R-Mobility
R-mobility chess is a chess variant that completely removes draws from engine chess, and greatly reduces the number of draws in over the board games. In its simplest form, the side with the position with the fewest legal moves since the last pawn move or capture loses. Here not being in check counts as an extra ½ a legal move, and the first position achieving the eventual minimum takes precedence.
See OTB protocol below for practical play using a physical board and a score sheet.
Contents
Overview
R-mobility aka reset-mobility is a generalization of mate and stalemate: force your opponent to have as few legal moves as possible. R-mobility allows to convert an advantage in drawn games into favorable tiebreaks. Only the best r-mobility value since the last pawn move or capture counts.
The goal of r-mobility is to achieve a position after the last pawn move or capture where your opponent has as few legal moves available as possible. Not being in check is counted as an additional 0.5 move. A pawn move or capture resets the goals achieved so far, and only positions after it are considered.
When fewer legal moves are available to a player, this results in a worse scoring.
Being in check is considered worse than not being in check.
- Mate is 0 legal moves and in check, and thus is the worst possible result for the side being mated and the best possible result for the side doing the mating.
- Stalemate is 0 legal moves and not in check, and thus is the 2nd worst possible result for side being stalemated and the 2nd best possible result for the side doing the stalemating.
- 1 legal move in check is 3rd worst/best result.
- 1 legal move not in check is 4th worst/best result and so on.
The first side to achieve a best goal gets it.
A short syntax for the best goal achieved so far is the G-score ±Gn.m, where n is the number of legal moves and m is 0 if in check and 5 if not in check. A minus sign indicates that the best goal was achieved by black. A game ends according to the employed FIDE or ICCF rules: with mate, stalemate, 3-fold repetition or possibly 50-move rule. If a game ends due to the 50-move rule, then the position triggering the 50-move rule is ignored unless it is mate or stalemate. Once a game has ended the game result according to r-mobility is the best G-score achieved since the last pawn move or capture:
- ±G0.0 = mate
- ±G0.5 = stalemate
- ±G1.0 = 1 legal move and in check
- ±G1.5 = 1 legal move and not in check
If used for tiebreak purposes, then points decide tournament as usual and is 100% compatible with both FIDE and ICCF rules, except for tiebreak calculations unless added to the end of current tiebreaks. In this case the first (additional) tiebreak is number of times stalemating opponent - number of time being stalemated by opponent. The second tiebreak same, but for G1.0 result, the third tiebreak for G1.5 result, etc..
The reason the position triggering the 50-move is ignored is that otherwise one can make an unprotected adjacent check and get a good r-mobility result without the opponent being able to capture the checking piece.
Basic endgames
KPvK
| |
| Position after 1. Ke6 |
Mate or stalemate unless the pawn can be captured. Diagram for common stalemate result.
KBvK
| |
| Position after 1. Bf5 |
Usually G1.5. For example:
1. Bf5 (diagram)
Subgoal is to get positions where the lone king is forced further towards edge.
The game continues with
1... Kh5 2. Kf4 Kh6 3. Kg4 (diagram)
Now black king has only 1 legal move and is not in check (G1.5).
Players can continue game until a threefold happens or 50-move rule kicks in, but unless black blunders, white will never achieve a better result (stalemate, or one legal move while in check) and thus players might as well agree on the game result here.
| |
| Position after 3. Kg4 |
Stalemate is possible if the the lone king is near any corner and the other king is nearby in a suitable position.
1. Kf6 (diagram) Kf8 2. Bd7 Kg8 3. Be6+ Kh7 4. Bf7 Kh8 5. Kg6
| |
| Position after 1. Kf6 |
KNvK
| |
| Position after 1. Nd5 |
Usually G3.5 (diagram) but G1.5, G2.5 and stalemate are possible depending position. Rarely G2.0, G3.0 and G1.0.
KvK
| |
| Position after 1. Ke5 |
Usually G5.5, example:
1. Ke5 (diagram) Kg6 2. Ke6
Threefold will soon follow, as neither side is able to improve on the result.
G3.5, G8.5, G2.5, G1.5 and G4.5 results also possible depending on position.
With G8.5 or -G8.5 position (diagram) if either side tries to go closer to other king, will then lose to G5.5, for example in diagram position after
1. Kd5 Kf5
white has 5 legal moves and thus black wins game with -G5.5.
| |
| Position after 1... Kxg5 |
Thus both players have to keep distance and threefold follows soon and result stays at -G8.5.
