Think Nuclear

This is a little game I invented to relieve boredom while spending Christmas in Berkeley. It has the feel of traditional dominoes, but can be played by one person. The challenge lies in planning the selection of tiles in advance so as to place as many tiles as possible. Since some tiles are not visible at the beginning of the game, the entire sequence cannot be planned, and therefore, some risk is involved.

Rules

The traditional double-six domino set (28 pieces with zero to six spots) is used. The specific rules used for placing the dominoes—e.g., whether doubles serve as spinners—are up to the player. Draw 14 tiles to form two rows of seven tiles with each row having five tiles with the pips visible and two tiles face down.

Highest double from either row is placed first. If no such double is available, the heaviest domino is placed. However, the first domino must be playable by the visible dominoes in the other row. Skip all dominoes without a visible tile in the other row that can be played off of it. If two playable dominoes are tied as the heaviest, the player chooses which is placed first.

During each turn, if both rows have the same number of total tiles (visible and unseen), any visible tile can be played. Otherwise, only visible tiles from the row with the larger number of tiles can be played.

The number of visible tiles in each row must always be greater than the number of unseen tiles. That is, when a row has two visible and two unseen tiles, reveal one of the unseen tiles, and when a row has one visible and one unseen tile, reveal the unseen tile.

If a playable tile is available, it must be played. If no tiles can be played, flip one of the unseen tiles from the row with the most tiles. If both rows have the same number of tiles, flip any unseen tile. If the flipped tile is not playable, continue flipping eligible unseen tiles until a playable tile is revealed, which must be played.

If the row with the most tiles has no unseen tiles (or if both rows with the same number of tiles have no unseen tiles) and no playable tile is available, the game is blocked and ends.

The player wins if the last tile is played. Otherwise, the player’s score is the number of pips on the unplayed tiles, including any unseen tiles. Lower scores are better.

Example

After shuffling the tiles face down, 14 tiles are drawn and arranged in two rows, with the four tiles on the right remaining face down.

The highest double is 5-5, on the top row, and since there is a five on the bottom row, it is the first tile that is placed.

The next tile must come from the bottom row, since it has more tiles. The tile must have a five.

Now, any of the eight visible tiles can be played, since both rows have the same number of tiles; however, the only tile that can be played is 5-3.

The next tile must come from the top row, but none of the visible tiles can be played. Therefore, the an unseen tile on this row is revealed.

The newly revealed tile can be played.

Note that a tile from either row can now be played, even though the top row has more visible tiles. The total number of tiles (visible and non-visible) in each row determines which tiles can be played.

At this point, the bottom row has two visible and two unseen tiles. Since the number of visible tiles must be greater than the number of unseen tiles, one of the unseen tiles is revealed.

The game continues until either all tiles are played or the game is blocked because all tiles have been revealed and no eligible tile can be played.