Double-12 dominoes: how many tiles, pips and sets

A domino set named "double-n" has one tile for every pair of numbers from 0 to n, with each pair appearing once. The number of tiles is (n + 1) × (n + 2) ÷ 2. For a double-12 set that is 13 × 14 ÷ 2 = 91.

In a double-n set, every number appears on n + 1 tiles: once alongside each of the other numbers, and on its own double. Because the double shows the number twice, each number appears on n + 2 tile ends.

• Double-12: each number is on 13 tiles and 14 ends. In the 12-12 round, only 12 tiles besides the engine carry a 12, and those are all the tiles that can start the trains.
• Double-9: each number is on 10 tiles and 11 ends.
• Double-6: each number is on 7 tiles and 8 ends.

That is why, in Mexican Train, it pays to notice how many tiles of a number are already on the table: once most of them are gone, a train ending in that number is close to a dead end.

Each number k appears on n + 2 ends, so the total number of pips in a double-n set is (n + 2) × (0 + 1 + … + n), which works out to (n + 2) × n × (n + 1) ÷ 2. A double-12 set has 14 × 78 = 1,092 pips. A neat consequence: the average tile in a double-n set has exactly n pips, so a double-12 tile averages 12. The heaviest tile is the top double: 24 pips for the 12-12.

In Mexican Train the pips left in your hand are your score for the round, so these numbers matter: being caught with three average double-12 tiles costs about 36 points.

Most double-12 sets give each number its own pip color, so matching a 10 to a 10 doesn't mean counting dots. There is no single standard: colors vary from maker to maker, and two numbers can look alike in some sets. The colors we use in our online game are below.

• The dominoes, usually a double-12 set of 91 tiles.
• A hub or station: a round piece with a center slot for the engine double and slots around the edge where each player's train starts. Many have eight or more slots.
• Train markers: small plastic trains, one per player, placed on a train when it is open to everyone.
• A case or tin to keep everything together, and usually a rules sheet.

None of the extras are essential. You can play with any double-12 set, put the engine in the middle of the table and use coins as markers. Keep the score on paper or on our Mexican Train score sheet.

If you mostly play Mexican Train with family, a double-12 set covers it. If Chicken Foot is your table's game, a double-9 set is the usual pick. For the full game rules, see the Mexican Train rules.