# Longest DTC in the endgame KQPKQ depending on the place of the white pawn

I remember some statistics by Guy Haworth from the endgame KQPKQ (queen + pawn vs queen).

One of the statistics was the maximum DTC depending on the place of the white pawn (due to symmetry, it can be assumed that the pawn is on the queenside), but I cannot find it anymore.

Does anyone know where the statistics are?

I watched a Karsten-Mueller-DVD about this endgame and he stated that the bishop pawn gives the best winning chances. Perhaps, the statistics can approve this claim.

• It would also be nice to have the longest DTZ. Feb 5, 2015 at 21:18

## 1 Answer

Here is a partial answer.

The paper Chess Endgames: Data and Strategy by Tamplin and Haworth reports, among other things, the maximum depth-to-conversion (DTC) and depth-to-zeroing (DTZ) among winning KQPKQ positions. Table 1b in the appendix indicates a maximum DTC of 114 among winning white-to-move positions, and Table 2a indicates a maximum DTZ of 71 for the same.

That article unfortunately does not include separate maximum DTC or DTZ metrics for the 4 respective queenside pawn options, but I can at least confirm that the maximum DTZ of 71 involves a rook pawn, and this maximal example was already given in Thompson's pioneering 1986 tablebase paper Retrograde Analysis of Certain Endgames. On p.138, the following position and maximal play line are indicated:

``````[Event "Thompson 1986"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "KQPKQ"]
[Black "Maximum DTZ"]
[Result "1-0"]
[FEN "8/q7/P6k/Q7/8/8/8/6K1 w - - 0 1"]

1.Kg2 Qg7+ 2.Kh1 Qf6 3.Qd2+ Kg7 4.Qd7+ Kg6 5.Qd3+ Kg7 6.Qg3+ Kf8 7.Qb8+
Kf7 8.Qc7+ Kg6 9.Qc4 Qf3+ 10.Kh2 Qe3 11.Qf1 Qe5+ 12.Kh1 Qh8+ 13.Kg2 Qa8+
14.Kg1 Qa7+ 15.Kh1 Qd7 16.Qf2 Kh5 17.Qe2+ Kg6 18.Qe4+ Kh5 19.Qc4 Qa7 20.
Qe2+ Kg5 21.Kg2 Qd4 22.Qf2 Qe4+ 23.Qf3 Qd4 24.Qe2 Kg6 25.Qb5 Qe3 26.Kf1
Qe4 27.Kf2 Qd4+ 28.Kf3 Kh6 29.Qc6+ Kg7 30.Qc7+ Kg6 31.Qg3+ Kh5 32.Qh3+ Kg5
33.Qe6 Qd1+ 34.Qe2 Qd5+ 35.Kf2 Qf5+ 36.Kg1 Qb1+ 37.Kg2 Qg6 38.Qc4 Kh5+ 39.
Kf2 Qf6+ 40.Ke3 Qe5+ 41.Kd3 Kg5 42.Kc2 Qe3 43.Kb2 Kg6 44.Qb5 Kh6 45.Kc2
Qe6 46.Kc3 Qd6 47.Kc4 Kg7 48.Qg5+ Kh8 49.Qh5+ Kg7 50.Qg4+ Kf7 51.Qf5+ Kg7
52.Qc8 Qf4+ 53.Kb5 Qf6 54.Qc6 Qb2+ 55.Kc5 Qf2+ 56.Kd6 Kg6 57.Kd5+ Kh7 58.
Qc7+ Kh8 59.Qc3+ Kh7 60.Kc6 Qf5 61.Kb6 Qe6+ 62.Kb7 Qe4+ 63.Kb8 Qb1+ 64.Kc7
Qa2 65.Qc6 Kh8 66.Kb8 Qb3+ 67.Qb7 Qg3+ 68.Ka8 Qh3 69.Qc6 Qg4 70.Qc3+ Kh7
71.a7 1-0
``````
• The point of all those moves is hard to determine. Feb 6, 2015 at 12:06
• @TonyEnnis, I agree. It's remarkable just how inscrutable optimal play uncovered by tablebases often seems.
– ETD
Feb 6, 2015 at 12:12