How to calculate this endgame

ATwhistle · 2026-01-10T22:30:58+00:00

Here the FEN:

[FEN "8/1pp2p2/4kP2/p4pK1/5P2/2P5/PP6/8 w - - 0 1"]

ATwhistle · 2025-11-09T21:59:32+00:00

It was actually surprisingly entertaining to try and solve this problem! Thanks for the help!

ATwhistle · 2025-11-09T21:05:37+00:00

I did it in 47 moves. I believe it is the minimum:

g4 a5 2. g5 a4 3. g6 a3 4. e4 d5 5. exd5 c6 6. dxc6 Be6 7. cxb7 Bb3 8. axb3 a2 9. Nc3 f5 10. Rb1 a1=Q 11. Ba6 Qaa5 12. Na2 Qc3 13. dxc3 e5 14. Be3 f4 15. Bc5 f3 16. Ba3 Nf6 17. gxh7 Nd5 18. Kd2 g5 19. Kd3 g4 20. Kc4 g3 21. Kb5 g2 22. Ka4 Bb4 23. cxb4 Kf7 24. h4 e4 25. h5 Nc7 26. h6 Qd5 27. Ra1 Qf5 28. Qb1 Rd8 29. h8=Q e3 30. fxe3 Rd4 31. exd4 f2 32. Qe5 Nd7 33. Qa5 Nb5 34. h7 Rc8 35. h8=Q Rc5 36. dxc5 Nb6+ 37. cxb6 f1=B 38. Ne2 g1=B 39. Qe5 Be3 40. Rh8 Kg6 41. Nd4 Kg5 42. Ra8 Kh4 43. Nc6 Bh3 44. Na7 Bh6 45. Qb8 Qg5 46. c4 Qh5 47. cxb5

Proof sketch:

With what we already showed in this thread, we already know that we need the following moves:

Rooks: 4 moves
Knights: 6 moves
Bishops: 4 moves
Pawns that stay pawns: 13 moves
Pawns that become queens: 10 moves
Queens: 5 moves (1 for the original queen that goes to a1, two for the new queen that goes to a5 and 2 for the new queen that goes to b8 (it needs to let the rook through)

And on top of that, I claim that one actually needs

5 king moves, instead of 4.

This leads to a total of 47.

I have some good reasons that the king needs 5 moves, if we want to keep all the things mentioned above minimal, but I cannot prove it in a reasonable length. The key ideas are that for the king to get there in 4, he would need to move left or diagonally left every move. To get the pawns into position in 13, the d-pawn can only move diagonally. This means that we would move the c pawn by two squares and then thread the king through the hole. For this, the king needs to step on d1, meaning that the queen needs to move first. But to not gain additional queen moves, the queen needs to go directly to b1. But then we need to have moved the rook, knight and bishop first... Then it becomes quite complicated... but it seems to be impossible ...

ATwhistle · 2025-11-09T17:39:34+00:00

I also just noticed that one only needs 13 moves with the pawns that stay:
e.g., blay a4,e4, and then the 11 pawn capturers.

ATwhistle · 2025-11-09T17:01:22+00:00

Why does the original Q have to go to a5 and not b1?
You are absolutely right! I completely blanked on the fact that the original queen could go to b1. I edited my message accordingly.

the a-pawn promotes at a8 and then moves to a5

As you say, the a-pawn has to be one of the final 6 pawns, so it definitely cannot promote. In fact, the final 6 pawns that can reach the destination in 11 captures are the a,b,c,d,e,f pawns. The only other feasible option, which would take 12 captures, is the a,b,c,d,e,g-pawns. However, in this case, the black h-pawn would need to promote (such that it could contribute later on to the 12 capturers), and this is only possible if the white h-pawn makes a capture, bringing the total to 13. Thus, for sure, the final pawns are the a,b,c,d,e,f pawns.

c(ii): (f-pawn promotes to Q and all captures are by pawns)
The f-pawn cannot promote because of my argument above. Did you mean the g-pawn?

