Few nice mancalas

Although the label was the wrong color and contained many spelling errors, most of it was in place, including the inscription “ May contain nuts ” in tiny font.
sir terry pratchett

Go or ur ? One can argue for a long time which of the games is older, but it will win, in this confrontation, most likely, Mancala . Archaeologists prefer to deal with material evidence, but as soon as it comes to board games, everything quickly goes into the realm of speculation. It was found a lot of boards, but much less information about how to play them. The ancients did not bother with a detailed description of the rules.

With Mancala, the situation is exactly the opposite. This is not a single game, but a very numerous family. In West Africa alone, there are dozens (if not hundreds) of varieties. Board (as a material artifact) for such games is not required. It is enough to take a handful of pebbles and dig a few holes in the sand. Not surprisingly, archaeologists have difficulty determining the age of these games. They simply have nothing to look for! But for the attentive researcher of the "board games", mancalas are no less interesting than the birds of the Mockingbird family for Charles Darwin .

To date, the directory Zillions of Games contains more than two thousand applications . It cannot be said that there were no mancal among them at all. In any case, the double-row and four-row versions of games are presented very thoroughly. Here is a set of games provided by just one of the applications:


This is indeed a worthy list, but, as I wrote above, the number of mancal is in the hundreds, and here are the most familiar of them, let's say. There are much more amazing and wonderful varieties of this game. And now I want to do them! But for a start, it is worth making a small glossary of terms so that people who are not familiar with the subject have at least some chance to figure it out.
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Tchuka ruma

I decided to start with a simple one. Chuka Ruma is not a traditional game (in the sense that it is not 5,000 years old, but only 120), but according to the rules it is very similar to Dacon , which is widespread in Indonesia. Except that Chuka Ruma is designed for the game of one person. Yes, this is the only known mancala solitaire. Here's what she looks like:


It is required to transfer all the stones to the “barn” (extreme right well), observing the following rules:

• At the beginning of the game, you can take all the stones from any hole (except the “barn”) and perform cyclic seeding , laying the stones from left to right and moving from the “barn” to the extreme left hole.
• If the last stone falls into the "barn", the player gets the right to repeat the move by re-selecting any non-empty hole, except for the "barn" (this is the rule that makes Chuku Rumu similar to the Mangals of the Chongkak and Dakon families).
• If cyclic seeding is completed in any other hole - the player loses (solitaire did not converge).

This remarkable “mind gymnastics” was first (in 1895) described by the French mathematician Henri-Auguste Delannoy in correspondence with his colleague Edouard Lucas. Any resemblance to the "Dacon" is not accidental, since, apparently, it was this game that Henri-Auguste used as a prototype.


Here's what happened in the end:



I must say that AI Axiom clicks such puzzles "like nuts". The initial alignment (two stones in four holes) ZoG decided on the minimum settings of the "duration of the course." For more complex layouts, the settings had to be “tweaked”, because, otherwise, the program got into a dead end. In the process of testing, another “solved” alignment was found, for those who like to “break their brains” .

Ohojitxi

This very original mancala is played in the Republic of Côte d'Ivoire. Externally, it looks like an ordinary double-row mancala, with six holes on each side, but since the board is “vertical” when playing, it is more appropriate to rank it not as a double row, but as a six-row mancala. Sowing once , counterclockwise and only on its territory - in three rows facing the player.

Surprises don't end there! The goal of the game is not to capture the enemy’s stones, but to get rid of your own. Captured stones are transferred to the enemy (placed in one of his holes). The one who gets rid of all his stones first will win. Capture serial , if the last stone falls into the hole with three stones (complementing them to four) - the stones are captured. Together with them, stones are captured from all previous (against the direction of sowing) holes containing four stones. If initially all 24 stones were in the same hole, the game could be completed in one move!



In general, the game is pretty funny. At first glance, it is not much different from the previous solitaire (since sowing is always carried out only on its territory), but if the enemy has time to “collect four” before you, be sure, he will try to choose the hole in such a way as to maximize frustrating all your plans ( and you have to start all over again). The only limitation is that he cannot choose the same hole each time.


It is pleasant to play Okhochich in the presence of a large amount of free time. The party of equal rivals can last a very long time. In order to collect the last stones, you have to spend a lot of moves. As a rule, the enemy manages earlier and everything starts from the beginning. Serial capture helps break the vicious circle, but it still needs to be folded. When the program plays “with itself”, the average duration of the game is about 500 moves (however, it beats me so fast that I don’t have time to figure out what happened).

