
Loss in 25: 14026063 ( 0.01%)
Loss in 24: 18144508 ( 0.01%)
Loss in 23: 24060008 ( 0.01%)
Loss in 22: 31428521 ( 0.02%)
Loss in 21: 42360228 ( 0.02%)
Loss in 20: 58653707 ( 0.03%)
Loss in 19: 82955991 ( 0.04%)
Loss in 18: 119830150 ( 0.06%)
Loss in 17: 175573444 ( 0.09%)
Loss in 16: 256141998 ( 0.13%)
Loss in 15: 370478710 ( 0.19%)
Loss in 14: 533206405 ( 0.27%)
Loss in 13: 759437125 ( 0.39%)
Loss in 12: 1075140426 ( 0.55%)
Loss in 11: 1501769772 ( 0.76%)
Loss in 10: 2062537242 ( 1.05%)
Loss in 9: 2760108814 ( 1.40%)
Loss in 8: 3616801094 ( 1.84%)
Loss in 7: 4669263327 ( 2.37%)
Loss in 6: 5884128878 ( 2.99%)
Loss in 5: 7187820878 ( 3.65%)
Loss in 4: 8460001084 ( 4.30%)
Loss in 3: 9310373842 ( 4.73%)
Loss in 2: 8473083572 ( 4.31%)
Loss in 1: 4283571140 ( 2.18%)
Total tables: 3042
Combined: 8 ( 0.3%)
Half-combined: 3009 ( 98.9%)
Separate: 25 ( 0.8%)
Individually saved slices: 224411
Combined: 207409 ( 92.4%)
Half-combined: 17002 ( 7.6%)
Separate: 0 ( 0.0%)
Total positions: 196798418060-
Kirill Kryukov
- Posts: 518
- Joined: Sun Mar 19, 2006 4:12 am
- Full name: Kirill Kryukov
Re: Mate in 69 on 4x4 board
Hi John! You've been busy! It looks like you've already completed the solver run for 10-piece 3-pawn endgames, good job! 
If all goes well, I guess I will get there in another week or two. I took a long break from this, only recently picking this up again. How far did you get overall, and have you noticed any problems?
As for being a doubter, I guess you're right. I treat all results are preliminary until they are reproduced by three different groups and methods.
For one example, I recently found that I previously miscounted the total number of unique legal positions in 4x4 chess: I thought it was 3,677,542,994,054,890, but now I found that it's actually 3,677,542,994,054,888. The off-by-two error is from summing the partial numbers in Excel, which is unable to work with large numbers without rounding. Can you believe it?
If all goes well, I guess I will get there in another week or two. I took a long break from this, only recently picking this up again. How far did you get overall, and have you noticed any problems?As for being a doubter, I guess you're right. I treat all results are preliminary until they are reproduced by three different groups and methods.
For one example, I recently found that I previously miscounted the total number of unique legal positions in 4x4 chess: I thought it was 3,677,542,994,054,890, but now I found that it's actually 3,677,542,994,054,888. The off-by-two error is from summing the partial numbers in Excel, which is unable to work with large numbers without rounding. Can you believe it?
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jkominek
- Posts: 70
- Joined: Tue Sep 04, 2018 5:33 am
- Full name: John Kominek
Re: Mate in 69 on 4x4 board
What? For all the accountants in the world, professional and amateur, who use excel to tally currencies, that's startling. You weren't using an old 32 bit version were you?
I was 4x4 busy in 2021-2022 during which I was feeling the need for diversion, or perhaps procrastination. Computer chess fits that role rather well for me. I went for the full 10 men gamut but encountered some crashes so did not complete it all. A quick grep says 93 files are missing. A couple are kqqrbnkqrn and kqrrbnkqrn. I was able to climb the mountain for 9 vs 1 and 8 vs 2, but not 7-3, 6-4 or 5-5.
If you are interested in comparing to the stats files I generated, or even the data files, configure an old-fashioned anonymous sftp site and I'll upload them.
I was 4x4 busy in 2021-2022 during which I was feeling the need for diversion, or perhaps procrastination. Computer chess fits that role rather well for me. I went for the full 10 men gamut but encountered some crashes so did not complete it all. A quick grep says 93 files are missing. A couple are kqqrbnkqrn and kqrrbnkqrn. I was able to climb the mountain for 9 vs 1 and 8 vs 2, but not 7-3, 6-4 or 5-5.
