Odds and Evens: Rules, Odds and the Roman Finger Game
Odds and evens is one of the oldest ways to settle a choice between two people. It needs no coin and no phone, only a hand each. It is quick enough for the playground and still used to decide who kicks off or who goes first. Here are the rules, the small bit of maths most people never notice, and a history that goes back to ancient Rome.
How to Play Odds and Evens
- One player calls "odds", the other "evens".
- Both say "one, two, three, shoot" (or any count you agree on).
- On "shoot", each player shows some fingers on one hand at the same time.
- Add the two numbers. If the total is even, "evens" wins; if it is odd, "odds" wins.
Agree on two things before you start: whether a closed fist (zero) is allowed, and whether it is one round or best of three. Those small rules matter more than you would think.
Is Odds and Evens Fair? The Hidden Maths
If both players show 0 to 5 fingers completely at random, the game is exactly 50/50: 18 of the 36 possible pairs give an even total.
If a fist is not allowed and players show 1 to 5 fingers, things change slightly. Three of those numbers are odd (1, 3, 5) and two are even (2, 4). An even total comes from odd + odd or even + even, which is 9 + 4 = 13 of the 25 pairs. So with random hands, "evens" wins 52% of the time and "odds" only 48%.
In real life people are not random. Each player can choose odd or even with their own hand, and neither knows what the other will do. Game theorists use the same idea, under the name "matching pennies", as the classic example of a game where the best plan is to be unpredictable. If you want a perfectly even result, allow the fist, or use a Coin Flip instead.
One Hand or Two?
- One hand each (0 to 5 fingers) is the usual version, and it is 50/50 with random choices.
- Both hands (0 to 10 fingers) feels more random, but it does not make the game fairer. What counts is only whether each player's total is odd or even, and each player still chooses that.
- Several players: everyone shows fingers and the total decides between two teams. For picking one person out of many, a Random Name Picker is quicker.
Morra: The Ancient Version
Odds and evens has a famous older cousin called morra. Two players show fingers at the same moment and each shouts a guess of the total. Whoever guesses right scores a point. It is fast, loud and still played in parts of Italy and around the Mediterranean.
The Romans played it too and called it micatio, from micare digitis, "to flash the fingers". Because the fingers are shown and counted in an instant, cheating is easy if nobody is watching. That is the point of a Roman saying recorded by Cicero: an honest man is someone "you could play morra with in the dark".
Odds and Evens Around the World
In Brazil, par ou ímpar ("even or odd") is the standard way for children to decide who picks first for football or who starts a game. Many other countries have a playground version, often next to Rock Paper Scissors as the other quick hand game. A coin-based form, where each player hides a coin heads or tails up, is described in our coin flip games.
Odds and Evens vs Rock Paper Scissors vs a Coin Flip
- Odds and evens: two players, no props, about 50/50 (exactly 50/50 if a fist counts as zero).
- Rock Paper Scissors: can end in a draw, so it may take several rounds, but it feels like more of a contest. See the RPS strategy research.
- Coin Flip: exactly 50/50 and nobody can influence it, best when the stakes are higher.
Whichever you use, agree on it before you play. More ideas are in how to decide who goes first and how to break a tie.
FAQ
How do you play odds and evens?
One player calls odds and the other evens. On a count, both show some fingers on one hand. If the total is even, evens wins; if it is odd, odds wins.
Is odds and evens 50/50?
With random hands, yes, if a closed fist (zero) is allowed. If players must show 1 to 5 fingers, evens wins 13 of 25 combinations, about 52%.
Is it better to pick odds or evens?
Against a random player, evens is slightly better when zero is not allowed. Against a real person, it depends on what they tend to show, so being unpredictable matters more.
What is morra?
Morra is an ancient finger game. Both players show fingers at the same time and shout a guess of the total; the right guess scores. The Romans called it micatio.
What is odds and evens called in Brazil?
It is called par ou ímpar, and children use it to decide who picks first or starts a game.