Afrika

Yes, it is through this letter! The word is German. I mean, the game was invented by the German - Ralf Gering. And it happened in 2004. This is a scandalous mancala! First, she is less than 120 years old. In addition, she collected 5 "hate ratings" on BoardGameGeek . Later it turned out that they were all from the “virtuals” of the same person (I suspect that it was something personal) and out of five was left one, the very first.

Seriously speaking, this game is too unlike any other mancala. According to the "gameplay" it is much closer to Checkers . It's all about the capture mechanism. In "Africa" ​​it is mandatory! Other mancalas also have “forced” moves (the rule of “hunger” - in most African mancalas), but there they are not of such paramount importance! If there is a possibility of capture - the player must take! And this is what makes the game unique.


The rules are simple. Sowing once , always from its row, counterclockwise, without entering the "barns". Capturing is carried out from an opponent’s non-empty hole located opposite the player’s empty hole and can only be made from holes containing the minimum number of stones (if there are two stones in one hole and three stones in the other hole, you can only take one from two). Capture is considered a separate move and takes precedence over "sowing." Such rules naturally lead to the tactic of “give less to take more”:


The diagram perfectly illustrates the concept. We give away one stone in order to take four in return (I’ll say right away that such an obvious move subsequently leads to a dead end, the problem has a better solution). The great thing about this is that the enemy cannot ignore our sacrifice. He is obliged to take a stone and, losing a turn, cannot protect his own. This is much more “sente” than the meaning put into this concept in Go. As in Checkers , the rejection of forced moves will make the game much less interesting.

As a rule, in games with “obligatory take”, “reverse game” is of certain interest (it is possible for many to be a surprise, but “ Giveaway ”, in tactical terms, is much more difficult game than ordinary checkers). In November 2010, Benedikt Rosenau proposed a “reverse” version of the game, based on the rules of “Africa.” Of course, I implemented both versions of the game.


Statistically , the first player has a slight advantage, but I did not enter Komi (2.5 points) for the second player. The first person goes and a small advantage in the fight with the machine will not be superfluous.

Gabata

Having finished “warm up”, I started two games that were most interesting for me. Both are played on a unique three-row board and are spread on the east coast of the Somali Peninsula. Actually, the board gives the name of the first of them. Gabat is a very archaic gaming system. Some researchers consider it the ancestor of all mankal. The shape of the board dictates an unusual seeding scheme. It is easier to show than to explain:


Arrows indicate the direction of sowing. Sowing cyclical and start the course can only be from their wells (bottom row and three right wells in the second row). In principle, most of the games traditionally played on the “Gabat” board could be played on a regular, double-rowed board, but in the “Gabat” itself three-rowness is used when capturing. If the last stone falls into an empty hole, the player captures all the opponent's stones located in the same board column .


It is easy to see that captures performed in different columns are not equivalent. There are possible captures from two holes at once, as well as situations in which nothing will be captured at all (for example, at the end of a turn in one of the three initial holes of the enemy). The player gets the right to perform another move, a stone that made a seizure (an unlimited number of times) and this rule introduces even greater tactical diversity into the game. Gabatu is often called “pirate mancala” and this is only partly related to the fact that it is played on Somalia territory:



When one of the players cannot complete the next move, his opponent captures all the stones remaining on the board. The game continues for several rounds (this is typical for all games on the Gabat board). Starting the next round, players lay out the stones captured in the previous round, in their holes, three each, starting from the left, in the bottom row. If there are less than three stones in the last hole, the stronger player completes it to three of their stones. The remaining stones of a stronger player immediately go to his “barn”. Wins the one who collects all the stones.

Selus

This game is my favorite! It is played on the same board as Gabat (and also using cyclic seeding ), but with a completely different capture mechanism. In it, players build traps ("wegue"). It is not allowed to walk from the wegue , but any stone that falls into them becomes the property of the player who created them. It is easy to build a trap - if the last stone of sowing falls into a hole with three stones (complementing it to four), the hole becomes wegue . The amount of wegue is unlimited!

It is impossible to call such a capture mechanism unique. There are several Selus related games with a similar stone pick. In the Kazakh mancala " Togyz Kumalak " a player can build a "tuzdyk" (but only one per game), collecting three stones in the hole. Selus’s uniqueness lies in the fact that stones that fall into the hole can be captured (including by “taking” them from the enemy). If the last stone of sowing falls into the wegue , it is captured in the player's barn, taking another stone with it from the trap.



If the capture is performed from its wegue , the player gets another move, but there is one exception. The leftmost hole, in the bottom row, is called “ayemi” (“eye”). ayemi , ayemi , ( , wegue ). , wegue ayemi !

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— ! Axiom — .