Chapter 11/Advanced
The endgame and repeated positions
Single-tile turns, victory priority and threefold repetition
Count the changing board
The opening leaves two tiles on the board. While players can place two reserve tiles, each later turn removes one opposing tile and adds two own tiles. Occupancy therefore grows by one per completed turn. This useful count describes the opening and middle game, but it is not a permanent limit on the length of a game.
After turn 62, a game that has continued normally has 63 occupied cells. Blue has 31 tiles on the board and Red has 32. Blue has one reserve tile left. That shortage changes the number of placements, not the result: the next turn can still continue after a successful defense.
Play the reserve you have
Remove one opposing tile first. If no opposing winning line survives, place two own tiles when two are available. If only one remains, place that tile and hand the turn to the opponent. You cannot voluntarily stop after one when another placement is available. Removed tiles always return to their owner’s reserve.
Look at the board · 1/2
Break A1–D1 even though only one Blue tile remains
Study fragment · Stroke: complete line · Dashed square: focus cell · ×: removed tile
Your removal replenishes the other color, not your own. In a normal late game, removing one tile and placing your single remaining tile keeps the total occupancy unchanged. The opponent can then use the tile you returned. Both colors can keep changing the position without running out of all possible moves.
Now try it yourself · Defend before placing your last tile
Defend before placing your last tile
One Blue tile remains in reserve · Remove without leaving a Red line
Tap a red tile to remove it
Victory still comes first
A small reserve never protects you from a surviving opposing line. Imagine that Red has two disjoint lines and Blue has one reserve tile. Blue removes a red tile, but the other red line survives: Red wins immediately. Blue does not get a placement or a draw to escape that result.
Look at the board · 1/2
The row and column share a 4
Study fragment · Stroke: complete line · Dashed square: focus cell · ×: removed tile
If Blue instead breaks every red line, Blue places the available tile and continues the game. That single tile can create a new threat. Red must then remove before the threat is judged. Evaluate the actual defense and reply instead of assuming that the late-game reserve means an automatic draw.
Now try it yourself · The final diagonal
The third occurrence is a draw
The game automatically ends in a draw when the same position occurs for the third time. A position includes every tile’s square, color and number, the player whose turn it is, the phase of the turn and the number of placements still pending. The three occurrences need not be consecutive.
Two matching pictures do not count as the same position if a different player acts next, or if one picture is before removal and the other is before placement. Clocks and turn numbers do not change position equality. A second occurrence still permits play; the third ends the game immediately. A winning defensive resolution keeps priority.
Now try it yourself · Avoid removing an endpoint
Choose whether to repeat
With single-tile turns, a pair of players may repeatedly return tiles to the same squares. Unlike the earlier growth phase, the board can now repeat in full. Before making a familiar move, consider whether you are choosing a draw or whether a different square or number could improve your position.
There is no longer a fixed ending at turn 63. A game can continue with new positions until a line survives, a position repeats three times, or an online player resigns, loses on time or accepts a draw. Saving, reconnecting and undoing an unfinished turn preserve the relevant repetition counts.
Now try it yourself · Only one removal keeps the game alive
What to remember
- Place two reserve tiles when possible, or the one you have left
- Resolve surviving opposing lines before continuing the turn
- The same board, player, phase and remaining placements occurring three times is a draw