What's the most distant chess position?

Question

It's well known that the combinatorial explosion means that there are many, many, possible chess games. And yet most games are decided within 100 moves, and Wikipedia says that the longest tournament chess game took 269 moves. And most positions can be reached relatively quickly.

So what's a legal chess position that takes the most moves to reach? It may be extremely difficult to prove that it takes the number of moves you say; please provide either a proof game or a description explaining why it takes as many moves as you say.

For the purposes of this puzzle, the 75-move rule does not apply.

Answer 1

This question was asked on Chess Stack Exchange a couple of years ago: Which chess position requires the most moves to reach? Just like @loopywalt here in the comments, I remembered Tim Krabbé's diary entry #397:

Harry Goldsteen has put some research into this and came up with a position which is reachable only in 185 moves:

[FEN ""]
[StartPly "371"]

1.a4 g5 2.Ra3 g4 3.h3 g3 4.Rh2 gxh2 5.Nf3 h1=R 6.d3 d5 7.Kd2 e5 8.Nh2 a5 9.Ke3 d4+ 10.Kf3 e4+ 11.Kg3 e3 12.Qd2 exd2 13.Rb3 d1=B 14.Bf4 b5 15.Nd2 bxa4 16.Rb7 Be6 17.Ne4 Ba2 18.Nd6+ Kd7 19.Nc8 Kc6 20.Nb6 Kb5 21.Be5 Bb1 22.Bf4 a3 23.Be5 a2 24.Bf4 a1=B 25.Be5 { As in the 183- and 184-move games, White makes many waiting moves. Black ´leads´, as Goldsteen puts it - he must play optimally, although some changes in move-order are possible for him, too. } 25...Kb4 26.b3 Kc3 27.Nd5+ Kd2 28.Nb6 a4 29.Nc8 a3 30.Nb6 a2 31.Nc8 Bb2 32.Nb6 a1=B 33. Nc8 Bc1 34.Nb6 Bc3 35.Nc8 Bcb4 36.Nb6 c5 37.Na4 c4 38.Nb2 c3 39.Kf3 cxb2 40.c3 Bdc2 41.Ke4 Ne7 42.Bc7 Nd5 43.Be5 Ne3 44.Bc7 Nd1 45.e3 h5 46.Be2 Qh4+ 47.Kd5 Na6 48.Bg4 hxg4 49.Kc4 g3 50.Rb5 gxh2 51.Rb7 Re1 52.Rb5 h1=R 53.Rb7 Nc5 54.Bh2 Ne4 55.Rb5 Ng3 56.Rb7 Rhf1 57.Rb5 Nh1 58.g3 { Now White has created the smallest possible box in which Black´s promoted Rooks and Bishops manoeuver like tar through a sieve. } 58...Ke2 59.Rb7 Kf3 { The black King makes room for the white Rook so it can go to g2. In the next phase, the black Rooks must leave the box, otherwise the white Rook cannot pass. } 60.Rb5 Bfc5 61.Rb7 Re2 62.Rb5 Ba2 63.Rb7 Bcb1 64.Rb5 Rc2 65.Rb7 Re1 66.Rb5 Ree2 67.Rb7 Bd2 68.Rb5 Be1 69.Rb7 Rc1 70.Rb5 Bc2 71.Rb7 Ra1 72.Rb5 Bcb1 73. Rb7 Rc2 74.Rb5 Rc1 75.Rb7 Bc2 76.Rb5 Bab1 77.Rb7 R1a7 78.Rb5 Ba2 79.Kd5 Ra1 80.Kc4 Bab1 81.Kd5 R1a6 { Now the white Rook can enter via a5. } 82.Ra5 f5 83.Ra1 Ba2 84.Rc1 Bcb1 85.Rc2 Qh5 { Or Qg4; the Queen must be able to reach e2 in one move. } 86.Re2 Bd2 87.Re1 Bc2 88.Rg1 Bab1 89.Rg2 { The Rook has arrived. } 89...Ra1 90.Kc4 Ba2 91.Kb5 Rc1 