Dice Relay Race Game: Rules, Baton Passes and Odds

Dice relay is a 4 × 100 m race for two to four teams of up to four players. Each team runs four legs, and between the legs comes the moment everyone fears: the baton pass. A perfect pass saves time, but a dropped baton can throw the whole race away. Every team starts on 40.0 seconds, the dice add or take off time, and the fastest team wins. A race takes about ten minutes.

What you need

• Two six-sided dice, or a dice roller set to two dice.
• A score sheet with a row for each team and seven boxes: four legs and three baton passes.
• A pencil, a short stick or a rolled-up piece of paper as a baton to hand from player to player, just for fun.
• A random name picker to draw the lanes.

Drawing the lanes

Put every team’s name into the random name picker and draw them one by one: the first team gets lane 1, the next lane 2, and so on. Lanes do not change anyone’s chance in this game, but they set the order of turns. Inside each team, the players decide who runs the first, second, third and last leg.

How to play

1. Every team starts with a time of 40.0 seconds.
2. Legs: the runner of the first leg rolls two dice and changes the team time with the leg chart.
3. Baton pass: the next runner rolls two dice for the pass with the changeover chart, then rolls again for their own leg.
4. Keep going until all four legs and three passes are done. In each round, every team runs one leg, in lane order.
5. The fastest team time wins. If two teams have the same time, it is a photo finish: each anchor rolls two dice, and the higher total wins.

This is a simple home version, not an official game. In a real 4 × 100 m relay, the baton has to be passed inside a marked changeover zone, and a team that drops the baton or passes it outside the zone usually loses any chance of a medal. Jamaica set the men’s world record of 36.84 seconds at the 2012 Olympics in London. The best possible time in this game is 37.8 seconds.

The leg chart

In the tables below, “Roll” is the total of the two dice, the middle column is what happens to the team time, and “Chance” is the exact probability out of the 36 ways two dice can land.

A steady leg is the most common result, because 6, 7 and 8 are the most likely totals, as our guide to dice probability explains. Slow and fast legs are equally likely, so the four legs almost cancel out on average.

The changeover chart

A dropped baton happens 1 time in 12 at each pass. Over three passes, a team drops the baton at least once in about 23% of races, so even the fastest runners can lose. A perfect pass is twice as likely as a drop, but it saves much less time.

How fast will your team run?

This table shows the time of one team. “Chance” is the exact probability of running that time or faster, rounded.

The average team time is about 40.3 seconds, a bit slower than the 40.0 start because dropped batons cost so much. The most common time is 39.8 seconds, for example a race where the legs even out and one pass is perfect.

What time wins?

With four teams, the winner is the fastest of the four. In this table, “Chance” is the exact probability of each winning time, rounded.

Most races with four teams are won between 39.4 and 39.8 seconds. Because most changes come in steps of 0.2 seconds, two teams share the fastest time in about 19% of races, so the photo finish roll comes up often.

Tips

• Pass a real baton, or a pencil, from player to player at each changeover. It makes the game feel like a race.
• Let the whole team cheer during the pass roll. It is the most exciting moment.
• With fewer players, one player can run two legs.
• Keep each team’s best time as a record to beat next time.

Classroom ideas

• Decimals: add up the tenths of a second for each leg and pass, and check the team times.
• Probability: why does a team drop the baton at least once in about 23% of races? Work out 1 minus the chance of three clean passes.
• Teamwork: after the game, talk about why passing matters as much as speed in a real relay.
• Data: run five races and record every team time. Which team was the most consistent?

Variations

• 4 × 400 m: start at 3 minutes and double every time change in the leg chart.
• Strict rule: a dropped baton ends the race for that team, as it often does in real life.
• Mixed relay: teams of two players each run two legs.
• Swimming relay: use the same rules, but call the legs backstroke, breaststroke, butterfly and freestyle.

For more relay games to play outside, see our relay race ideas. For more track races with dice, try the dice hurdles race or a dice marathon.

Want one short race for each runner? Try our dice 100m sprint game.

FAQ

How do you play a relay race with dice?

Each team starts on 40.0 seconds. Roll two dice for each of four legs and for each of the three baton passes, and change the time with the charts. The fastest team time wins.

How many teams can play?

Two to four teams, with up to four players each. One player can also run every leg for a team.

How often is the baton dropped?

1 time in 12 at each pass, so a team drops it at least once in about 23% of races.

What is the fastest possible time?

37.8 seconds, with four flying legs and three perfect passes.

What time usually wins?

With four teams, usually between 39.4 and 39.8 seconds.

What is the real 4 × 100 m relay world record?

For men, 36.84 seconds by Jamaica at the 2012 Olympics in London.