Dameo

Dameo is an abstract strategy board game for two players invented by Christian Freeling in 2000. It is a variant of the game draughts (or checkers) and is played on an 8×8 checkered gameboard.

Dameo starting position. A common opening move for White is to move the line of two men at c2 and d1 to b3 and c2. This is executed by moving the checker at the back of the line to the front: 1. d1b3. Less common opening moves are 1. d1d4 and 1. d1g4. Of course, it does not have to be the last man of a line: 1. d2d4 is also common.[1]

Game rules
The Coup Turc combination in Dameo illustrates several rules.[2] White wins with 1. c1e3 a5:c5 2. e1c3. Black is now obligated to capture the maximum number of men (four) with the multi-jump 2... c5:c1:h1:h3:d3 and must stop on d3, since the jumped men on c3 and d1 remain on the board until the multi-jump has been completed (the already-jumped man on c3 may not be jumped more than once, and the jumped man on d1 prevents Black from jumping the man on d2). The captured men are now removed, and White proceeds with the multi-jump 3. d2:d4:d6:b6:b8+.

Dameo is played on an 8×8 checkerboard with 18 pieces per player. Each player’s pieces are arranged so that the bottom three rows, from the perspective of the player, are filled from a1 to h1, b2 to g2, and c3 to f3, forming a distinctive trapezoid shape.

  • The player with the lighter pieces moves first. Then turns alternate.
  • The pieces, called men, can only move forward, either straight ahead or diagonally.
  • In addition, men can jump over one or more other subsequent men of the same color in a straight line forward or diagonally, provided that the square ahead of the line is free.
  • When a man reaches the last row of the opposite side of the board, it is crowned, or promoted, to a king. The king can move in 8 directions to any available number of cells, like a queen in chess. King promotion greatly increases a man's ability to break the opponent's position, and results in a larger percentage of games ending in victory. Dameo has very few draws.[3][4]
  • Capturing involves jumping over enemy pieces and removing them from the board. All captures in Dameo are orthogonal only. A man may capture forwards, backwards and sideways by a short leap to an unoccupied space one square directly beyond the captured piece. If a jump is possible it must be done, even if doing so incurs a disadvantage.
  • A king may capture by a long leap to any unoccupied square opposite the captured piece, so long as there is no other piece obstructing the path of the king.
  • Multiple successive captures in a single turn must be made if, after each jump, there is an unoccupied square immediately beyond the enemy piece. One must play with the piece that can make the maximum number of captures.
  • A jumped piece is removed from the board at the end of the turn. For a multi-jump move, captured pieces are not removed during the move; they are removed only after the entire multi-jump move is complete.
  • The same piece may not be jumped more than once.
  • A player with no valid move remaining loses. This occurs if the player has no pieces left, or if all the player's pieces are obstructed from moving by opponent pieces.
  • A game is a draw if neither player can win the game.
  • A game is considered a draw when the same position repeats three times by the same player (not necessarily consecutively).[5]

History

Dameo has its origins in Christian Freeling's 1988 game Bushka, inspired by the traditional Madagascar game Fanorona. Freeling describes his first experience with Fanorona as a "shock,"[6] and he felt the game to be very volatile on the whole. Fanorona's capture methods of approach and withdrawal, however, struck him as being unique among Alquerque derived games, which generally feature capture by jumping over pieces. While capture by withdrawal seemed uninviting, capture by approach left an impression on him and he began thinking of ways to incorporate it into a draughts framework.[6] At first the translation was straightforward, and Bushka was essentially International draughts with a 9x11 board size and capture by approach or "contact." Freeling found this to be functional, but uninspiring due to the need for connected vacant squares to achieve more complicated mutli-capture moves.

He returned to Fanorona which allows a single man to capture whole lines of men by its capture method rather than just a single man. This allows a player to "...carve deeper into an opponent's position..."[6] and achieve similar capturing power to multicapture moves in draughts, but it didn't sit right with Freeling due to the oddity of "...one man axing a whole phalanx." He let the idea sit for awhile before coming up with the concept of Linear movement and capture, where whole lines of two or men move and capture together as a phalanx. He says that, in retrospect, it was an obvious choice to " ...let the capture of a line of men be by a line of men."[6] This development largely led to the completion of Bushka as it stands today lacking only the later reversion to the 10x10 board and a starting count of 15 men.

