Tuesday, June 9, 2015

Endgame Caveat #6: Rule of Five

While researching rook endgames, I came across a Wikipedia article on Rook and Pawn Versus Rook Endgame. I was surprised to learn of a Rule of Five credited to Soltis and Mednis. When I Googled Rule of Five, a bogus-sounding roulette betting system showed up.

The Rule of Five applies to the rook plus pawn versus rook endgame, specifically to Lucena-like positions where the king is already cut off. Otherwise, the defending king that blockades the passer should draw. From the Wikipedia page: "Add the number of rank of the pawn to the number of files the defender's king is cut off. If the sum is more than five, it is usually a win. Otherwise it is normally a draw." Wikipedia shows the following diagram which I have marked up.

Rule of Five: White wins with either side to move

Since the cutoff number has to be at least 1, Lucena with a safe pawn on the 5th rank should always win: 5 + 1 > 5 Rule of Five fulfilled. However, the long side defense may play a role here. I'll probably devote another post to the long side defense soon. Where the rule seems to be helpful is if the cutoff number grows and the pawn gets further back: e.g. pawn on the 4th + 2 cutoff files, pawn on the 3rd + 3 cutoff files and pawn on the 2nd + 4 cutoff files. But even on the Wikipedia page, there is a caveat: knight pawns seem to be exempt. Lucena already has the rook pawn exemption. If this Rule of Five doesn't apply to knight pawns, then it is only good for center pawns and bishop pawns. It seems to be a rule of limited usefulness because of excessive caveats. Likely that's why I haven't heard of it in 25 years of chess.

From the above diagram, the winning technique is good to know. In fact it will be discussed in my next post of how the previous Practical Rook Endgame could have been closer to the tablebase theory. From the Wikipedia diagram, White runs forward with his king with his sights set on a square like c6. If the rook attacks the pawn and the king would have to backtrack, then a timely Rd1 is called for. White's advanced king will drive the defending rook away from the blockade and with the help of a threatened, Re1+, the Black King is also kept out of the drawing blockade. Again, I recommend the 6-man tablebases at for accurate move to move evaluations and distances to checkmate. 1.Kc4 Rc8+ 2.Kb5 Rd8 3.Kc5 (3.Rd1 is a little more efficient) 3...Rc8+ 4.Kb6 Rd8 5.Rd1 Kf6 6.Kc6

Black to move

Instead of 6.Kc6, Wikipedia gives 6.Kc7 Ra8 7.d5, but 6.Kc7 Rd5 7.Kc6 Ra5 is a bit more testing because only 8.Re1! wins. 8.d5? fails to 8...Ke7 and Black can get to a Philidor draw.

Wikipedia shows a caveat as a study by Cheron from 1923

This is a similar diagram as the original Rule of Five except everything is moved left two files and the defending king is pushed back one rank. The pawn is a knight pawn and the Rule of Five seems to have its same 4 + 2 > 5 fulfillment. However, the tablebases show a draw with best play. Attempts to advance the king will be mercilessly met with endless rook checks until the king goes back into hiding at b3. One interesting thing about the diagram above is that White can use waiting moves to see if Black knows that he is only safe with moves like Ke5 and Ke6. A careless Ra8 or Rc8 leads to b5!. A careless Rb7 and Ka4 wins because Black now lacks checking distance. White can try to snooker Black by playing rook waiting moves like 1.Rd2 If 1...Ke7?, White wins with 2.Rd4! Ke6 3.Kc4! Rc8+ 4.Kb5! Ke5 5.Rh4 and now with the pawn protected, the White King will settle in the northwest corner of the board, eventually escorting the pawn to victory. If Black ventures 1.Rd2 Ke5! 2.Rd1 Ke4?, White uses a bridge-like maneuver to get his pawn past midfield without losing the Lucena. 3.Rd6 Ke5 4.Ra6 Kd5 5.Ka4! Kc4 6.Rc6+ Kd5 7.b5 and White's King will invade the northwest corner with a decisive Lucena.

The draw with Black biding his time with Ke6 and Ke5 has come up before in Endgame Caveat #5: The Space Invaders defense AKA The Frontal Check Defense.

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