Dice Cross-Country Game: Rules, Team Scoring and Odds
Dice cross-country is a muddy, hilly race for two to six runners, and it can also be played as a team race. Every runner starts on 30:00, runs two laps with a flat section, a hill and a stretch of mud on each lap, and finishes with a sprint. On every hill you choose: climb steadily, or push hard and risk running out of breath. The fastest time wins, and in the team race the lowest team score wins. A race takes about ten minutes.
What you need
- Two six-sided dice, or a dice roller.
- A score sheet with a row for each runner and boxes for two laps of flat, hill and mud, plus the final sprint.
- A pencil for each player.
- A random name picker to set the order of turns and to split players into teams.
Who goes first
Put every runner’s name into the random name picker and draw them one by one. That is the order of turns for the whole race. For the team race, draw the names into two teams of three as well. The order does not change anyone’s chance of winning.
How to play
- Every runner starts with a time of 30:00.
- Flat: roll two dice and change your time with the flat chart.
- Hill: say “steady” or “push” before you roll. A steady climb always adds 10 seconds. A push means you roll two dice and check the hill chart.
- Mud: roll one die and check the mud chart.
- Run two laps of flat, hill and mud, with every runner taking each section in turn.
- Final sprint: roll two dice. A roll of 2, 3 or 4 adds 10 seconds, 5 to 9 changes nothing, and 10, 11 or 12 takes off 10 seconds.
- The fastest time wins. If two runners have the same time, the higher sprint roll wins, and if that is also a tie, they each roll one die.
This is a simple home version, not an official game. Real cross-country races are run on grass, mud and hills instead of a track, and the distance changes from race to race. In team scoring, each runner scores their finishing place, a team adds up the places of its best finishers, and the lowest total wins. How many runners count depends on the race.
The flat chart
In the tables below, the first column is the roll or choice, the middle column is what happens to your time, and “Chance” is the exact probability: out of the 36 ways two dice can land, or out of 6 ways for one die.
| Roll | Flat section | Chance |
|---|---|---|
| 2, 3 or 4 | Heavy legs: add 20 s | 6 in 36 |
| 5 to 9 | Steady running: no change | 24 in 36 |
| 10, 11 or 12 | Fast stretch: take off 20 s | 6 in 36 |
The hill chart
| Hill | Result | Chance |
|---|---|---|
| Steady climb (no roll) | Add 10 s | always |
| Push, roll 2 to 5 | Out of breath: add 40 s | 10 in 36 |
| Push, roll 6 to 12 | Strong climb: take off 10 s | 26 in 36 |
A push goes wrong 10 times in 36, because 2 to 5 are the less likely totals with two dice, as our guide to dice probability explains. On average a push adds about 3.9 seconds, against 10 seconds for a steady climb, so pushing is faster on average but much less predictable.
The mud chart
| Mud die | Result | Chance |
|---|---|---|
| 1 | Shoe stuck: add 30 s | 1 in 6 |
| 2 or 3 | Slipping: add 10 s | 2 in 6 |
| 4, 5 or 6 | Good footing: no change | 3 in 6 |
A shoe gets stuck 1 time in 6 on each mud section, so over the two laps, a runner loses time to a stuck shoe at least once in 11 of 36 races, about 31%.
How fast will you run?
This table shows the time of one runner who always pushes or always climbs steadily. Each column gives the exact chance of running that time or faster, rounded.
| Race time | Always push | Always steady |
|---|---|---|
| 29:20 or faster | about 4% | never |
| 29:40 or faster | about 17% | about 0.7% |
| 30:00 or faster | about 35% | about 8% |
| 30:20 or faster | about 53% | about 32% |
| 30:40 or faster | about 71% | about 65% |
| 31:00 or faster | about 85% | about 89% |
| 31:20 or faster | about 92% | about 98% |
A runner who always pushes finishes in about 30:24 on average, and a runner who always climbs steadily in about 30:37. In a race between one of each, the pusher wins about 58% of the time and they tie about 8% of the time. The steady runner almost never has a disaster: their slowest possible time is 32:10, against 33:10 for a pusher.
What time wins?
With six runners who all push, the winner is the fastest of the six. In this table, “Chance” is the exact probability of each winning time, rounded.
| Winning time | Chance |
|---|---|
| 29:10 or faster | about 7% |
| 29:20 | about 15% |
| 29:30 | about 20% |
| 29:40 | about 24% |
| 29:50 | about 18% |
| 30:00 or slower | about 16% |
Most six-runner races are won between 29:20 and 29:50. Times move in steps of 10 seconds, so two or more runners share the fastest time in about 19% of races, and the sprint roll decides the winner.
The team race
With six runners in two teams of three, all three runners score. The winner of the race scores 1, second place scores 2, and so on. Add up each team’s places: the lowest total wins. The six places add up to 21, so a team with 10 or less always wins and a tie is impossible.
In this table, “Ways out of 20” counts how many of the 20 possible sets of three places give each team score. If both teams play the same way, every set of places is equally likely, so a team takes all of the first three places 1 time in 20.
| Team score | Ways out of 20 | Result |
|---|---|---|
| 6 (places 1, 2, 3) | 1 | Win |
| 7 | 1 | Win |
| 8 | 2 | Win |
| 9 | 3 | Win |
| 10 | 3 | Win |
| 11 | 3 | Lose |
| 12 | 3 | Lose |
| 13 | 2 | Lose |
| 14 | 1 | Lose |
| 15 (places 4, 5, 6) | 1 | Lose |
Tips
- If you are well ahead after the first lap, a steady climb on the second hill keeps you safe.
- In the team race, talk with your team about who should push and who should play safe.
- Draw the course on paper with a hill and a mud patch, and move a counter for each runner.
- Keep a list of the best times as a club record board.
Classroom ideas
- Time: practise adding and taking away seconds from 30:00, such as 30:00 + 40 s − 10 s.
- Probability: why does a push add about 3.9 seconds on average? Work out (10 × 40 − 26 × 10) ÷ 36.
- Combinations: list all 20 ways a team of three can take three of six places, and check the team score table.
- Risk: half the class always pushes and half always climbs steadily. Compare the results after five races.
Variations
- Longer race: run three laps instead of two and start on 45:00.
- Bigger teams: with teams of five, only the best four places count, as in many real team races.
- Wet day: a mud roll of 1 or 2 means a stuck shoe.
- Relay: each runner in a team runs one lap, and the team time is the sum.
For more running races with dice, try the dice steeplechase, the dice marathon or the dice 100m sprint.
FAQ
How do you play cross-country with dice?
Every runner starts on 30:00. Run two laps of a flat section, a hill and a mud patch, rolling for each, then roll for the final sprint. On each hill, choose a steady climb or a push. The fastest time wins.
How many players can play?
Two to six runners. With six players, you can also run it as a team race with two teams of three.
Is it better to push or climb steadily?
Pushing is faster on average, about 3.9 seconds lost per hill against 10, but it goes wrong 10 times in 36.
What is the fastest possible time?
28:50, with two fast stretches, two strong climbs, good footing in the mud and a fast sprint.
How does team scoring work?
Each runner scores their finishing place. Add up the places of each team, and the lowest total wins. With two teams of three, a team with 10 or less always wins.
What time usually wins?
With six runners who all push, usually between 29:20 and 29:50.