Two dice – which total comes up most often?
Choose the total you think will come up most often, and roll. The chart and the 6×6 table show why some totals come up more often than others.
First choose your prediction in the box above – then the roll buttons will switch on.
| Total | How many times | Your rolls (%) | Chance from the table |
|---|
Table of all outcomes
How do you play?
You roll two ordinary dice (kostki) and add the dots. First choose your prediction – the total you think will come up most often. Then roll: once, 10 times or 100 times at a time. The chart and the table show how many times each total came up.
Why does 7 come up most often?
Each die has 6 faces, so there are 6 · 6 = 36 pairs of outcomes – the squares in the table. Six squares give a total of 7: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. Only 1 square gives a total of 2: 1 and 1. So the probability of 7 is 6/36 = 1/6, and of 2 it is 1/36.
What is the average total?
The average total of many rolls gets close to 7. With 10 rolls you might get, for example, 6,2 or 8,1, but with hundreds of rolls the result gets closer and closer to 7. To find the average, add up all the totals and divide by the number of rolls.
What is the most common mistake?
Thinking that each total from 2 to 12 has the same chance – one in eleven. There are 11 totals, but they are not equally likely: total 7 has 6 squares and total 12 only 1. We count squares – pairs of outcomes – not the totals themselves.
Is this in the eighth-grade exam?
The Polish curriculum lists simple random experiments: tossing a coin, rolling one die or drawing a ball. In 2025, question 10 on probability was answered correctly by 56% of pupils, and in 2024 question 8 (drawing a balloon from a box) by 61%. The game practises the same reasoning: probability is the number of favourable outcomes divided by the number of all outcomes. Rolling two dice is not usually in the exam – counting the 36 pairs needs the multiplication rule, which is not in the requirements (point XII.1). It is an extra exercise.
Curriculum: point XII.2 for grades 7–8 (Polish core curriculum, Dz.U. 2024 poz. 996). Sources: CKE report 2025; CKE report 2024 (in Polish).
Questions about the game
What is the probability of a total of 7 with two dice?
6/36, which is 1/6. Six of the 36 possible pairs give 7.
Which total comes up least often?
Totals 2 and 12. Each comes from only one pair out of 36, so the probability of each is 1/36.
Is the game free?
Yes. You play in the browser, with no sign-up and no e-mail.
Mini glossary: English – Polish
- die (plural: dice) – kostka do gry
- roll – rzut
- total of the dots – suma oczek
- probability – prawdopodobieństwo
- random experiment – doświadczenie losowe
- average – średnia
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