Dice Tug of War: A No-Tech Maths Version
Dice tug of war is a no-screen version of maths tug of war for two players of any age. You need paper, a pencil, two dice and one counter, and you can start in under a minute.
Draw a line of 11 boxes and put the counter in the middle box. Each player owns one end.
Each player rolls both dice and adds them, saying the sum aloud.
The higher total moves the counter one box toward that player. A tie moves nothing.
Reach your end box to win.
A round, played through
Sam rolls 4 and 5 and says "4 and 5 is 9". Priya rolls 6 and 6 and says "double 6 is 12". Priya's total is higher, so the counter moves one box toward her end. Next round Sam rolls 3 and 2 for 5, and Priya rolls 1 and 4 for 5. It is a tie, so the counter stays put and they roll again.
Variations for different skills
Skill | Do this with the dice | Who wins the round |
|---|---|---|
Counting on | Use one die and count on from 10 | Higher total |
Multiplication | Multiply the two dice | Higher product |
Subtraction | Take the smaller from the larger | Larger difference |
Negative numbers | First die minus second die | Higher answer, including below zero |
How long does a game take?
Two players rolling two dice each will tie about 11% of the time (146 ties in 1,296 possible rolls). Each result that is not a tie moves the counter at random one way or the other, and on average that takes 25 moves to travel the 5 boxes from the middle to an end. So an 11-box game lasts about 28 rounds on average, which can run past 10 minutes. A 7-box track needs only 9 moves on average, or about 10 rounds, so use that when time is short.
Why is the dice version worth playing?
There is no clock, so players have time to explain their thinking. Ask each player to say how they worked out the answer before moving the counter. Who wins depends entirely on the dice, so a beginner can beat a stronger player fairly. That is the opposite of the online game, where speed decides almost everything. It suits anyone who finds timed games stressful. For more no-screen games, see our printable versions.
Which totals are most likely to win?
This is a useful maths lesson in its own right. With two dice, some totals are much more common than others.
| Your total | Ways to roll it (of 36) | Chance the other player rolls lower |
|---|---|---|
| 2 or 12 | 1 | 0% for a 2, 97% for a 12 |
| 4 or 10 | 3 | 8% for a 4, 83% for a 10 |
| 7 | 6 | 42% |
| 9 | 4 | 72% |
Ask players to predict which total comes up most often, then keep a tally for ten rounds and compare. A roll of 7 ties 17% of the time, which is why games have some rounds where nothing moves.
Ways to add skill
- Let players choose whether to add or multiply after seeing the dice, and explain their choice.
- Roll three dice and make the largest answer you can using any two.
- Use a target: the closest total to 20 wins, using addition and multiplication.
Those versions reward thinking as well as luck, which makes them better for confident players.
Frequently asked questions
How many dice do you need for dice tug of war?
Two dice are enough, with one die as an easier option for beginners.
How long is a shorter game?
Use seven boxes instead of 11.
Is there a time limit?
No. The dice version has no clock.