If you are interested in comparing to the stats files I generated, or even the data files, configure an old-fashioned anonymous sftp site and I'll upload them.
Code: Select all
=========== kppppppppk ===========
Win in 1: 672 ( 20.33%)
Win in 2: 393 ( 11.89%)
Win in 3: 737 ( 22.29%)
Win in 4: 905 ( 27.37%)
Win in 5: 541 ( 16.36%)
Win in 6: 40 ( 1.21%)
Win in 7: 3 ( 0.09%)
Win in 8: 1 ( 0.03%)
Draw: 14 ( 0.42%)
=========== kpppppppkp ===========
Win in 1: 8277 ( 18.73%)
Win in 2: 7010 ( 15.86%)
Win in 3: 8238 ( 18.64%)
Win in 4: 11167 ( 25.27%)
Win in 5: 7461 ( 16.88%)
Win in 6: 1659 ( 3.75%)
Win in 7: 170 ( 0.38%)
Win in 8: 57 ( 0.13%)
Win in 9: 37 ( 0.08%)
Win in 10: 14 ( 0.03%)
Win in 11: 10 ( 0.02%)
Win in 12: 2 ( 0.00%)
Win in 13: 1 ( 0.00%)
Draw: 90 ( 0.20%)-
jkominek
- Posts: 70
- Joined: Tue Sep 04, 2018 5:33 am
- Full name: John Kominek
Re: Mate in 69 on 4x4 board
Also, with your program I made partial progress into 11 men territory. Among what I generated max dtm is Win in 73.
Code: Select all
=========== kbbbbnkrbpp ===========
Win in 1: 17342628 ( 14.11%)
Win in 2: 9533453 ( 7.75%)
Win in 3: 6999709 ( 5.69%)
Win in 4: 6091405 ( 4.95%)
Win in 5: 5928654 ( 4.82%)
Win in 6: 6477194 ( 5.27%)
Win in 7: 7003876 ( 5.70%)
Win in 8: 7343855 ( 5.97%)
Win in 9: 6965958 ( 5.67%)
Win in 10: 6084605 ( 4.95%)
Win in 11: 5181025 ( 4.21%)
Win in 12: 4129470 ( 3.36%)
Win in 13: 3129790 ( 2.55%)
Win in 14: 2325821 ( 1.89%)
Win in 15: 1740685 ( 1.42%)
Win in 16: 1290191 ( 1.05%)
Win in 17: 970523 ( 0.79%)
Win in 18: 749031 ( 0.61%)
Win in 19: 616378 ( 0.50%)
Win in 20: 528411 ( 0.43%)
Win in 21: 446838 ( 0.36%)
Win in 22: 378149 ( 0.31%)
Win in 23: 325437 ( 0.26%)
Win in 24: 278856 ( 0.23%)
Win in 25: 232325 ( 0.19%)
Win in 26: 188224 ( 0.15%)
Win in 27: 145263 ( 0.12%)
Win in 28: 113688 ( 0.09%)
Win in 29: 89018 ( 0.07%)
Win in 30: 68070 ( 0.06%)
Win in 31: 51139 ( 0.04%)
Win in 32: 40321 ( 0.03%)
Win in 33: 33987 ( 0.03%)
Win in 34: 28641 ( 0.02%)
Win in 35: 25502 ( 0.02%)
Win in 36: 22589 ( 0.02%)
Win in 37: 20051 ( 0.02%)
Win in 38: 17976 ( 0.01%)
Win in 39: 15975 ( 0.01%)
Win in 40: 14247 ( 0.01%)
Win in 41: 13321 ( 0.01%)
Win in 42: 10962 ( 0.01%)
Win in 43: 8779 ( 0.01%)
Win in 44: 7813 ( 0.01%)
Win in 45: 6637 ( 0.01%)
Win in 46: 5142 ( 0.00%)
Win in 47: 3973 ( 0.00%)
Win in 48: 3023 ( 0.00%)
Win in 49: 2588 ( 0.00%)
Win in 50: 2030 ( 0.00%)
Win in 51: 1231 ( 0.00%)
Win in 52: 841 ( 0.00%)
Win in 53: 552 ( 0.00%)
Win in 54: 379 ( 0.00%)
