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Very neat! The key is to get the white King involved ASAP with Kg4 and it will end up a draw as the rook will be traded for both pawns.
Full references: Prokes, Schackvärlden, 1939, honor mention.
A very instructive and useful manoeuvre is to be found here.
Prokes was a great study composer,
An easier study by him with the same material is very funny:
Prokes Mlada Fronta, 1946
wKd1,Re1/bKd6,Pf3,g3
8/8/3k4/8/8/5pp1/8/3KR3 w – – 0 1
win
Another procedure, more artistic and less likely to happen in games, is required to mop the two pawns.
likely draw…1.Kg4! e2[ 1…d2 2.Kf3 Kd3 3.Ra1! e2 4.Ra3+ Kc2 5. Ra2+ Kd3 6.Ra3+ leads to a draw] 2.Rc1+ Kd4 3.Kf3 d2 4.Rc4+!Kd3 5.Rd4+ Kxd4 6.Kxe2 Kc3 7.Kd1 Kd3stalemate
I can achieve a draw but I am suspecting that there is a win here for White
1.Kg4 e2
2.Rc1+ Kd4
3.Kf3 d2
4.Rc4+ Kxc4
5.Kxe2 d1=Q+
6.Kxd1
Looks like a loss for white for me. Black will have a queen and king using which it can wn the game.
Looks like a loss for White to me. Black will be left with a Queen and king at the end.
The white king is just close enough to draw. Were he on the sixth rank at h6, g6, f6, or e6, he would be lost, and were he on the fourth rank at g4 already, white would win. Let’s see the proper way to get the half-point:
1. Kg4
The obvious move to bring the king closer, and certainly the only move that draws here:
1. …..d2 (e2 and Kc3 will follow)
2. Kf3!
Another only move. Wasted effort like Rf4+ just allows the black king to reach d3 to support e2 when the rook returns to f1. Of course, a move like Kf4 just allows an immediate e2 to win the game. Continuing:
2. …..Kd3!
Now, it is black who must play precisely. If he protects with Kd4, white puts the king on e2: [2. …Kd4? 3.Ke2 Ke4 4.Rb1 Kd4 5.Rb3 Ke4 6.Re3 with check wins]. Continuing:
3. Ra1!
The only drawing move, and the keystone move of this problem. In fact, if the position were transposed one file to the left, white would be lost here since the rook couldn’t keep enough distance from the black king- for example, 3.Rb1 here loses to e2 followed by Kc2 in response to 4.Rb3+. Also, moves like 3.Rg1/h1 lose to e2 instantly since there are no checks from that side of the board due to white’s king being in the way. Continuing:
3. …..e2!
Here, black will lose if he tries Kc2: [3. …Kc2? 4.Ke2! Kc3 (or 4. …Kb2 5.Rf1 Kc2 6.Rd1 Kc3 7.Ke3 Kc2 8.Ke2+-) 5.Ke3 Kc2 6.Ke2+-]. Continuing:
4. Ra3! Kc2
5. Ra2!= White will just keep checking from the a-file until black moves to attack the rook from the b-file, and then white will capture at e2 and d2/d1. The point is that black can’t both attack the rook and keep control of d2/d1 at the same time.
Now, back at move 1, black could try playing e2 first, but this will still be a draw with proper play:
1. Kg4 e2
2. Rc1!
White must have this tempo, or he will lose since black will play d2 on any other rook move along the 1st rank, and will play Kc3 to win if white plays 2.Rf4+. With the check from c1, black is forced to lose time since his king can’t get to d3 because his pawn is on the square. Continuing:
2. …..Kd4
If black tries Kb3, white still draws: [2. …Kb3 3.Kf3! d2! (or 3. …Kb2? 4.Rg1/h1 Kc2 5.Ke3 Kc3 6.Rc1 Kb2 7.Kd2+-) 4.Rb1! Kc2 5.Ke2 Kb1 6.Kd2=]. Continuing:
3. Kf3! d2 (what else?)
4. Rc4!
The only move of course. Otherwise, black will queen with pawn protection at d1 or e1. Continuing:
4. …..Kd3 (Kc4 5.Ke2 Kc3 6.Kd1=)
5. Rd4! Kc3 (Kc2? 6.Ke2+-)
6. Ke2 Kd4
7. Kd2=.
And, finally, at move 1, black cannot play a king move without losing himself:
1. Kg4 Kc3?
2. Kf3! Kd4
If d2, then Ke2 wins for white, and if e2, Rg1/h1 wins for white (left as an exercise). Continuing:
3. Ra1
I think this is the precise way, but white should win with other rook moves, too. Continuing:
3. …..e2
Or, if d2 [3. …d2 4.Ke2 Ke4 5.Ra3 Kd4 6.Rd3+-]. Continuing:
4. Rb1 Kc3
5. Ke3 Kc2
6. Re1 Kc3 (d2 7.Re2 and 8.Rd2+-)
7. Rc1 Kb2
8. Kd2 Kb3
9. Kd3+-