Play Mexico Online

What Is Mexico?

Mexico is a two-dice elimination game played in the open. Each round every player rolls, the rolls are ranked, and the lowest roll costs its owner a life. There is no bluffing and almost no arithmetic; the whole game is a ladder of 21 possible values, a top roll called Mexico (a 2 and a 1) that beats everything, and one decision repeated round after round: keep this roll, or roll again?

The decision has teeth because of the game’s one clever rule. The first player of each round may roll up to three times, and whatever number of rolls they take becomes the ceiling for everyone else. Keep a strong first roll and the rest of the table gets only one shot. Push for something better and you hand everyone else the same freedom. Add the rule that a Mexico doubles the round’s penalty and you have a bar game that runs on nerve and nothing else.

Mexico shares its ranking with the bluffing game Mia and is best thought of as that game with the cup removed. If you like the roll-until-you-are-happy rhythm, the three-dice bar game Cee-lo has the same feel with a banker, and Sevens Out turns two-dice rolling into a push-your-luck race.

A Short History of Mexico

Mexico is a bar and drinking game, and like most of them it has no inventor and no first printing. Its ranking is identical to that of Mia, the northern European bluffing game known as Mäxchen or Meiern in Germany and Meyer in Denmark, and the relationship is obvious: strip Mia of the cup, the hidden roll and the announcements, and what remains is a roll-off in which the lowest visible roll pays. The name “Mexico” for the 2-1 roll appears in Dutch and Scandinavian versions of the two-dice game as well as in English-speaking bars, and one German name for Mäxchen is simply Mexikaner. Nobody has documented which came first, the honest roll-off or the bluffing game, so any claim that one “descends” from the other is a guess.

The game as English-language sources describe it, with three rolls for the first player, a roll cap for everyone else, and doubled stakes on a Mexico, took shape as a money game in which each round’s loser pays a betting unit into a pot and the last player with money takes the lot. The same structure is played for drinks, with the loser of the round taking a swallow, and for lives, which is the version on this page. A separate, drinking-oriented game called Mexican or 21 is sometimes confused with it; that game keeps Mia’s bluffing and uses the same ranking, and the name overlap is one reason internet rule sets for “Mexico” contradict one another. Greek players are said to call the honest roll-off acey-deucey, which is otherwise the name of a backgammon variant, another sign of how loosely the name travels. Treat the history as folklore; the rules below are the ones most sources agree on.

Mexico Rules

Equipment

• Two six-sided dice
• A surface with a rim or a dice cup, because a die that rolls off the table has to be re-rolled and arguments follow
• Life counters for each player. Money, chips or a third die turned to show the lives left all work. The version on this page starts everyone with six lives

Object

Be the last player with lives. Every round exactly one player, the one with the lowest roll, loses a life (or two). Lose your last life and you are out.

Ranking the Rolls

The two dice are read with the higher die first, so a 4 and a 6 is 64. The values are then ranked as follows, from highest to lowest:

How a Round Works

1. The first player rolls. They may roll up to three times, stopping after the first, second or third roll. Only the final roll counts; there is no picking the best of three.
2. The roll count becomes the limit. If the first player stopped after one roll, every other player gets one roll this round. If they used all three, everyone may use up to three. Later players may always roll fewer times than the limit.
3. Everyone else rolls in turn, clockwise from the first player, each stopping when they like within the limit.
4. Mexico ends a turn. A player who rolls 2-1 stops at once, because nothing beats it, and the round’s penalty is doubled.
5. The lowest roll loses. When everyone has rolled, the player with the lowest-ranked final roll loses one life, or two lives if any player rolled Mexico during the round.
6. Ties for lowest are settled by a sub-round: the tied players roll once each, and the lowest of those rolls loses. Repeat if they tie again. Everyone else is safe.
7. The loser starts the next round. If the loser has just been eliminated, the next player in turn order starts.
8. Last player with lives wins.

Penalty Summary

Worked Examples

All examples use the three-player game on this page: you, Rosa and Diego, six lives each.