Like capture by approach, the linear movement mechanic inspired Freeling to look at incorporating it into other games. His first attempt was similar to his attempt with capture by approach, he simply added the concept to International draughts. His reasoning was that it would speed up the game, allowing for quicker entry into the mid and late game. The way it worked out however was largely to create gridlock and slow down the game considerably as it added "defensive" capabilities to both sides without adding any compensating offense.[7] Freeling eventually abandoned the concept in draughts until 15 years later when he encountered Croda.[8]

Croda was invented in 1995 by Ljuban Dedić of Croatia, Associate Professor of Mathematics at the University of Split and the 1989 International Checkers champion of the former Yugoslavia.[1][9] A variant of Turkish draughts, Croda was the result of a search for a checkers variant with the smallest percentage of draws. In it Ljuban Dedić replaced the sideways movement of the man in Turkish draughts with a diagonally forwards movement and filled the back rank with men for a total of 24 compared to Turkish draughts' 16. He also replaced Turkish draught's rule of removal of captured pieces during a turn with removal of captured pieces at the end of the turn.

Croda was the missing piece Freeling needed to apply his concept of linear movement to a draughts game. He described his idea for the invention of the game as follows:

You can't force an unwilling game anymore than an unwilling donkey, and Dameo remained a vague notion for fifteen years or so, before jumping into existence in two minutes.

This is what happened. After Bushka, which implicitly revolves around linear movement and capture, I started wondering about linear movement in a draughts game. The idea was to speed the game up compared to other draughts games rather than to make it the 'backbone', because linear capture is not a logical concept in draughts. I eventually labelled the idea as a 'loose end', because I could not see a satisfactory solution. The main problem was that I was rather specifically thinking in terms of International Draughts. In that game movement and capture follow the same lines: the diagonal subgrid. Introducing linear movement would bring on a strong suspicion of gridlock to the opening. It appeared so dull and dead that I abandoned the idea for the time being. And that was a long time.

Till the early spring of 2000 in fact. I had been composing Hexdame problems with one of the greatest authorities on Draughts endgames, Leo Springer, who lives a few miles away. Generally speaking Hexdame has been well received in the Draughts community, probably because the translation is so literal, and the combinatorial power so similar. Anyway, one afternoon he shows me a Draughts variant called Croda, and what did I think of it?

It didn't look all that appealing at first sight, but after reading the rules I realized it was brilliant in its simplicity. Ljuban Dedić, himself a deserving Draughts player known for openly criticizing the game's well known flaw[lower-alpha 1] – the Draughts equivalent of 'coming out of the closet' – had basically replaced the sideways move in Turkish Draughts, with a diagonally forwards one, therewith retaining all advantages of the square plane, while defining movement simply as 'forwards'.

The inevitable didn't take long: a couple of weeks later, the lingering idea of linear movement superimposed itself on Croda, and with it came the realization that it would cause no gridlock because movement and capture didn't necessarily follow the same lines. The game assembled itself within a minute or two, including an initial position that not only provides an identifiable image, but counters the build up of too many forced along the sides, a well known characteristic of the square plane, and of Croda itself, for that matter.[7]


While fundamentally similar to Croda, the addition of linear movement, the added diagonal movement of the king, as well as the initial set-up all add to how the game is played and the tactics and strategies available to players.

Since its creation Dameo has been featured in Abstract Games...for the competitive thinker,[10] has online tournaments on Littlegolem,[11] Brainking,[3] and igGamecenter,[12] is featured on apple's app store,[13] and is the subject of Belarusian Checkers Expert[14] Aleh Tapalnitski's book Meet Dameo.[5]

Strategy

Dameo's depth in tactics and strategies compare favorably to other draughts/checkers variants due in large part to its double grid and linear movement of men. Familiar concepts such as majority capture, ladders and bridges, and the coup turc[5] are present, along with unique tactics and strategies, such as the Oblique Hit and the King's Trap.

Majority Capture
Majority Capture: If Black moves his king on b1 to f1 trying to capture White’s men on f2 and f5, white can respond by moving his man on a3 to a4. Due to the maximum capture rule Black must move f1 to f6 instead of capturing White’s man on a4. This allows White to respond by capturing all of Black’s men on a5, b6, c7, d8, e7, and Black’s King on f6.