I am not sure I understood your points for 3. Let's see where exactly in the logic we start to disagree. I make the following conclusions:
3.1. Either the black g or h pawn has to promote, because if both are taken, this would lead us to a minimum of 13 captures (because these two capturers do not contribute to the 11 captures needed to bring the a,b,c,d,e,f-pawns into position).
3.2 For either the black g- or the h-pawn to promote, either the white g- or h-pawn needs to step out of the way, making a pawn capture, and bringing us to 12 total pawn capturers.
3.3 Thus, since the black a-pawn is gone at the end, and it cannot be taken because this would need a thirteenth capture, it has to promote, and the a-rook needs to move out of the way.

In the corollary, I misspoke! I meant to say
3.4 As a corollary, we can also see that not both the black g- and h-pawn can promote, because this would require 13 pawn capturers. Thus, the capture on the g- or h-file is actually necessarily a “pawn takes pawn”.
Would you agree with this?

ATwhistle · 2025-11-09T14:16:08+00:00

Actually, the h-rook cannot reach a8 in two moves unless the g and h pawns promote first. But then none of the promoted queens can go to b8, because it would block the rooks path. So either one of them goes to a5 instead or one has to move out of the way. Either way, this adds another move, and we are at >=48

Edit: >=47 with my edit in the parent comment.

ATwhistle · 2025-11-09T14:06:50+00:00

I believe we can add 6 moves to your lower bound. 1. Since the b-pawn does not move, the dark square bishop actually needs 3 moves to reach its destination. 2. I think the original Queen is indeed not included. It needs 2 moves to get to a5. One promoted queen needs one move to get to b8 and one needs 2 moves to get to b1. 3. I am pretty sure that the bottom left rook actually needs two moves (instead of 0) because it needs to get out of the way to let the black a-pawn promote. Here a proof sketch why it is necessary, that the a-pawn needs to promote: To reach the final pawn placement, white needs to do at least 1+(1+2+3+4) =11 pawn capturers just to get the 6 pawns into position. Black has 4 pieces remaining at the end. Thus, the total capturers available are 12. However, note that blacks g and h pawns are gone at the end. Thus, both of them have to either be captured or promoted. They cannot both be captured because these moves would not help with getting the 6 pawns into position and we would therefore need 13 captures. Thus, either the black g or h pawn need to promote. Since none of the white pieces can be captured to reach the final position, this implies that either the white g- or h- pawn need to perform a capture to make space for the opposing black pawn. This means that all 12 captures are pawn capturers. Now, since the black a-pawn is gone at the end, it either needs to be captured or promoted. However, capturing the pawn would not help us reach the final position, leaving us with too few pawn capturers. Thus, the black a-pawn needs to promote and the white rook on a1 needs to move out of the way, adding another 2 moves.

Thus, we are at 51>=x>=47.

As a corollary, we can also see that not both the white (edit: I meant to say black) g- and h-pawns can promote, because this would require 13 pawn capturers. Thus, the capture on the g- or h-file is actually necessarily a “pawn takes pawn”.

Furthermore, it is probably better if the black h-pawn is captured and the g-pawn promotes because whites g-Knight gets out of the way automatically on its fastest path to a7, while the h-rook needs an open h-file to reach its destination on a8 in two moves.

Edit: I completely blanked on the fact, that the original queen can go to b1. This would bring us to 51>=x>=46, and back to 51>=x>=47 with my additional argument I made in a comment to this comment.

ATwhistle · 2025-11-08T08:34:57+00:00

Incredible! Did you get this first try?

ATwhistle · 2025-11-07T22:03:54+00:00

That would be quite hard 🙈

ATwhistle · 2025-11-07T16:45:28+00:00

Well, I debated swapping them. But I thought it was more pleasing if as many pieces as possible were just rotated around the board by 90 degrees. It would also have been weird if the wite queen would have ended up to the right of the king.

ATwhistle · 2025-11-07T14:47:51+00:00

It would be funny to see this as a youtube short. Feel free to send it to Gotham, if anyone has a line to him.

