Neva Checkers

Checkers for four players
Valery Trubitsyn

The initial position. Pieces can only be moved on dark squares of the game board (see the initial position at pic. 1). The players have 6 pieces each of contrasting colors: black, white, red and green. The players move pieces in turns, clockwise. The lot determines the first move. In order to avoid possible confusion in taking turns, each corner of the board corresponds to the four periods of the day and night: night, morning, afternoon and evening. Black pieces are located in the NIGHT corner, white in the MORNING, red – in the DAY, green – in the EVENING. For example, if the “red” player captures the white piece, the white can’t respond to the offender, as the move will be against the rules: after afternoon comes evening, not morning. Pieces can move in any directions, players take turns clockwise.

To record the moves we suggest using two digit code, in which the 36 squares of the playing board are marked by a combination of two digits.

Object of the game – the game is won when one player has captured all of his opponents’ pieces. Each player plays for himself, game played in pairs is also possible, though.

How do the pieces move? The pieces of each player move to the opposite corner of the board, according to traditional rules.(see рic. 2). Pieces can’t move backwards. To demonstrate this rule 4 arrows of different colors are drawn on the board.

Picture 2.

A man becomes a king when it reaches the square in the opposite corner of the board (there is only one “corner square” for each color). If the corner square is reached by means of a jump a man doesn’t become a king. When a man becomes a king the turn to move passes to another player.

Capturing of the pieces is done according to traditional rules; the only difference is that one player may capture pieces of two or three opponents by means of one move. When a player moves he may never avoid capturing opponents’ pieces, however, the well-known rule of capturing the greatest possible number of opposing units refers to kings only. A player can’t stop halfway when capturing: the move must be completed. Capturing the opponent’s pieces is done by means of jumping over the pieces in any direction. To avoid the possible confusion the rule of the Turkish attack is used: when capturing many pieces one piece can’t jump over the same opposing piece twice. In such situation it is recommended to turn the “killed” pieces upside down, not removing them, and then to remove them all after the attack is finished.

In the game played in pairs the allies have to capture each other’s pieces otherwise the complicated combinations may turn into primitive moves. The allies should help each other by skillful combinations and capture each other’s pieces if needed.

Neva checkers rules were first published in the book “Igra ? Igra !” (“Game ? Game!” (editor V. N. Belov)-L., Lenizdat, 1987, page 134)). The main advantages of the game are several multi-player strategies and very simple rules.

In multi-player games the chances of skilled and inexperienced players are almost equalized, as instead of one return move a player gets several return moves, which, in their turn, may be treated as competitive. Games for two players also have many variations, but they don’t leave much space for the battle strategies diversity. Being excessively popularized, it seems that multi-player strategies are used only in shady card games. As for the real life a bilateral battle is sometimes reduced by some movie-makers to the primitive and funny level: while one tough guy fights another his enemy stands still waiting to get hurt. Meanwhile, real battles stand far from primitive strategies. In real battles forestalling moves from several opponents prevail over the alternating return moves. The suggested game is an attempt to fill the existing gap in multi-players checkers. Even a very skillful in two-players games person will soon understand that his power is pretty limited. In multi-players games (like in real life) the final result doesn’t completely depend on a well-planned combination. Sometimes our plans are ruined like a house of cards when collide the reality. To avoid this we should use a more complicated strategy level, where the number of banal tactics and strategies is strongly reduced.

Despite the seemed complexity the game is easy to understand as most of the rules come from traditional checkers. The game is won when all the opposing men are captured. From the educational point of view the game may be regarded as a model of a multisided conflict situation.

Training game.

N	White	Red	Green	Black
1	25-24	55-54	52-42	31-32
2	36-35	56-55	51-52	13-23
3	15-25	54-44	63-53	32-33
4	16-15	66-56	61-51	21-31
5	35-45!!	55:35	41:21	11:31
6	25:45:43:63:61:41:21	64-63	42-32!	22:42:62:64:66 – King
7	24:22	56-55	-	K66:36:16
8	21-31	55-54	-	12:32
9	31-41	54-53	-	K16-66
10	41-51	53-43	-	33:53
11	51-61 King	-	-	53-63
12	K61:64	-	-	K66:61
13	14-24	-	-	K61-21
14	15-25	-	-	32-33
	Whites surrendered.

Comments on the training game.

Move 4. Any move of blacks leads to failure. The “black” player chooses the lesser of two evils, giving out one man on the side of the desk.

Move 5. Using such a unique situation the “white” player comes up with a brilliant combination. The combination was a success only because the three intermediate moves were already defined by an obligatory capture in passing, which resulted in a possibility to plan and carry out a global attack (USING the right moment) on all opponents at the same time!!!