92.Kc4 Bab1 93.Kb5 Ra1 94.Kc4 Ba2 95.Kb5 Be1 96.Kc4 Bcb1 97.Kb5 Rc2 98.Kc4 Re2 99.Kb5 Bc2 100.Kc4 Rc1 101.Kb5 Bab1 102.Kc4 Ra1 103.Kb5 Rha8 104.Kc6 Bd2 105.Kb5 Re1 106.Kc4 Rg1 107.Kb5 Ba2 108.Kc4 Bcb1 109.Kb5 Rc2 110.Kc4 Bc1 111.Kb5 Re2 112.Kc4 Ree1 113.Kb5 Ref1 114.Kc4 Bc2 115.Kb5 Bd2 116.Kc4 Rc1 117.Kb5 Bab1 118. Kc4 Ra1 119.Kb5 Ba2 120.Kc4 Be1 121.Kb5 Bcb1 122.Kc4 Rc2 123.Kb5 Ke2 { The black King must enter the box now; his first goal is a3. } 124.Kc4 Kd2 125.Kb5 Kc1 126.Kc4 Re2 127.Kb5 Kd2 128.Kc4 Bc2 129.Kb5 Rc1 130.Kc4 Bcb1 131.Kb5 Rc2 132.Kc4 f4 133.Kb5 Kc1 134.Kc4 Rcd2 135.Kb5 Bc2 136.Kc4 Kb1 137.Kb5 Ka1 138.Kc4 Bab1 139.Kb5 Ka2 140.Kc4 Ka3 141.Kb5 Ba2 142.Kc4 Bcb1 143.Kb5 Rc2 144.Kc4 Rc1 145.Kb5 Bc2 146.Kc4 Ra1 147.Kb5 Bcb1 148.Kc4 Rc2 149.Kb5 { Only now can the black Queen treacle into the box. } 149...Qe2 150.Kc6 Qd2 151.Kd5 Qc1 152.Kc6 Re2 153.Kd7 Qd2 154.Kc6 Bc2 155.Kb5 Rc1 156.Kc6 Bcb1 157.Kd7 Rc2 158.Kc6 Qc1 159.Kd7 Rcd2 160.Kc6 Bc2 161.Kd7 Qa1 162.Kc6 Bcb1 163.Kb5 Rc2 164.Kc6 Bd2 165.Kd7 Bc1 166.Kc6 Ree1 167.Kd7 Rce2 168.Kc6 Bd2 169.Kd7 Bc2 170.Kc6 Qc1 171.Kd7 Bab1 172.Kc6 Ka2 173.Kd7 Ka1 174.Kc6 Ba2 175.Kd7 Bcb1 176.Ke8 Qc2 177.Kd7 Bc1 178.Ke8 Rd2 179.Kd7 Ree2 180.Ke8 Rfe1 181.Kd7 Rgf1 182.Bg1 f3 183.Rh2 Ba3 184.Ke8 Bcb4 185.Kd8 Ba5+ { and the diagram has been reached. }

This is the current record, but

Goldsteen does not have proof that 185 is unsurpassable - in fact, he thinks it is likely that it can be surpassed.

My answer there contains a 'replayer' which you can use to play all the moves, but it doesn't work here, so this is the final position:

Answer 2

I will open the bidding at

166

I won’t offer a series of moves, but describe the position as

6 white knights on rank 1 avoiding locations B1 and G1; 4 white knights on rank 2 avoiding D2 and E2; 6 black knights on ranks 8 avoiding locations B8 and G8; 4 black knights on rank 7 avoiding locations D7 and E7 a white king on, say, G8 and a black king on, say, B1.

To see that this would take at least as many moves as claimed, note that

It can only be achieved if all 16 pawns are promoted (which requires at least 80 moves) to knights that then return to the opposite two ranks (requiring at least 56) to this we add a minimum of 7 moves each for the kings and 2 moves each for the starting knights.

In fact

To achieve all 16 promotions, at least 8 captures must occur on ranks 2-7 where the captured piece is not a pawn or a knight, so an additional 8 moves will be needed. One might be able to squeeze out 4 more moves using two remaining non-knight pieces in positions that cannot be reached from their starting position in one move.