Dice Discus Game: Rules, Fouls and Odds

Dice discus is a throwing contest for two to six athletes. Every throw has two parts, just like the real thing: a spin across the circle and the release of the disc. Two dice set the spin, one die sets the release, and a bad roll on either one is a foul. Everyone gets three throws, and the best one counts. A contest takes about ten minutes.

What you need

• Three six-sided dice, or a dice roller. Two dice are the spin dice and one die is the release die, so use a different colour if you can.
• A score sheet with a row for each athlete and three boxes for their throws.
• A pencil.
• A random name picker to set the throwing order.

Who throws first

Put every athlete’s name into the random name picker and draw them one by one. That is the throwing order for all three rounds. The order does not change anyone’s chance of winning, but the last thrower knows the mark to beat, which makes the final round exciting.

How to play

1. On your turn, roll the two spin dice and the release die together.
2. If the spin dice show 2, you slipped in the circle. If the release die shows 1, the disc landed outside the sector. Either way the throw is a foul and scores no distance.
3. Otherwise, your distance in metres is 30 + 2 × the spin total + 2 × the release die. For example, a spin of 8 and a release of 4 gives 30 + 16 + 8 = 54 m.
4. Every athlete throws once per round, for three rounds.
5. Your best throw counts. The longest best throw wins. If two athletes tie, the one with the better second-best throw wins, and if that is also a tie, they roll the spin dice once more.

This is a simple home version, not an official game. In real discus, the athlete spins about one and a half turns inside a 2.5 m circle and must stay in it until the disc lands, and the disc must land inside a marked sector. The men throw a 2 kg disc and the women a 1 kg disc. The women’s world record of 76.80 m, set by Gabriele Reinsch in 1988, is longer than the men’s record, which at the time of writing is a little over 74 m. The longest possible throw in this game is 66 m.

The spin chart

In the tables below, the first column is the roll, the middle column is what it adds to the distance, and “Chance” is the exact probability. For the spin, there are 36 ways two dice can land; for the release, there are 6 ways one die can land.

The release chart

A good spin is the most common result, because 6, 7 and 8 are the most likely totals with two dice, as our guide to dice probability explains. The release is where most fouls happen: 1 time in 6, against 1 time in 36 for a slip.

How far will one throw go?

Spin and release together make 216 equally likely results. This table groups the distances. “Chance” is the exact probability out of 216, with a rounded percentage.

About 1 throw in 5 is a foul. A throw that counts goes about 52 m on average, and only 1 throw in 216 reaches the full 66 m.

How far is your best of three?

This table shows the chance that an athlete’s best throw reaches each distance, rounded. The average best throw is about 55.5 m.

Three fouls in a row are rare: it happens about 7 times in 1000 contests, and that athlete has no mark at all.

What wins?

With six athletes, the winner is the one with the longest best throw. In this table, “Chance” is the exact probability of each winning distance, rounded.

Most six-athlete contests are won with 60 m or more. Distances move in steps of 2 m, so two athletes share the longest throw in about 26% of contests, and the second-best throw often decides the winner.

Tips

• Use a different colour for the release die, so nobody mixes it up with the spin dice.
• Write down every throw, not just the best one. You need the second-best throw for ties.
• Draw a sector on paper with lines every 10 m and mark each throw with a dot.
• After a foul, the next thrower can cheer, but only after the score is written down.

Classroom ideas

• Mental maths: work out 30 + 2 × spin + 2 × release for each throw.
• Probability: why is a foul 41 in 216? A slip happens in 6 of the 216 results, and a release of 1 without a slip in 35 more, so 6 + 35 = 41.
• Fair contest: talk about why the best of three is fairer than one throw.
• Data: make a bar chart of every distance thrown by the class. Which distance came up most?

Variations

• Six rounds: after three rounds, the best three athletes get three more throws, as in a real final.
• Wind: flip a coin before each round. Heads means a head wind, which helps the discus fly: add 2 m to every fair throw that round.
• Safe spin: before you roll, you may choose a safe spin: it can never slip, but the spin total counts only once instead of twice.
• Hammer throw: use the same rules, but call it the hammer, and a release of 1 hits the cage.

For more throwing events with dice, try the dice shot put or the dice javelin, or play all ten events in a dice decathlon.

Want to choose how many turns to spin? Try our dice hammer throw game.

FAQ

How do you play discus with dice?

Roll two spin dice and one release die. A spin of 2 or a release of 1 is a foul. Otherwise the throw goes 30 + 2 × spin + 2 × release metres. Everyone gets three throws, and the best one counts.

How many players can play?

Two to six athletes. With more players, the contest just takes a little longer.

How often is a throw a foul?

41 times in 216, or about 19% of throws.

What is the longest possible throw?

66 m, with a spin of 12 and a release of 6. It happens 1 time in 216.

What usually wins?

With six athletes, usually a best throw of 60 m or more.

Why is the women’s discus record longer than the men’s?

The women throw a 1 kg disc and the men a 2 kg disc. The women’s record of 76.80 m by Gabriele Reinsch has stood since 1988.