Move 6. The "Green" player is put in a very difficult situation: after the brilliant combination of the “white” player he’s got only one third of all his men, that is the least number among the other players. After a while, the “green” decides to leave the game and to spite his offender, who made the fatal move. As a result of the “green’s” insidious move, the “black” player gets a king, and the white player is condemned to an unequal battle with the “black”.

Move 8. The whites have a weak hope to become a king on the square 61 on the side of the board.

Move 10. The "Red" player, like a dying swan, makes a noble gesture and helps the weakest one. He could have rush under the attack of a white piece (as he will loose anyway) but he decides to make the situation for blacks more complicated by the means of the remaining last move.

Move 11. The "White” player managed to get a king, but the help of the reds turned out a clumsy assistance, as the black piece, which suddenly appeared close to the dramatic scene, has already prepared a trap for the white king.

Moves 13-14. Short agony of whites.

SUMMARY.

It is obvious that multi-player checkers is not just an entertainment, but the whole set of game collisions of psychological character. According to the rules the chances of the players were equal at the beginning of the game. But when the white player stepped on a winning path, challenging all of his opponents, he was suddenly attacked by the weakest player, who twice became a casual victim in the battles of more lucky and successful players, as he couldn’t affect them. Only in the end of the game the weakest “red” player tried (not for his own success though) to influence the course of events, having forgotten that he was strongly attacked by the “white” player in the beginning. So, why help him? It would be really interesting to trace why and how “secret unions”, joint strategies, tactics and strong coalitions are formed. But this lies beyond the topic of our discussion.

In this multi-player game the "Black" player won not because of his skill, but because of fate, by chance (which is absolutely impossible in games for two players)

This all happened due to emotional impulse of a weakest player who couldn’t win, but who managed to change the course of the game dramatically and to define the winner. This is a new variation in the game of checkers.

Are we objective calling the game “new”? Actually, the history of multiplayer checkers goes back in centuries. For example, in Russia in 1884 there was an attempt to introduce “Checkers for four and 2 players”. A year later Konstantin Lebedev designed “New checkers for four”. The rules of the game are described in the article by the same title (M., The printing house of the Society of Useful Knowledge Spreading, Mokhovaya, house of duke Gagarin1895, page15). The game used a standard checkerboard, bigger in size though- 13x13 with 85 squares.

Each player started with 12 pieces, placed not in the corners of the board. It was a game played in pairs and capturing allies' checkers was not obligatory. So, the game was played on a huge board in a pretty slow pace, and was not a multi-player game in fact.

Checkers for three players failed to become popular too. In 1938 in Leningrad А. Маrkovich and Е. Bazhenova designed "Checkers for three" on a two-colors triagonal board with 69 squares. Each player started with 12 pieces.

Thus the optimum ratio of total number of pieces to the number of squares in European Checkers (3:4) was broken again.

In Orel in 1984 "Prompribor" plant started the production of "Trio checkers" (unfortunately, the author of the game was not mentioned in the advertising). The author used the transformed version of a widely known tetragonal checkers structure, as he understood that it’s virtually impossible to create a good game based on a triagonal structure. The game was played on a hexagonal board of tetragonal structure (!) with anisotropic triangular cut in the center of a board. Such board shape is known to experts by Robert Zubrin's chess patents (USA, 1972), Fred Kipfer’s (Switzerland, 1976), Dutch experts Van der Leiken and Spilborg (1979.) It was the board designed by the latter authors that was taken as a basis for the game in Orel, where 3 players started with 12 pieces. However, a” black hole " in the center of a board makes the game a bit incomplete - it is possible to insert a hex there!

But this version didn’t provide a solution to the problem as well. I failed to find a decent variation of checkers for three neither in other authors’ variations, nor in my own. But the paradox is that Neva checkers solve this problem easily, because during one game the players move alternately from multi-players strategies for 4 and 3 players to a classical two-players strategy. As for the other parameters, the Neva checkers are definitely better than other multi-players checkers variations mentioned above.

To make a set of Neva checkers is really easy. You should buy a set of traditional Russian checkers and paint 6 white pieces into red color, 6 black pieces – into green. After that the only thing to do is to draw a game board on a hard paper.

And now a sad story about my games traveling all over the country and abroad. Two publishing houses in Minsk “Literatura” and “Harvest” started to edit my early publications, but, seems, they were in such a hurry that they forgot to mention the author’s name. That would be ok (well, what can one expect from the pioneers of provincial business?), but to our deep surprise a widely known and reputable Moscow publishing house ACT joined them too. Well, dear Sirs, nowadays the truth can be discovered with the speed of sound, so why put yourself in such an awkward situation?