Breakthrough (board game)

Breakthrough is an abstract strategy board game invented by Dan Troyka in 2000 and made available as a Zillions of Games file (ZRF). It won the 2001 8x8 Game Design Competition, even though the game was originally played on a 7x7 board, as it is trivially extensible to larger board sizes.

abcdefgh
8
a8 black pawn
b8 black pawn
c8 black pawn
d8 black pawn
e8 black pawn
f8 black pawn
g8 black pawn
h8 black pawn
a7 black pawn
b7 black pawn
c7 black pawn
d7 black pawn
e7 black pawn
f7 black pawn
g7 black pawn
h7 black pawn
a2 white pawn
b2 white pawn
c2 white pawn
d2 white pawn
e2 white pawn
f2 white pawn
g2 white pawn
h2 white pawn
a1 white pawn
b1 white pawn
c1 white pawn
d1 white pawn
e1 white pawn
f1 white pawn
g1 white pawn
h1 white pawn
8
77
66
55
44
33
22
11
abcdefgh
Initial position.

Rules

The board is initially set up as shown on the first diagram. To play the game on a different-sized board, just fill the two front and two back rows with pieces; the board need not be square.[1]

Choose a player to go first; then play alternates, with each player moving one piece per turn.

abcdefgh
8
b6 black cross
c6 black cross
d6 black cross
c5 white pawn
f3 black pawn
e2 white pawn
f2 white pawn
g2 white pawn
8
77
66
55
44
33
22
11
abcdefgh

A piece may move one space straight or diagonally forward if the target square is empty. In the second diagram, the white piece on c5 can move into any of the marked squares.

A piece may move into a square containing an opponent's piece if and only if that square is one step diagonally forward. The opponent's piece is removed and the player's piece replaces it. For example, the black piece can capture either the white piece e2 or the one on g2; it would replace them if it chose to capture. Note that capturing is not compulsory, nor is it "chained" as in checkers; a player can only capture one piece in a turn.

The first player to reach the opponent's home row — the one farthest from the player — is the winner.[1] If all the pieces of a player are captured, that player loses. A draw is impossible[2] because pieces can only move ahead (or be captured), and the piece closest to the opponent's home row always has at least one forward diagonal move available.

Strategy

Although the rules are quite simple (and were the simplest rules in the 2001 8x8 Game Design Competition), the strategy is complex and sophisticated.[2] Generally, an effective offensive strategy is to recognize and attack "pivotal" pieces which are in positions to block multiple routes to victory. An effective defense is to arrange multiple blocking pieces in a blocking pattern (since a single defending piece can not effectively block a single attacking piece).[2]

Game Solving

Smaller variants of the game have been solved:[3]

  • 6x5 : second player win
  • 5x5 : second player win
  • 3x7 : second player win

References

  1. Arneson, Erik. "Breakthrough - Designed by Dan Troyka." About: Board / Card Games
  2. Handscomb, Kerry. "8x8 Game Design Competition: The Winning Game: Breakthrough ...and two other favorites." Abstract Games Magazine, Issue 7, Autumn 2001.
  3. Saffidine, Abdallah. "Solving Breakthrough with Race Patterns and Job-Level Proof Number Search"
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