Tingles, Bumps, and Punches

By Ralph Betza

Racing Kings

Racing Kings is one of V. R. Parton's games, and I found it very pleasing to play. The main delight, in my view, is the way friend and foe are so tangled up at the start of the game: captures are already possible but they are undesirable, attempts to develop your pieces cause enemy captures to become playable, and all in all it's frustrating.

The delight comes when you succeed in untangling and developing. If we couldn't endure frustration to gain the delights of success, we wouldn't be chess players at all, don't you think?

Vertical Cylinder Chess

The shape of the board is said to be a vertical cylinder because a Rook on h1 can move one square to the right and land on a1.

Cylindrical Chess is one of those games that everybody knows. We learn it as toddlers from our playmates, and play it blindfold as we walk down the street coming home from elementary school.

Pisces and Taurus

Every little fish, when first learning Cylindrical Chess, thinks of allowing pieces to wrap top-to-bottom, the same way they wrap sideways. The shape of the board thus formed is not spherical, but rather is a donut, an inner tube, a torus.

Alas, the King's in check. It's the first chess variant everybody invents, but it doesn't work.

Wouldn't it be nice if it worked? The Kings so close might even cause a tangling like Racing Kings, and the thought of that tangling set me tingling; and so I thought about it, and here's what I came up with:

Horizontal Cylinder Peace Bump Chess

I will describe the simplest game first.

Simple Rules of Horizontal Cylinder Peace Bump Chess

Rule Zero: follow the usual rules of chess except as follows.

Rule 1: The top and bottom of the board are joined, so that a Rook advancing from a6 to a7 to a8 could then continue by advancing to a1; or, alternatively, retreating from h2 to h1, the next step would be h8.

Rule 2: Retreating moves that cross their own baseline may not be captures. In other words, the K on e1 cannot capture the K on e8.

Design Notes

In my article on Features of the Chessboard I proposed a speed bump which would slow pieces down. My first attempt at Horizontal Cylinder used a speed bump between the wraparound ranks, but it was a failure; and the inspiration came "peace bump".

It is a one-way peace bump, between squares; a funny feature. You don't really need the phrase "peace bump" to describe the game, but I couldn't find a name for the game! So it's Peace Bump Chess, a horrid name.

It's a one-way peace bump because I think it's easier to describe that way, especially when you get into the torus form of the game. The ability to capture with a move that passes forward across the end line does not affect the game very much!

Sample Game

1. e2-e4 e7-e5 2. Bf1-c4 Bf8-c5

Notice that Bc4xf7+ is no threat because the Ng1 cannot capture on f7.

3. Ng1-f3 Ng8-f6 4. Nf3-g5? O-O? 5. Bc4xf7+ Rf8xf7? 6. Rh1-h8+ and wins. Better was 4...d7-d5! or 5...Kg8-h8 (with dangerous threats).

Critique

It is not quite as tangled as Racing Kings, but the everpresent menace from the rear is an excellent feature reminiscent of my Race Chess.

The extremely simple rules make it easy to teach your friends the game, and they make it easy to include the game in small articles and anthologies about chess variants. Because the game also provides very interesting possibilities, I wouldn't be surprised to see this game become very widely quoted and played.

Endgame

Rook plus King versus King is a win. The trick is that the K on e8 cannot capture the Rook on d1, and so can be forced towards the side of the board, where it can be mated using the same trick.

King plus two minor pieces cannot usually checkmate the bare King, and K plus a piece of Rookish value also usually cannot do so.

A mating position can be constructed with K+B+B versus K, but the mate cannot be forced.

Because a larger preponderance of force is needed to finish the game, it is possible that Bare King should be counted as a win lest the game be too drawish.

Different Armies

This game uses the normal 8x8 board, but the ability to wrap from top to bottom makes the board seem larger. Therefore it is not value-preserving: the pieces do not have their accustomed values.

Therefore Horizontal Cylinder Peace Bump Chess should not be played using the well-known Different Armies.

Advanced Rules

You may not make a null move by moving a piece around the end to land on the square where it started its move.

Torus Peace Bump Chess

Simple Rules of Torus Peace Bump Chess

Rule zero: The rules of Horizontal Cylinder Peace Bump Chess are used except as follows.

Rule 1: The sides of the board are also joined, so that a Rook moving from g2 to h2 takes its next step to a2.