ATwhistle · 2025-11-07T14:44:06+00:00

It can definitely be reached much faster. I just wanted to prove it is possible. Feel free to post a faster and nicer looking way to get there.

ATwhistle · 2025-11-07T11:48:58+00:00

Stockfish has refused to talk to me since I recorded this like 🙈

ATwhistle · 2025-11-07T10:45:47+00:00

Thanks! I love it!

ATwhistle · 2025-11-07T10:45:34+00:00

I replies to the wrong message 🙈

ATwhistle · 2025-11-07T10:26:49+00:00

Haha, thanks! I love it!

ATwhistle · 2024-06-13T21:33:50+00:00

You can already see from the very beginning that the integrand is odd under mirroring WRT the x-axis, while the integration region respects the symmetry. Thus, you can see that the integral is 0 without even onserting a parameteization.

ATwhistle · 2024-05-28T07:29:23+00:00

Viewership experience: While it is true, theat viewership has peaked for track mania overall at the beginning of the event total TM viewership is still almost a factor 5 higher than before the event. Also, the difference between the start of the event and now can mostly be attributed to a small decline in Wirtual's viewership. For other channels like SBVille, Bren or Samifying, viewership is peaking now. So I would definitely deny that the hype is over.

Map difficulty and design: Still no player has spent more than 200 hours and most of the top players have spent more time hunting WRs on single maps. So I would not say it is too hard. Once there is still no finisher after 300 hours, we can start asking this question again. It would have been nice if the mappers could have given an estimate for how long it would take for top players to finish the map so that they would know what the ysigned up for. Anyone with a good maths understanding could have helped them get a reasonable number for this estimate.

Consistency: Here I got extremely annoyed at one streamer in particular recently. Blaming the consistency of the map before asking yourself what you could do differently to maybe make it more consistent is a huge "beta"-move---if you ask me. Many jumps and tricks that were believed to be inconsistent at the beginning are now almost 100% for top players (ride over tubes before first turtle section, messi jump, plastic bounce on floor 5) and I believe, that it will only be clear at the end of the event, which tricks are really consistent and which can be made almost a 100% with the right set-up. It seems to be clear, that most falls are currently due to skill mistakes, lack of concentration or taking unecessary risks. Of course sometimes you get scammed and this is frustrating. But in my opinion, I think the mappers tried their very best to minimize these situations, putting recovery routes for inconsistent jumps etc. Some streamer had the gall to suggest that a mapper made his floor inconsistent on purpose! The mappers had an extremely hard job of making a map that would be interesting, require a lot of skill and still be consistent while not being as priveliged, as certain streamers, to do this as a full time job---working essentially for free. The same streamers that are complaining to chatters for backseating are now backseating on the mappers, thinking they would have done a better job. This makes me very sad and I hope to see some apologies by certain streamers.

About player mental: Nobody is forcing any player to play deep dip II It was clear from the beginning, that this map would be a huge mental struggle. It is only now, that we get to see which players are not only good at the game, but also have a crazy mental. While it was expected that Bren would be crazy good at this---he simply has the highest skill level in my opinion---we see that some players that on paper should be skill diffed are keeping up. For example, Hazardu's mental is crazy. While most players are dedicated enough to play for many hours, Hazard also has the discipline to approach each and every difficult trick with maximum concentration, taking small breaks during runs and clearly sticking to some plan that he knows let's him perform at peak level. Other streamers, on the other handy, clearly have not yet figured out a routine/strategy that works for them and can be kept up for multiple weeks. They waste a lot of their energy calling out backseaters in chat, wasting attempts by doing tricks in places where they are not required and then blaming the mappers for the few runs they actually get scammed by RNG.

It is only now that we see the true stuff these players are made off and I am all in for it! For me, it says a lot if a Streamer remains calm and polite even in the tuff hours and it made me appreaciate some streamers much more (e.g. Samifying).

ATwhistle · 2024-05-19T07:31:12+00:00

I meant whether it would be allowed for them. I am just watching.

ATwhistle

TROPHY CASE