Majority Capture is a fundamental part of Dameo. The substance of it is the sacrifice of two or more men in order to manipulate the opponent's position to set up a devastating counterattack. This usually takes the form of board spanning multiple captures for material advantage, but can be for the sake of a positional advantage ending in the promotion to a King as well. Majority capture often plays a role in more specific or localized tactics such as the Ladder Strike, Coup Turc, or Oblique hit.[5]

Ladder and Bridge
Ladder: If Black moves his man on f6 to f5 trying to gain material advantage, White can respond by moving his man on e5 to c7 with linear movement. This forces Black to move his man on b7 and capture white’s men on c7 and d6 landing on d5 because of the maximum capture rule. White can then counterattack with his man on g5, capturing Black’s men on f5, d5, c4, and b3 winning the game.

In a ladder strike, the capture resembles moving up or down stairs, as the men are positioned (or forced into a position) where a row of men are lined up diagonally. Clever positioning of your own piece can allow for a majority capture wherein the piece simply "goes up or down the stairs" by alternating capture up (or down) with right or left movement. Setting up this type of majority capture often involves an opponent's piece carelessly placed between two of your own pieces.

A bridge is a simple set up for the ladder strike, where pieces are sacrificed one by one, to position an opponent's man into an ideal position for a ladder strike. They "bridge" the starting position into a winning ladder strike position[5]

Coup Turc
Coup Turc: White moves to win by playing his man on f2 to d4 by linear movement. Because of the maximum capture rule Black is forced to respond by playing his king on d8 and capturing White’s men on d4, e2, g3, and f4 landing on e4 (because of the rules where pieces aren’t removed from the board until the end of the turn combined with rule that forbids jumping over the same piece twice). This leaves White’s man on e3 free to counterattack by capturing Black’s king on e4 along with his men on e6 and f7.

In Dameo captured men are removed at the end of the turn and not during the turn itself. This, combined with the rule that disallows jumping over the same piece twice, makes the Coup Turc[lower-alpha 2] possible. In essence, the tactic is the same as a majority capture, the goal being the manipulation of an opponent's man or king to an advantageous position for a multi-piece capture. The coup turc manages it by forcing an opponent's piece to capture in a sequence ending on a square next to a piece it already captured, lining up perfectly for the player's piece to then counterattack with a majority capture.[5]

Oblique Hit
Oblique Hit: The opposing squares make the combination of linear movement with majority capture possible. It's generally most useful for the player closest to the King's Row.

The oblique hit combines the rules regarding linear movement and maximum capture. In the diagram on the left, white wins by moving c3 to e5 (bottom left white man to the square just to the right of bottom right black man). Black has two captures available, d5 to f5, capturing the man white just moved, and c5 to e3 capturing the man on c4 and then immediately after the one on d3. However maximum capture takes precedence, so black must capture the two men on c4 and d3. This leaves white open to capture the black men on d5 and c6 landing one square away from the King's row (c7). If black moves his man closest to the king's row he won't be able to reach it before white or stop white's other man from reaching the other king's row first.[5]

King's Trap
King's Trap: If Black’s man on b2 tries to enter the King’s row on b1, white can leave his men there forcing Black to capture c1 and f1 landing on g1. This allows white to capture Black’s king with his man on h1. If Black’s man on d2 tries to enter the King’s row on d1 or e1, he leaves himself immediately open to capture on white’s turn.

The king's trap is a defense that takes advantage of Dameo's linear movement[lower-alpha 3] . Because of forced capture, if a man lands on the king's row and is crowned, the opponent can, if they have at least four men in a line on the king's row, move the man second closest to the king forward. This forces the king to jump the piece closest to him and land in the empty space directly next to the remaining two men on the king's row, allowing for a counter capture on the next turn. The move is also possible when there is a line of three men ending on the one of the corners.

Another king trap made possible by Dameo is the a1,c1,f1, and h1 configuration (pictured). If a man lands on b1 or g1, then on his next turn, because of maximum capture and the king's long range, he's forced to capture men until he lands on g1 (if he started on b1) or b1 (if he started on g1). This allows the opponent to engage in a counter capture of the king on their turn because of their man in the corner. If the oppenent's man lands on either d1 or e1, it leaves him open for immediate capture by the opponent's man on c1 or f1 respectively.[15]

Variants

Two 10x10 variants, together known colloquially as “Big Dameo,” have been invented, adapting Dameo rules to a larger board size with more pieces. One of these has the men initially arranged with the first 4 ranks filled with ten men, then eight, then six, and then four creating a trapezoid shape proportionally comparable to standard Dameo.