• You open and roll 6-3. A fresh roll beats 6-3 only one time in three. Keep it. Rosa and Diego now get one roll each and each has a 33% chance of beating you; the chance that both do is about 11%, and if either one fails to beat you, you are safe.
• You open and roll 4-1, then 5-3, and stop. You used two rolls, so Rosa and Diego may roll up to twice. Your 5-3 is beaten by a single roll 56% of the time, and by “roll once and roll again if it is lower” a good deal more often. Opening with a middling roll after two tries is the weakest position in the game.
• Rosa opens, keeps 5-4 after one roll. Diego rolls 4-2. You roll 3-2. You have used your single roll and hold the lowest value. You lose one life and open the next round.
• Diego opens with three rolls and ends on 4-3. Rosa rolls 6-1 on her first roll and stops. You roll 4-3. You and Diego are tied for lowest. Sub-round: one roll each. You roll 5-1, Diego rolls 3-1. Diego loses a life.
• You open and roll Mexico on your first roll. Your turn ends at once, everyone else is limited to one roll, and the loser of the round pays two lives. The other players cannot beat you; the round is between them.
• Rosa rolls Mexico as the second player. Diego and you roll 5-2 and 5-1. Your 5-1 is lowest and, because of Rosa’s Mexico, it costs you two lives.
• Rosa has 1 life, you and Diego have 3. Rosa opens and stops on 6-5 after one roll. You each get one roll. Whoever of you and Diego rolls lower loses, unless one of you rolls a double or Mexico to beat Rosa’s 6-5 and the other does not; with 6-5 the second-highest plain roll, Rosa is safe 78% of the time against each of you.

The Odds

Two dice produce 36 equally likely outcomes. Mixed rolls such as 5-4 occupy two of them (4 and 5, 5 and 4), doubles occupy one, and Mexico, being a mixed roll, occupies two. Hence:

• P(Mexico on one roll) = 2/36 = 5.6%
• P(any double on one roll) = 6/36 = 16.7%
• P(Mexico or a double) = 8/36 = 22.2%, the chance of beating 6-5, the best plain roll
• P(beating 5-4) = 18/36 = 50%, which makes 5-4 the median roll
• P(beating 6-1) = 16/36 = 44.4%, P(beating 6-3) = 12/36 = 33.3%, P(beating 6-5) = 8/36 = 22.2%

Multiple rolls change the picture. If you roll up to three times and stop as soon as you have 5-4 or better, the chance that you end the turn at 5-4 or better is 1 − (16/36)³ ≈ 91%. If you roll once and re-roll only when below 5-4, the chance of finishing at 6-1 or better is about 64%. That is why a first player who stops after one roll with a merely average value is in trouble whenever the others are allowed two or three rolls; once the limit is three, the median result for a player who keeps rolling until satisfied moves up to around a double.

The odds against several opponents multiply in your favor rather than against you. Holding 6-3 against two opponents who each get one roll, you are safe unless both beat you: (1/3)² ≈ 11%. Against one opponent with one roll you are safe two times in three. The probability that at least one of n single rolls shows a Mexico is 1 − (34/36)ⁿ: 5.6% for one roll, 10.8% for two, 15.7% for three, and 20.4% for four, so in a three-player round where everyone rolls once, a doubled penalty turns up about one round in six.

Mexico Strategy

1. Use the roll cap as a weapon

As first player, a single roll of 6-1 or better is worth keeping because it caps the table at one roll each and leaves every opponent below 50% to beat you. Rolling again for something prettier hands everyone two rolls, and their odds of beating you climb sharply.

2. Keep anything above the median on the first roll

The break-even point for re-rolling is the median, 5-4. Below it a re-roll improves you more often than not; above it a re-roll is more likely to make things worse. As a later player the target moves: you only need to beat the lowest roll already on the table.

3. Play against the lowest roll, not the highest

The only thing that matters is not being last. If the table shows 6-4 and 3-2 and you roll 4-1, you are safe and should stop; chasing the 6-4 gains nothing. The game on this page tells you exactly which value you need to beat.

4. Roll again when you are already lowest

If your roll would be lowest on the table and you have rolls left, there is no reason to stop; a life is lost whether you end on 3-1 or 4-2. Use every roll you are allowed.