Note that a retreating move which crosses the sideline may be a capture.

Rule 2: "Bare King" is a win.

Design Notes

A square board should probably be required -- on an empty 8x10 torus board, the Bishop can move to all squares of its own color, and an 8x9 board would be even worse.

The Bare King rule seems necessary because you need lots of material to checkmate with.

Useful Diagram

In order to play any form of Torus Chess with skill, you must learn this diagram that shows how the pieces wrap:

 e4 f4 g4 h4 a4 b4 c4 d4
 e3 f3 g3 h3 a3 b3 c3 d3
 e2 f2 g2 h2 a2 b2 c2 d2
 e1 f1 g1 h1 a1 b1 c1 d1
 e8 f8 g8 h8 a8 b8 c8 d8
 e7 f7 g7 h7 a7 b7 c7 d7
 e6 f6 g6 h6 a6 b6 c6 d6
 e5 f5 g5 h5 a5 b5 c5 d5  

Torus Peace Bump Punch Chess

Torus Peace Bump Chess is a good game, but I dislike using the "Bare King" rule. My proposed solution is to start the game with a more powerful lineup of pieces so that the King more easily be checkmated.

Replace the Rook with a Gryphon, denoted FtR. K plus Gryphon versus K is still a draw, but K + FtR plus anything else should usually win. Notice that on the empty torus board, a Gryphon on e4 attacks e5 -- it goes to d5, c5, b5, a5, h5, and eventually arrives at e5, the long way around.

Replace the Knight with a Nightrider (NN). An NN on b1 combined with a Gryphon on d1 checkmates a K on d5. The main reason to use the Nightrider in this game is that finding its path as it wraps around the edges will drive you crazy.

Replace the Bishop with Aanca, WtB. King plus Gryphon plus Aanca versus King is a win, though it's tricky to see how to do it (try it yourself!). King plus NN plus WtB versus King is extremely hard; I can construct a mating position (can you find it?) but am not sure it can be forced. Perhaps having a draw with some combinations of pieces actually adds to the interest of the endgame.

Replace the Queen with Amazon, RNB. A defended Amazon next to the King gives an easy checkmate.

Yes, that looks good. It's a pleasingly powerful army with lots of punch. Let's hope it works.

Design Notes

What a lot of power on the board, and the torus board merely makes the pieces more powerful!

This lineup, the Punch Chess army, would also make a good game on the non-torus and non-cylindrical 8x8 board!

Playtesting

The danger of having the NN on the torus board is that White might have a winning first move. I could simply take away the Nightriders, but I really want them in the game; so I need to do some difficult analysis.

The prime candidates are 1. NNg1-e5 or 1. NNg1-a5, which threaten both NNe5-g4+ and NNe5-c4+, winning the Gryphon on a8.

I will not even look at the symmetrical defense, which is expected to lose on principle. The only Black moves that defend against both threats are 1...RNBd8-e6 and 1...f7-f6 (releasing the Aanca to cover c4, and blocking the check from g4).

However, 1. NNg1-e5 f7-f6 2. NNe5-f3 (attacks both Amazon and Gryphon via f3-d4-b5-h6-f7-d8 and f3-h4-b5-d6-f7-h8 (I told you the NN on the torus board was insane!)) b7-b5 3. c2-c4 double check appears to be strong. Therefore the Amazon defense must be examined.

Central Right Nightrider Attack

If 1. NNg1-e5 RNBd8-e6, the only moves that defend e5 while renewing both threats are 2. RNBd1-c3, 2. RNBd1-e3, and 2. NNb1-a3.

In response to 2. NNb1-a3, 2...Ke8-d8 defends neatly.

1. NNg1-e5 RNBd8-e6 2. RNBd1-c3 Ke8-d8 3. NNb1-h5 (threatens 4. NNh5-b4) c7-c6 (attacks e5, pins the Pf2, blocks the check from b4), and Black looks comfortable.

1. NNg1-e5 RNBd8-e6 2. RNBd1-e3 Ke8-d8 3. NNb1-h5 (threatens 4. NNh5-f4) c7-c6!? 4. NNh5-f4 WtBc8xe5 5. NNf4xe6+ WtBe5xe6 is interesting because the NN are so powerful in the opening; but if that does not work out, there is 3...g7-g5 followed by 4...a7-a6 driving back the NN with gain of time.