KNNvK
Stalemate unless a knight can be captured or mate in 1 is available.
TCEC
The TCEC rules include r-mobility as a tiebreak criterion. The only time it was needed so far was in the Top 4 engine bonus of Season 18, see the final standings at [1].
A script to add the RMobilityResult tag to the results is at [2]. It needs the python-chess library. Usage: python parallel_tag_rmobility.py input.pgn output.pgn
R-mobility tablebases are used when they are available.
The r-mobility tiebreak criterion is the number of r-mobility points scored over all games played. Here the 50-move rule is ignored for tablebase positions. For a game with the final r-mobility result ±Gn.m, the awarded points for the winner/loser are computed using the formula ½±½^(1+2*(n.m)), yielding the following values:
| Result | Winner | Loser |
|---|---|---|
| G0.0 | ½+1/2=1.000000 | ½-1/2=0.000000 |
| G0.5 | ½+1/4=0.750000 | ½-1/4=0.250000 |
| G1.0 | ½+1/8=0.625000 | ½-1/8=0.375000 |
| G1.5 | ½+1/16=0.562500 | ½-1/16=0.437500 |
| G2.0 | ½+1/32=0.531250 | ½-1/32=0.468750 |
| G2.5 | ½+1/64=0.515625 | ½-1/64=0.484375 |
| G3.0 | ½+1/128=0.507812 | ½-1/128=0.492188 |
| G3.5 | ½+1/256=0.503906 | ½-1/256=0.496094 |
| G4.0 | ½+1/512=0.501953 | ½-1/512=0.498047 |
| G4.5 | ½+1/1024=0.500977 | ½-1/1024=0.499023 |
| G5.0 | ½+1/2048=0.500488 | ½-1/2048=0.499512 |
| G5.5 | ½+1/4096=0.500244 | ½-1/4096=0.499756 |
| G6.0 | ½+1/8192=0.500122 | ½-1/8192=0.499878 |
| G6.5 | ½+1/16384=0.500061 | ½-1/16384=0.499939 |
| G7.0 | ½+1/32768=0.500031 | ½-1/32768=0.499969 |
| G7.5 | ½+1/65536=0.500015 | ½-1/65536=0.499985 |
| G8.0 | ½+1/131072=0.500008 | ½-1/131072=0.499992 |
| G8.5 | ½+1/262144=0.500004 | ½-1/262144=0.499996 |
| G9.0 | ½+1/524288=0.500002 | ½-1/524288=0.499998 |
| G9.5 | ½+1/1048576=0.500001 | ½-1/1048576=0.499999 |
| G10.0 | ½+1/2097152=0.500000 | ½-1/2097152=0.500000 |
| G10.5 | ½+1/4194304=0.500000 | ½-1/4194304=0.500000 |
Full points only version
The result of a game of r-mobility chess can also always simply be scored as 1-0 or 0-1, depending on which side achieved the best goal. Due to the likely inherent advantage of the side to move first, a komi as used in Go can be employed. Here a value of ¼ can be added to the G-score that white needs to achieve in order to win. For example if G3.75 is used as komi, then white has to get G0.0, G0.5, G1.0, ... or G3.5 to win, otherwise black wins the game. In this case the result would always be 1-0 or 0-1, and there are no draws.
OTB games
For over the board games one could limit the application of the r-mobility rules to 1-3 legal moves, and use the full range only for ICCF and engine games. The 50-move rule applies to all positions as usual, including tablebase positions. For OTB play an alternative is that the 50-move rule is counted from the last record on the score sheet.
OTB protocol:
- The G-score of a position is the number of legal moves, plus 0.5 if not in check.
- If a move leads to a position with a G-score ≤ 3.5, we record it on the score sheet, but only if this a new lowest G-score since the last pawn move/capture.
- A finished game is a draw if there are no recorded G-scores since the last pawn move/capture, otherwise the side with the most recent G-score loses. The best possible result is of course mate, G0.0.
Whole game mobility
For whole game mobility (wg-mobility) all positions in a game are included. 2-5 piece tablebases have been generated for wg-mobility, and longest records and statistics are available at [3]. R-mobility is often the same, but there are crucial differences and some games are longer and more natural for r-mobility.
