Three-fold change of Pronkin piece in proof games

29 Apr. 2021 | by Peter Wong

In December of 2019, after taking a long break from composing proof games, I attempted a challenging task in that genre that elaborates on what’s called the Pronkin theme. In this paradoxical idea, at the final position of a proof game, a piece seemingly on its home square turns out to be a promoted unit, replacing the original piece that was captured at some point. A game may contain multiple instances of such deceptive play, with four Pronkin impostors being the most that have been achieved (see a great example in the Walkabout of 30 Aug. 2014). Another way to intensify the theme involves setting up more than one solution (or twins), where each part requires a different home-square unit to be the impostor. Since multi-phase proof games are not simple to construct even with basic themes, those that demonstrate this type of changed Pronkin piece are uncommon and normally two-part affairs. Take for example the eponymous first-prize winner (No.141) by Dmitry Pronkin himself. I wondered if it was possible to extend this idea to three phases, showing a different type of promoted piece each time. And indeed, what about four phases – wouldn’t it be great to combine a four-fold change of Pronkin with the Allumwandlung theme!?

Online problem databases provide an invaluable resource for uncovering what has been accomplished in various fields, and the Chess Problem Database Server (PDB) seems the most comprehensive for proof games. A search on that site reveals but a single case of a triple Pronkin change, composed by Michel Caillaud some twenty years ago. Should I then try to make a four-phase rendition that incorporates an AUW? Well, I thought, if such a task is really possible, then a three-phase version should be relatively easy to achieve, and I should aim for a sound setting of the latter first. So I began to construct such a problem, making sure to use a combination of thematic pieces different from Caillaud’s. As it turned out, I was sorely mistaken about how this could be “easy” in any sense of the word. I spent a whole two weeks on the task, practically full-time, obsessively churning out versions that Euclide (the proof-game solving program) would then demolish in seconds. But persistence paid off and a correct setting eventually emerged. Shown below are Caillaud’s problem and mine, and they make an interesting comparison.

Michel Caillaud
StrateGems 1998, 3rd Prize

Proof game in 11
Twin (b) Pd7 to d6, (c) Pd7 to d5

(a) 1.d3 a5 2.Be3 a4 3.Bb6 a3 4.e3 axb2 5.a4 Ra5 6.Ra3 Rf5 7.Rc3 Rf3 8.Sa3 b1=R 9.Ke2 Rb5 10.Kxf3 Ra5 11.Kg3 Ra8.
(b) 1.d3 a5 2.Be3 a4 3.Bb6 a3 4.e3 axb2 5.a4 d6 6.Ra3 Bg4 7.Rc3 Be2 8.Sa3 b1=B 9.Kxe2 Ba2 10.Kf3 Be6 11.Kg3 Bc8.
(c) 1.d3 a5 2.Be3 a4 3.Bb6 a3 4.e3 axb2 5.a4 d5 6.Ra3 Qd6 7.Rc3 Qa3 8.Sxa3 b1=Q 9.Ke2 Qb5 10.Kf3 Qd7 11.Kg3 Qd8.

Peter Wong
The Problemist 2020

Proof game in 18½
Twin (b) Pa2 to a4, (c) Pc2 to c5

(a) 1.Sc3 h5 2.Se4 h4 3.Sg3 hxg3 4.b4 Rh3 5.gxh3 g2 6.Bb2 gxh1=B 7.Bf6 exf6 8.b5 Ba3 9.Bg2 Ke7 10.Bxb7 Kd6 11.Bd5 Se7 12.Be6 dxe6 13.b6 Bd7 14.b7 Be8 15.bxa8=S Sd7 16.Sb6 Ba8 17.Sa4 Sd5 18.Sc3 Qe7 19.Sb1.
(b) 1.a4 h5 2.Ra3 h4 3.Rg3 hxg3 4.b4 Rh3 5.gxh3 g2 6.Bb2 gxh1=B 7.Bf6 exf6 8.b5 Ba3 9.Bg2 Ke7 10.Bxb7 Kd6 11.Bd5 Se7 12.Be6 dxe6 13.b6 Bd7 14.b7 Be8 15.bxa8=R Sd7 16.Rb8 Ba8 17.Rb2 Sd5 18.Ra2 Qe7 19.Ra1.
(c) 1.c4 h5 2.Qb3 h4 3.Qg3 hxg3 4.b4 Rh3 5.gxh3 g2 6.Bb2 gxh1=B 7.Bf6 exf6 8.b5 Ba3 9.Bg2 Ke7 10.Bxb7 Kd6 11.Bd5 Se7 12.Be6 dxe6 13.b6 Bd7 14.b7 Be8 15.bxa8=Q Sd7 16.Qb8 Ba8 17.Qb3 Sd5 18.Qd1 Qe7 19.c5+.

The Pronkin pieces in Caillaud’s position are the c8-bishop, a8-rook, and d8-queen, while in mine they are the b1-knight, a1-rook, and d1-queen. The French GM executes the theme with impeccable economy, both in terms of the game length and the minimal captures required. As I wrote to the retro sub-editor of The Problemist: “The really striking thing about Caillaud’s is that the thematic pieces are captured on different squares, whereas mine is typical for a Pronkin change and they are captured on the same square, though this square is also hidden (not a visible pawn capture). Mine has the advantage of the three phases starting with different moves. The AUW is another plus! What makes the task so frustratingly difficult is the need to fix a single path of each thematic piece as it returns to its home square. Because of this, I view the obtrusive a8-bishop as the “unsung hero” of the problem – not only does it complete the AUW, but its corner-to-corner move rules out 16.Qb7? [and 16.Qe4/Qf3?] to force 16.Qb8!”

And the proposed four-phase, genuine synthesis of the Pronkin theme and AUW? In theory such a proof game may well exist; even in my three-phase problem, one can envisage a fourth part with a thematic c1-bishop, commencing with 1.d3 h5 2.Bf4 h4 3.Bg3 hxg3 to fit the scheme. In practice, however, I’ve become a bit sceptical about the feasibility of the task. Given little certainty of success, I’m not prepared to spend, say, a month full-time on the project! That said, there’s scope in this area of changed Pronkins for problemists to explore, relating to other unrealised but more manageable tasks. For instance, a triple change of Pronkin similar to the above problems, but with another combination of thematic pieces: knight/bishop/rook and knight/bishop/queen. Or a four-fold Pronkin change that doesn’t incorporate an AUW because two of the promoted pieces are of the same type. Since it’s probably the most straightforward to implement a Pronkin with a rook, a quadruplet setting that involves a pair of them would be more viable, and still a record.