The other, available for play on an iphone app in the custom rules settings, fills only the first three ranks, as in Dameo, but with more men (ten, eight, then six).[16]

Trivia
  • Freeling considers Dameo one of his six most important games, along with Emergo, Grand Chess, Storisende, Sygo, and Symple.[17]
  • Nick Bentley, creator of the 2018 abstract strategy game "Blooms,”[18] and the 2020 strategy game “Oceans,”[19] included Dameo in his list of "The best unpublished modern abstract games."[20]
  • Dameo's draw margin at high level play is estimated to be around 21%.[4] For comparison, the draw margin of chess at high level play has hovered around 50% since 1993.[21]
  • Dameo's game tree complexity is estimated to be around 10^107.[4] Its upper bound state-space complexity is ~10^40.[22]

See also

Notes
  1. Meaning the high margin of draws between players in professional international draughts matches.
  2. Sometimes known as the Turkish hit.
  3. If a square in the second row is empty for the man being moved forward, then linear movement is unnecessary

References
  1. Freeling (Summer 2002), p. 10
  2. Freeling (Summer 2002), p. 11
  3. "BrainKing - Game rules (Dameo)". brainking.com. Retrieved 2020-10-13.
  4. "Full Report for Dameo by Christian Freeling". mrraow.com. Retrieved 2020-11-16.
  5. Tapalnitski, Aleh (2017). "Meet Dameo!" (PDF). Mind Sports. Retrieved 2020-07-31.
  6. "Bushka - Page 2". www.mindsports.nl. Retrieved 2020-10-13.
  7. "Organicity". www.mindsports.nl. Retrieved 2020-07-31.
  8. "Symple - Page 5". www.mindsports.nl. Retrieved 2020-10-13.
  9. Handscomb (Spring 2002), p. 7
  10. Freeling, Christian. "Dameo." Abstract Games... for the competitive thinker Issue 10, 2002, pp. 10-12, www.abstractgames.org/uploads/1/1/6/4/116462923/abstract_games_issue_10.pdf. Accessed 13 Oct. 2020.
  11. "Little Golem". www.littlegolem.net. Retrieved 2020-10-13.
  12. "igGameCenter :: Online games". www.iggamecenter.com. Retrieved 2020-10-13.
  13. "Casual Checkers & Draughts". App Store. Retrieved 2020-10-22.
  14. "DameoBookReview". THE NEW ABSTRACT GAMES. Retrieved 2020-10-13.
  15. Moore, Rex. "Different King Traps in Dameo." Boardgamegeek.com, edited by W E. Martin, BoardGameGeek LLC, 20 June 2017, boardgamegeek.com/thread/1799713/different-king-traps-dameo. Accessed 8 Oct. 2020.
  16. "BoardGameGeek". boardgamegeek.com. Retrieved 2021-01-05.
  17. "The ArenA". www.mindsports.nl. Retrieved 2020-10-08.
  18. "Blooms". BoardGameGeek. Retrieved 2020-10-08.
  19. "Oceans". BoardGameGeek. Retrieved 2020-10-08.
  20. Bentley, Nick (2019-09-23). "Abstract Strategy Games: The Definitive Guide (2020 Edition)". Nick Bentley Games. Retrieved 2020-10-08.
  21. "Has the number of draws in chess increased?". Chess News. 2018-03-21. Retrieved 2020-11-25.
  22. Eklov, Erik (2019-03-06). "Board Game Complexity Part I: State-Space & Game-Tree". pipmodern. Retrieved 2020-11-16.

Bibliography

  • Freeling, Christian (Summer 2002). "Dameo". Abstract Games. No. 10. Carpe Diem Publishing. pp. 10–12. ISSN 1492-0492.
  • Kerry Handscomb, ed. (Spring 2002). "International Checkers Versus Croda". Abstract Games. No. 9. Carpe Diem Publishing. ISSN 1492-0492.

Further reading
  • Kerry Handscomb, ed. (Autumn 2002). "Dameo Problems". Abstract Games. No. 11. Carpe Diem Publishing. p. 9. ISSN 1492-0492.
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