In conclusion, 1. NNg1-e5 looks playable but not dangerous.

Left Rim Right Nightrider Attack

After 1. NNg1-a5, the defense 1...RNBd8-e6 does not attack a5. Rather than attempting to renew the threats by attacking both g4 and c4, it seems logical to try attacking the Amazon with 2. NNb1-c3 (c3-a4-g5-e6). Black must either play ...g7-g5 or move the Amazon to a square that defends both c4 and g4, and in order to regain the tempo lost by moving the RNB twice this square must also attack the NN at a5 and must not be counterattacked by any move that defends the NN.

After 1 NNg1-a5 RNBd8-e6 2 NNb1-c3 RNBe6-e5 3 NNa5-g1 RNBe5-c6! I think that White's advantage is no greater than it was before the first move, but the position makes me uneasy. For example, why not 1. NNg1-a5 RNBd8-e6 2 NNb1-c3 RNBe6-e5 3. h2-h4, defending a5 with a developing move? Oops, RNBe5xa1 would be strong. I'm not so uneasy any more.

1. NNg1-a5 RNBd8-e6 2. RNBd1-e3 RNBe6xe3 3. f2xe3 c7-c6+ looks equal, or 3. d2xe3 e7-e6+; in both cases 4. Ke8-d8 removes the double threat.

Therefore, 1. NNg1-a5 is not a bad move, but it does not seem to win.

Right Rim Left Nightrider Attack

1. NNb1-h5 threatens to fork Amazon and Gryphon from either f4 or b4, and at first it seems that simply moving the Amazon away should suffice.

1. NNb1-h5 RNBd8-e6? 2. a2-a4! is a good developing move which defends the Nh5 against possible attacks, opens the way for an FtR (FtRh1-a2-a3) and a WtB (WtBc1-b1-a2-h3-g4-f5-e6-d7) -- which attacks the Amazon!!! -- , and also for the other NN (NNg1-a2-f3-d4-b5-h6-f7).

1. NNb1-h5 RNBd8-e6 2. d2-d3 also attacks the Amazon (g1-d2-c3-a4-g5-e6), but allows RNBe6-h6+ which forks the NNh5.

After 1. NNb1-h5, either RNBd8-c6 or c7-c6 might work, but the Pawn move is more natural. 1. NNb1-h5 c7-c6 pins f2, but opens up a check from (e8-c7-a6-g5-e4-c3-a2-g1).

1. NNb1-h5 c7-c6 2. h2-h4+ NNb8-a6 with the threat WtBc8xa1!!

After 1. NNb1-h5, I believe that the NN will be driven back with loss of tempo.

Critique

This game has tremendously complex tactics, with the added difficulty of spotting the wraparound moves.

The "tangle" is achieved because the FtR and the WtB need Pawn moves to open their way, but Pawn moves also open the way for enemy NN.

I made an unbelievable number of errors in the opening analysis, which I had to go back and correct again and again and again. I can only hope that I finally got it right and that the game is playable, not a forced win for the first player.

In the first few moves, the possibility of moving across the end line plays no role in the game. If you survive a dozen or so moves, it will begin to have an effect.

In my opinion, Torus Peace Bump Punch Chess is one of the best games I ever invented for email or postal play, but the complexity of its tactics makes it too difficult for blitz. Played at traditional tournament speeds by grandmasters, it would be awe-inspiring.

Sample Game

1. NNg1-a5 f7-f6 2. c2-c3+ g7-g6 3. NNb1-h5? g6xh5? (a7-a6! gives discovered check via g8-a7-c6-e5-g4-a3-c2-e1, and then wins by 4...a6xh5) 4. RNBd1xh5+ (Capturing with the Aanca is not check!) WtBf8-f7 (defended by both RNBd8 and FtRh8) 5. NNa5-c4+ Ke8-f8 6. NNc4xa8 FtR h8-g6 (7. RNB h5-b4+?? WtB f7xb4), and Wtb f7xa8 is threatened. Is Black okay?

7. WtB c1-b3+! and wins

Incubus Peace Bump Punch Chess

Just to finish with something over-the-top, let me suggest playing on an 8x8x8 board, using the Punch Chess lineup, with wrapping from top to bottom allowed, just as it is allowed side- to side or front-to-back.

The shape of the board is not a four-dimensional sphere, it is an incubus.

I'm finished. This was hard work.