When is K vs K+R in antichess winning? How to win these endgames?

Question

Note: This is not a question on standard chess, where obviously K+R vs K is a win for K+R.

Here are two example K+R vs K positions in antichess, both having white to play and white having K+R.

Position #1 (This is a winning position after Kf5 according to lichess's antichess engine):

[Title "White to play and win - anti-chess"]
[FEN "5k2/8/8/8/6K1/8/8/3R4 w - - 0 1"]

Lichess analysis board

Position #2 (This is a drawn position according to the same engine):

[Title "White to play and draw - anti-chess"]
[FEN "5k2/8/8/8/8/6K1/8/3R4 w - - 0 1"]

Lichess analysis board

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In antichess, what are the principles / guidelines for determining whether or not a K+R vs K endgame is winning or a draw for the side with K+R?

Answer 1

in the upper position there is Kf5 Kg8 Re8 Kh8 Kg5 and the pattern continues

the strategy is very simple: if KR loses king then it is a win if KR loses R and there is no immediate sacrifice of the king, it is a draw from that follows, KR can only win if he can force the king onto a square where he can follow with a king sacrifice - how is that possible? WK is on the 8th rank BK is on the 5th rank the WK needs to come to the 7th rank, ROOK sacrifice! then BK comes to the 6th rank, KING sacrifice there is no possibility to force the WK from the 7th to the 8th rank so if the king escapes the edge, under typical circumstances, it is a draw

Answer 2

Using a table base, this is easy to explain.

In the first diagram it is lost in 3, 10 or 12 moves with optimal play because of the possibility of Kf5. All other white moves are drawn or lost.

Because white can cage the black K, it results in a win for white.

For simplicity I ignored alternate lines that where equally fast.

[Variant "Antichess"]
[FEN "5k2/8/8/8/6K1/8/8/3R4 w - - 0 1"]

1. Kf5 Kg7 {a R vs K end game is now certain} (1... Ke8 {loses faster} 2. Rd7 Kxd7 3. Ke6 Kxe6#) ( 1... Ke7 {loses faster} 2. Rd6 Kxd6 3. Ke5 Kxe5) (1... Kf7 {loses faster} 2. Ke6 Kxe6 3. Rd7 Kxd7#) (1... Kg8 {is the hardest try} 2. Re1 Kh7 3. Ke6 Kh6 4. Re4 Kh7 5. Re5 Kh8 6. Kf5 Kg8 7. Re6 Kh8 8. Rf6 Kg7 9. Rh6 Kxh6 10. Kg6 Kxg6#) 2. Kg6 Kxg6 {RvsK is lost for the K!} 3. Re1 Kg5 4. Re3 Kg6 5. Re4 Kg7 6. Re5 Kh8 7. Rf5 Kh7 8. Rf3 Kh6 9. Rf4 Kh7 10. Rf5 Kh8 11. Rf6 Kg7 12. Rf7 Kxf7#

The second diagram is drawn, because the black K can reach the e column which forces the white R from the d column. Because of this the K escapes from its cage and with optimal play it's a draw. According to the table base the possibilities seem endlessly, but they all draw.

E.g. If we choose Kf4 as the first move (for the parallelity with the first diagram), we can see that the e column must be abandoned within 3 moves to prevent a loss. Since black can't permanently shrink the cage on the K, there is no way to make progress. However, Black must constantly play accurate to keep the draw (e.g. only 1.Kf7 and 1.Ke8 are drawing), but with optimal play it is possible and eventually repetition or the 50 move rule will end the game in a draw.

Other moves than Kf4 are also drawn, just as it was in the first diagram.

Because white can't make progress to cage the black K, it is a draw.

[Variant "Antichess"]
[FEN "5k2/8/8/8/8/6K1/8/3R4 w - - 0 1"]

1. Kf4 Kf7 (1... Ke8 2. Rd7 (2. Ra1 {forfeits the control of the e column.}) 2... Kxd7 {Is a well known draw}) 2. Ra1 {forfeits the control of the e column.} (2. Rd2 Ke8 3. Rd7 (3. Ra2 {forfeits the control of the e column.}) 3... Kxd7 {Is a well known draw})

Note that it will take a very strong Antichess player to not lose this as black.