Horse Race Dice Game: Rules and Odds

The Horse Race Dice Game is a loud, fun way to teach chance. Eleven horses, numbered 2 to 12, line up at the start. Each roll of two dice moves the horse with that number one space forward, and the first horse to reach the finish line wins. Everyone picks a horse before the race, and by the end the class has discovered for itself that some numbers come up far more often than others.

What You Need

• Two six-sided dice, or our Dice Roller set to two dice on the board.
• A race track: 11 rows (or columns) labelled 2 to 12, each with the same number of spaces. Five to ten spaces works well.
• One counter per horse, or a pencil to shade in each space.
• Any number of players. Small groups of 2 to 6 work well, or the whole class can watch one track.

Picking Horses Fairly

Who gets which horse matters a lot in this game, so pick fairly. Put everyone’s name into our Random Name Picker and spin it. The first name chosen picks a horse, then the next, until every horse is taken. With fewer than 11 players, some horses are left without an owner but still race. With a big class, several children can share the same horse.

A good classroom trick is to let the first pickers choose freely and say nothing about the odds. Many children pick their lucky number or their age, and the surprise when 7 runs away from the field is the whole point of the lesson.

How to Play

There are many versions of this game. These are the most common rules, so agree on any changes before you start.

1. Line up the horses 2 to 12 at the start of the track.
2. Roll two dice and add them up. Take turns rolling, or let the teacher roll for everyone.
3. Move that horse one space forward. A sum of 9 moves horse 9.
4. Keep rolling until one horse crosses the finish line.
5. The owner of the winning horse wins. Record the winner and race again.

Which Horse Wins Most Often?

Two dice give 36 equally likely results, but the sums are not equally likely. Six results make 7, and only one result makes 2 or 12. We simulated 100,000 races on a 5-space track and 100,000 on a 10-space track. In the table, “Horse” is the sum, “Per roll” is the exact chance that the horse moves on one roll (6/36 means 6 of the 36 results, about 17%), and the two “Wins” columns are simulated estimates of how often each horse won on each track length.

Horse 7 is the clear favourite, and a longer track makes it even stronger, because luck has more time to even out. Horses 2 and 12 almost never win. A 5-space race lasted about 19 rolls in our simulation and a 10-space race about 48 rolls. For more on why sums of two dice behave this way, see our dice probability guide.

Can You Make the Race Fair?

A natural next question from the class is how to give every horse a fair chance. One idea is to give each horse as many spaces as the number of ways to roll it: 1 space for horses 2 and 12, 6 spaces for horse 7. We simulated that track too. In the table, “Spaces to finish” is the length of that horse’s track and “Wins” is how often it won, as a simulated estimate.

The fix goes too far: now 2 and 12 are the favourites, because a single lucky roll can win the race. Finding a track that is truly fair is a great open puzzle for older students. Let them test their own track lengths with the dice roller and keep a tally.

Teaching Ideas

• Predict first: ask everyone to guess which horse will win and write the guesses down. Compare them with the results after five races.
• Tally the winners: run 10 or 20 races and make a bar chart of winning horses. The hill shape around 7 appears quickly.
• List the ways: have pairs list every way to roll each sum with two dice. When they find six ways to make 7, the winners make sense.
• Talk about fairness: is it fair to pick horses by name picker if some horses are much better? What would make it fair?
• Horse 1: some teachers add a horse 1 to the start line. It can never move with two dice, which starts a good discussion about impossible events.

For a quieter dice game that practises the same sums, try Roll and Cover. For more short lesson games, see our classroom games with a random picker.

Variations

• Betting with counters: give each player a few counters to place on horses before the race. Winners on rare horses get more counters back. Use paper counters only, never real money.
• One die race: six horses, 1 to 6, all equally likely. Compare it with the two-dice race to show the difference.
• Scratched horses: before the race, roll four times and remove the horses that come up. Rolls of a removed horse do nothing.
• Difference race: move the horse for the difference between the dice, horses 0 to 5. Horse 1 is the favourite.
• Teams: split the class into teams that each own two or three horses and see which team wins most over ten races.

Where Does the Game Come From?

Dice horse racing games are old and come in many forms, from pub and party games to commercial board games, and rules vary a lot. The classroom version on a 2 to 12 track is shared widely by maths teachers, but we found no reliable record of who first made it.

For a game where children choose their own numbers and test which ones come up most, try Dice Bingo.

FAQ

How do you play the horse race dice game?

Line up horses numbered 2 to 12. Roll two dice, add them, and move the horse with that number one space. The first horse to reach the finish line wins.

Which horse wins the dice horse race?

Horse 7 wins most often because six of the 36 results add up to 7. In our simulation it won about 32% of 5-space races and about 42% of 10-space races.

Why does horse 2 almost never win?

Only double 1 moves horse 2, a 1 in 36 chance per roll, so it rarely gets far before horse 7 or its neighbours finish.

How do you make the horse race fair?

Give rare horses shorter tracks. Making each track as long as the number of ways to roll it overcorrects, so 2 and 12 become favourites. Testing other lengths is a good class project.

What does the horse race game teach?

It shows that the sums of two dice are not equally likely, and it practises addition, tallying, bar charts and predicting with chance.

Can you play the horse race game with an online dice roller?

Yes. Set our free Dice Roller to two dice, show it on the board, and pick horses with our Random Name Picker.