Win in 55: 366 ( 0.00%)
Win in 56: 319 ( 0.00%)
Win in 57: 307 ( 0.00%)
Win in 58: 198 ( 0.00%)
Win in 59: 123 ( 0.00%)
Win in 60: 100 ( 0.00%)
Win in 61: 80 ( 0.00%)
Win in 62: 77 ( 0.00%)
Win in 63: 36 ( 0.00%)
Win in 64: 16 ( 0.00%)
Win in 65: 17 ( 0.00%)
Win in 66: 14 ( 0.00%)
Win in 67: 9 ( 0.00%)
Win in 68: 4 ( 0.00%)
Win in 69: 1 ( 0.00%)
Win in 70: 2 ( 0.00%)
Win in 71: 2 ( 0.00%)
Win in 72: 0 ( 0.00%)
Win in 73: 2 ( 0.00%)
Draw: 19129884 ( 15.56%)
Loss in 45: 1 ( 0.00%)
Loss in 44: 0 ( 0.00%)
Loss in 43: 2 ( 0.00%)
Loss in 42: 0 ( 0.00%)
Loss in 41: 1 ( 0.00%)
Loss in 40: 3 ( 0.00%)
Loss in 39: 3 ( 0.00%)
Loss in 38: 1 ( 0.00%)
Loss in 37: 2 ( 0.00%)
Loss in 36: 15 ( 0.00%)
Loss in 35: 21 ( 0.00%)
Loss in 34: 64 ( 0.00%)
Loss in 33: 101 ( 0.00%)
Loss in 32: 225 ( 0.00%)
Loss in 31: 337 ( 0.00%)
Loss in 30: 513 ( 0.00%)
Loss in 29: 743 ( 0.00%)
Loss in 28: 1031 ( 0.00%)
Loss in 27: 1224 ( 0.00%)
Loss in 26: 1515 ( 0.00%)
Loss in 25: 1687 ( 0.00%)
Loss in 24: 1942 ( 0.00%)
Loss in 23: 1633 ( 0.00%)
Loss in 22: 1660 ( 0.00%)
Loss in 21: 2040 ( 0.00%)
Loss in 20: 2349 ( 0.00%)
Loss in 19: 3165 ( 0.00%)
Loss in 18: 4338 ( 0.00%)
Loss in 17: 6762 ( 0.01%)
Loss in 16: 8173 ( 0.01%)
Loss in 15: 10929 ( 0.01%)
Loss in 14: 14023 ( 0.01%)
Loss in 13: 18823 ( 0.02%)
Loss in 12: 24466 ( 0.02%)
Loss in 11: 28395 ( 0.02%)
Loss in 10: 31903 ( 0.03%)
Loss in 9: 36712 ( 0.03%)
Loss in 8: 40528 ( 0.03%)
Loss in 7: 45206 ( 0.04%)
Loss in 6: 50360 ( 0.04%)
Loss in 5: 58152 ( 0.05%)
Loss in 4: 73437 ( 0.06%)
Loss in 3: 100971 ( 0.08%)
Loss in 2: 133759 ( 0.11%)
Loss in 1: 75301 ( 0.06%)-
Uri Blass
- Posts: 10828
- Joined: Thu Mar 09, 2006 12:37 am
- Location: Tel-Aviv Israel
Re: Mate in 69 on 4x4 board
I see that you do not allow pawn in the second rank to go 2 squares forward.
I think natural generation of chess is to allow pawn in the second rank to go 2 squares forward(and in 4*4 board it means to promote if the squares are empty.
If you allow pawns in the first rank then generalization can include also enpassent capture of a pawn that promote.
I also guess that chess with 2 files and more than 4 ranks with enpassent may be interesting.
For castling I see no natural generation from 8 files to less than 8 files so if you want to make research of game with castling then the first game to try is 8 files and 3 ranks when white has king at e1 rooks at h1 rook a1 and black king e3 rook at h3 and a3 and you can decide if you allow castle.
