A board full of pegs, but for one empty hole, provides a surprisingly demanding abstract game. Polytaire looks familiar if you've played peg solitaire, but the hexagonal board and two-player rules require planning several moves ahead.
Abstract Game Design's Busy Decades
The 1950s and 1960s were fertile years for abstract games, puzzles, and mathematical play. Designers experimented with geometric boards, patterned movement, and sparse rules that produced hard decisions. The appeal was clear: a few pieces and a clean board could create a problem worth returning to.
Piet Hein belonged to that creative tradition. So did designers and writers such as Alexander Randolph, Claude Soucie, Sid Sackson, Martin Gardner, David Gale, and Solomon Golomb. Their work often began with a simple visual pattern, then tested what happened when a single movement rule changed.
Piet Hein was a Danish poet and game designer with a gift for finding depth in compact forms. Polytaire, developed in 1966, carries that spirit. The board is a simple hexagon of holes, but the move rules give every empty space a purpose.
At first glance, the game resembles French solitaire. Both games are about jumping one piece over another into an empty space, then removing the jumped piece. Polytaire takes the familiar jump-and-capture idea in a new direction.
The Board and Pieces at a Glance
Polytaire shares some family resemblance with Konane, the Hawaiian jump-and-capture game. Both reward players who can see openings and jump sequences, but Polytaire's hexagonal board, mixed-color interactions, and solo puzzle options make it a different experience at the table.
Polytaire uses a hexagonal array with 37 holes. The complete set includes 37 pegs: 18 light, 18 dark, and one unique colored peg.
The board has six possible jump directions from each position (except along the edges, or course). That is a major difference from the square or cross-shaped boards many players know from standard peg solitaire. A peg may jump over an adjacent peg and land in the immediately opposite open hole, then the jumped peg leaves the board.
Every legal move in Polytaire is a jump-and-capture. There are no other options.
The original Danish edition appeared in 1966. Its packaging was modest, but the hardwood boards left a stronger impression. Vintage copies vary in price, as any collector can tell you, but it sometimes seems unduly extreme. I found one online auction listing asking $750 for a 1966 original, while other copies appeared for under $100. Amazing.
How To Play Polytaire Solo
In the basic one-player game, the peg colors do not matter. Fill every hole except one. The center hole is the usual starting gap, though you can choose any hole for a different puzzle.
Every turn follows the same sequence (no surprises here):
- Choose a peg beside another peg.
- Jump it over that adjacent peg into the empty hole directly beyond it.
- Remove the peg that was jumped.
No other move is legal. Continue until only one peg remains, or until no legal jump remains and you have reduced the number of remaining pegs as far as possible.
The Advanced Red-Peg Version
For a harder solo challenge, replace any peg on the board with the red peg. The jump rules remain exactly the same, but the ending condition changes: finish with only the red peg still on the board. Choosing where to put the red peg also changes the shape of the puzzle before the first move begins.
The game is reported to have 1,369 possible starting configurations, all solvable. Playing a different one each day would give me enough material for roughly three years and nine months of daily puzzles!
Two-Player Polytaire Captures, too, but…
The two-player game gives Polytaire its most unusual twist: Eliminate your own pegs.
To set up the game, mix the light, dark, and red pegs together, then place them randomly in all the holes. Then remove the red peg to establish the single empty starting hole. One player will take the light pegs, and the other will take the dark pegs.
You can jump one of your pegs over a peg of either color, as long as the hole beyond it is empty. However, only a jumped peg of your own color comes off the board. If you jump over your opponent's peg, that peg stays where it is.
This reversal means that you’re not trying to wipe out the other side as usual. Instead, you’re trying to arrange the board so your own pieces are available to be jumped.
Jumping is still mandatory for every move, but if “chain jumps” are available after that first jump, they are entirely optional. Sometimes additional jumps are desirable, and you might spend some time setting up a nice string of jumps. But just as often you might find stopping after the first jump is more to your advantage in a subsequent turn.
A Little Something Different
Polytaire is easy to explain, but it does not stay simple for long. Each turn changes both the pegs and patterns available across the board.
The game rewards patience. Take some time to plan not only your own series of moves, but watch for your opponent’s opportunities, too. A jump to block their chain could save your bacon!
Polytaire is a good example of a vintage abstract game worth some table time. It’s simple to teach and learn, very portable, and different every time.
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