5. Watch the lives, not just the dice

When an opponent is down to one life, any round they lose ends their game. If you are the first player and can force a one-roll round, do it: fewer rolls mean more randomness, and randomness is on your side when you are not the one in danger.

6. Respect the doubled round

After a Mexico appears, two lives are at stake for whoever finishes lowest. A player with one or two lives should use every allowed roll to avoid the bottom, while a player with five lives can shrug and let the dice fall.

7. Do not reason from streaks

Rosa rolling three Mexicos in a row does not make a fourth less likely; it is 5.6% every time. Base every stop on the ranking table, the roll cap and the lives left, never on what “should” come next.

Common Mistakes

• Reading rolls numerically. 6-5 is not the best roll; it is eighth. Every double beats it, and Mexico beats everything.
• Re-rolling a strong first roll as the opener. A 6-3 on the first roll is a 67% favorite against any single opponent roll; rolling again for a double gives that away.
• Stopping early while lowest. If you are already at the bottom, keep rolling until the limit.
• Forgetting the roll cap. Later players may not roll more than the first player did, however bad their dice are.
• Confusing Mexico with Mia. In Mexico the dice are rolled in the open and there is no announcing, no believing and no calling. Anyone bluffing has wandered in from the Mia table.

Variants and House Rules

• Money game. Each round’s loser pays one unit into a pot (two after a Mexico), and the last player with money wins the pot. This is the version most English rule sets describe.
• Drinking game. The loser of each round drinks; a Mexico doubles the drink.
• Everyone tied loses. Instead of a sub-round, every player tied for lowest loses a life. Faster, and harsher on crowded tables.
• Mexico passes the dice. In some rules a player who rolls Mexico as the first player hands the dice to the next player, who then sets the roll cap for the rest of the round. Our game keeps the cap at the number of rolls the Mexico-roller actually took.
• Fixed rolls. Some casual versions ignore the cap and give everyone one roll, or everyone three. The cap is what makes the first seat interesting, so we keep it.
• Three lives. A shorter game; our six-life version usually lasts ten to fifteen rounds.
• Mexican (bluffing). The same ranking with a cup and announcements, which is the game we host as Mia.

If you enjoy the roll-or-keep tension, Pig and Sevens Out offer it as a race for points, and Left Center Right is the other three-seat elimination game on Dice.now where the dice decide everything.

Glossary

• Mexico: The roll 2-1, the highest value; it ends the roller’s turn and doubles the round’s penalty.
• First player / opener: The player who rolls first in a round and sets the roll cap.
• Roll cap: The number of rolls the first player took, which is the maximum for everyone else that round.
• Final roll: The roll a player stops on; the only one that counts.
• Median roll: 5-4, beaten by a fresh roll exactly half the time.
• Sub-round: A one-roll-each tie-break among players tied for lowest.
• Life: One of the six units each player starts with; the round’s loser gives one up.
• Doubled round: A round in which a Mexico was rolled, so the loser pays two lives.

Play Mexico Online on Dice.now

The game at the top of this page is three-handed Mexico against two computer opponents, Rosa and Diego, with six lives each. You open the first round. Press Roll to throw both dice and Keep to stop on the roll showing; the status bar counts your rolls left, and the hint under the dice tells you how often a fresh roll would beat what you are holding. If you open, you may roll up to three times and your count becomes the cap for Rosa and Diego, which the round card in the table panel spells out. If you roll later in the round, the message line tells you the roll you need to beat and how many rolls you are allowed. A Mexico ends your turn on the spot and marks the round as doubled.

The computer players roll in the open, one throw at a time. As opener they keep 5-4 or better on the first roll, 5-2 or better on the second, and whatever the third roll shows; as later players they stop as soon as they outrank the lowest roll already on the table and otherwise use every roll they are allowed. Ties for lowest are settled by a one-roll sub-round among the tied players. The lowest roll loses one life, or two if anyone rolled Mexico, and the loser opens the next round. The three seat cards show every player’s lives and the roll they kept, and the game log records each throw. The game ends when you lose your last life or when you are the last player standing; wins and games played are saved on your device only. Roll the dice.