Dice total probabilities
View the probabilities of dice totals in a table. The theoretical probabilities update immediately when you change the number of sides and dice. You can also compare them with actual roll results. Copy the table or save it as CSV.
What you can do
See which totals are most likely
Lists the probability of each total and how often it occurs on average. Check the most likely totals using colors and numbers.
Compare theory and trials
Run 5 trials per second and compare the observed proportions side by side. Trial counts and results are saved even when you leave the page, and you can resume from the paused state.
How to use
Choose the number of sides and dice
Starts with 2 dice with 6 sides each. Changing the settings updates the probability table immediately.
Read the theoretical probabilities
Check the probability and frequency of each total. Copy the table or save it as CSV.
Try and compare if needed
Start trials and pause whenever you like. Compare the trial count and observed proportions with the theoretical values.
When to use it
Check totals for board games
Check how likely 7 and 12 are with 2 dice with 6 sides each, and compare the likelihood of each total.
Learn probability through trials
Compare trials with theoretical values under the same settings to see how uneven results occur with small numbers of trials.
Reading probability tables and trials
Totals of 2 dice are not equally likely
With 2d6, there are 6 combinations totaling 7, and 1 each totaling 2 and 12. The probability of 7 is 6/36, while 2 and 12 each have a probability of 1/36.
Once in a certain number is an average frequency
About once in 6 rolls does not mean it will definitely occur within 6 rolls. In independent draws, past rolls do not change the probability of the next one.
Trial proportions differ from theoretical values
With few trials, uneven results are noticeable. Even with more trials, every proportion will not necessarily match the theoretical value exactly.
Frequently asked questions
Do I need to press a calculate button myself?
No. Choosing the number of sides and dice displays the theoretical probabilities for every total.
Can very small probabilities be displayed?
Probabilities below 0.01% are displayed as “Below 0.01%”, distinguishing them from a 0% probability.
Do trials continue when I leave the page?
Trials up to the point when you leave are saved and restored in a paused state when you return. No new trials are added automatically.
What happens to previous trials if I change the settings?
Stop any running trials before changing the settings. Trials under the previous settings are saved, and you can resume from where you left off when you return to the same number of sides and dice.
Input and results
- Theoretical calculation
- 4, 6, 8, 10, 12, 20, or 100 sides / 1–20 dice. Calculates every total.
- Trials
- 5 times per second. Counts, recent rolls, and frequencies are saved on your device for each set of settings.
- Save table
- Copy the theoretical table or save it as CSV. Includes all rows, even those hidden on screen.