No natural initial position and for natural initial position you need 4 ranks when white wins by 1.exf7# or 1.gxf7#
It may be interesting if somebody can prove that white is winning with 5 ranks and 8 files.
This position except white cannot go backward because there are no 1-3 ranks and white pawns are allowed to advace 2 squares in the first move(if the path is empty) and white can castle and black can also make enpessant and a line like d6 exd6 e7 fxe6 is legal.
[d]rnbqkbnr/pppppppp/8/PPPPPPPP/RNBQKBNR/8/8/8 w kq - 0 1
I think natural generation of chess is to allow pawn in the second rank to go 2 squares forward(and in 4*4 board it means to promote if the squares are empty.
If you allow pawns in the first rank then generalization can include also enpassent capture of a pawn that promote.
I also guess that chess with 2 files and more than 4 ranks with enpassent may be interesting.
For castling I see no natural generation from 8 files to less than 8 files so if you want to make research of game with castling then the first game to try is 8 files and 3 ranks when white has king at e1 rooks at h1 rook a1 and black king e3 rook at h3 and a3 and you can decide if you allow castle.
No natural initial position and for natural initial position you need 4 ranks when white wins by 1.exf7# or 1.gxf7#
It may be interesting if somebody can prove that white is winning with 5 ranks and 8 files.
This position except white cannot go backward because there are no 1-3 ranks and white pawns are allowed to advace 2 squares in the first move(if the path is empty) and white can castle and black can also make enpessant and a line like d6 exd6 e7 fxe6 is legal.
[d]rnbqkbnr/pppppppp/8/PPPPPPPP/RNBQKBNR/8/8/8 w kq - 0 1
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Kirill Kryukov
- Posts: 518
- Joined: Sun Mar 19, 2006 4:12 am
- Full name: Kirill Kryukov
Re: Mate in 69 on 4x4 board
For currencies, I guess this won't matter until you are a trillionaire, at which point presumably you either can afford to hire someone who knows what they are doing, or you don't mind about being a couple of cents off. But yeah, even though I don't normally trust Excel with anything important, this took me by surprise. Excel from the usual Office Pro, desktop version. In 2011 it must have been version 2009 or something, but a more recent version 2019 still has this problem. If I was not a douber, I would have continued trusting the wrong number instead of recalculating with another tool.
I think I know what you mean. To me computer chess is a combination of art, science, and therapy. Sorry about the crashes, it was probably hitting its own memory allocation limit, which happens with some 10-piece tables (kqqrbnkqrn and kqrrbnkqrn are among the most memory-demanding).jkominek wrote: ↑Fri Jan 31, 2025 1:56 amI was 4x4 busy in 2021-2022 during which I was feeling the need for diversion, or perhaps procrastination. Computer chess fits that role rather well for me. I went for the full 10 men gamut but encountered some crashes so did not complete it all. A quick grep says 93 files are missing. A couple are kqqrbnkqrn and kqrrbnkqrn. I was able to climb the mountain for 9 vs 1 and 8 vs 2, but not 7-3, 6-4 or 5-5.
Thanks, it would be cool to compare the stats! I will set up an account soon!
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Kirill Kryukov
- Posts: 518
- Joined: Sun Mar 19, 2006 4:12 am
- Full name: Kirill Kryukov
Re: Mate in 69 on 4x4 board
Very cool! I still have work to do with 10-piece endgames, and I'm using 5 metrics now, so this takes time. But I hope to also start building 11-piece tables sometimes this year. Maybe we can think of some way to collaborate if you still could use a distraction.
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Kirill Kryukov
- Posts: 518
- Joined: Sun Mar 19, 2006 4:12 am
- Full name: Kirill Kryukov
Re: Mate in 69 on 4x4 board
Yeah, double pawn step and castling does not feel natural for a 4x4 board to me, so I left them out for now. Or course this allows to not care about en-passant and castling rights, keeping the solver simpler, which is always nice. I may revisit these at some point in the future, but any contribution is welcome.
(As a side note, for standard chess I calculated the exact number of positions with castling rights, en-passant rigths, and both rights, for up to 8 pieces, in case anyone is curious: https://kirill-kryukov.com/chess/nulp/ )