The science of Mexican Train Dominoes: how math and probability come into play

Deploy math skills the next time you play Mexican Train with double twelve dominoes

Unlike our sister game at PlayBunco.com where players roll dice randomly, without need for skill, Mexican Train Dominoes requires luck and skill. With 91 dominoes in a typical Double-12 domino set used in Mexican Train, the tiles are numbered from 0-0 to 12-12. This means that there are 13 different values on each end of the domino and 13 different possible doubles (such as 0-0, 1-1, 2-2, and so on). The numbers grow when you use sets larger than double twelve dominoes.

Mexican Train Dominoes is a game best played with great strategy and critical thinking. To win, you'll need to lean on certain mathematical principles such as probability and statistics to keep track as each player plays and draws from the boneyard.

Assuming you've got a standard four people for Mexican Train game night, and all players have equal skill and experience, the probability of winning Mexican Train for each player is 25%. That's not hard math — each player has an equal chance of starting with the highest-scoring hand, and as the game progresses, each player has an equal chance of drawing the remaining dominoes needed to complete their private train.

Your chance of drawing a specific domino at the start is 1.1%

If you're playing Mexican Train with the standard four players, each player will start with 15 dominoes, leaving 60 in the boneyard. This means that at the beginning of the game, the probability of drawing any specific domino is 1/91, or approximately 1.1%.

However, the probability of drawing certain types of dominoes can be higher or lower depending on their quantity in the set and how they are distributed among the players.

For example, in a Double 12 set (most typical among Mexican Train fans), there are only one of each double, so the probability of drawing any specific double at the start of the game is 1/13, or approximately 7.7%. Conversely, there are 13 dominoes with a 0 pip count, so the probability of drawing a domino with a 0 on one end at the start of the game is 13/91, or approximately 14.3%.

Know the probability of drawing multiple dominoes from the boneyard

One of the essential elements of Mexican Train Dominoes is understanding the probability of drawing a specific domino from the boneyard. This is especially important when deciding which domino to play next, as players must consider which dominoes are most likely to be drawn in the next turn.

For example, if a player has a domino with a high pip count already played, they may be more likely to draw a lower pip count domino on their next turn, so it might be wise to hold onto your high pip count domino for a later turn.

We've generally advised playing high-pip count dominoes early in the game to ensure you get the lowest score if you think you'll lose the round. But before the game ends, it can rob your opponents of that one domino they need most to match and play their last domino.

Play offensively early, defensively later on

The best Mexican Train strategy is whatever plays all the dominoes fastest. That's usually an offensive approach early on playing the highest double and other high-scoring tiles with a string of matching end dots and doubles. This will pressure your opponents to build out their own or the public train.

Generally, you should favor your private train over the public train to control your second turn from the first round on.

As Mexican Train play progresses round to round and to other players, you can play defensively by blocking opponents from the domino they need. Players will signal which matching end they need by playing on the public train before the player places a train marker on their private train.

Block opponents by hoarding remaining dominoes

If a player can predict which dominoes their opponents need to play, they can try to block the next player by holding onto those dominoes themselves. This can be especially effective if the opponent has limited possible moves left, as it reduces their options and may force them to draw from the boneyard. On subsequent turns, this can really add up their pip count.

Likewise, if you know you're facing a loss because you have several domino tiles compared to the next player with only one or two domino tiles, you can play subsequent turns designed to gum up the Mexican Train tracks, as it were.

If you have a choice between playing a domino that empties your hand or one that does not, always play the domino that empties your hand through a string of matching ends of the same number. This will prevent other players from scoring additional points on your remaining dominoes.

But if you know an opponent needs a domino you have, and it does you no good to empty your hand, hold on to it to keep the train marker on their private train as long as possible. With any luck the next player before and after you might notice, too, blocking their train.

Pay attention to what's on the table

Chess grandmasters encourage players to "see the whole board", like great commanders on a battlefield. The same can be said for Mexican Train Dominoes. See the whole table and take command in your mind of what's played, what's missing, and who played what.

Using statistics, you can quickly calculate the likelihood of a particular domino being played by an opponent, almost like counting cards (but a lot less illegal). For example, if a player has already played a 6-6 domino, the likelihood of another player holding a 6-6 is eliminated. Thus it might be advantageous to hold onto other high pip count dominoes, as they may be more likely to be played later in the game.

Is monitoring domino tiles like card counting?

Domino matching and noticing what has and hasn't been played yet is not exactly like counting cards, though they do have similarities. We'd argue paying attention to what is plainly before a person's eyes doesn't count as cheating or "hacking" Mexican Train Dominoes. It's just noticing what dominoes and matches have been made and are likely to be made.

The big difference is in card counting, players must also factor in the probability of the remaining cards being dealt. In contrast to domino matching, where the probability of the remaining dominoes is generally fixed. Afterall, they will all be drawn from the boneyard eventually anyway.

Ready to test your math and stats skills in Mexican Train Dominoes?

Overall, understanding the principles of probability and statistics can give players a strategic advantage when playing Mexican Train Dominoes.

By considering the likelihood of certain events occurring and using this information to make decisions, you can increase your chances of winning and outsmarting opponents.

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