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36 equally likely combinations, but totals differ in how many combinations make them: 7 has six routes (1+6 through 6+1), while 2 and 12 have one each. That pyramid is why 7 rules craps, why 6 and 8 are the workhorse numbers in Catan, and why the 2 you need never comes.
What The Dice Probability Calculator Works Out
- Probability: the number of dice combinations that make your total divided by all 36 equally likely ordered pairs. Seven has six routes (1+6 through 6+1) for 16.7%; 2 and 12 have one route each for 2.8%.
- Odds: the same figure as bookmaker-style odds against, so 7 is 5 to 1 against and 12 is 35 to 1 against. Doubles of any kind are a flat 1 in 6 whatever the total.
- The full picture: the whole pyramid for two dice. It explains why 7 rules craps, why the 6 and 8 tiles are prized in Catan, why Monopoly's seven-squares-ahead zone is dangerous, and why the exact 2 you need never seems to come.
- Number of dice and sides (advanced): any set from 1d4 to 10d20. More dice pull the distribution towards a bell curve, which is why 3d6 character stats cluster at 10 and 11 and an 18 (1 in 216) feels earned, while a single d20 is flat and swingy.
- Exactly, or higher, or lower (advanced): switch from hitting a total to clearing a threshold, which is what most tabletop skill checks and damage rolls actually ask. Enter a custom target for totals outside the two-dice range.
- Average total and most likely total (advanced): the mean is dice x (sides + 1) / 2, so 2d6 averages 7 and 3d6 averages 10.5; the standard deviation shows how spread the results are. The mode is the peak of the pyramid.
- At least once in your rolls (advanced): 1 minus (1 minus the single-roll chance) to the power of the number of rolls. A 7 on 2d6 is 16.7% per roll but 84% over ten rolls; dice have no memory, so this is about volume, not luck owed.
- Expected rolls to hit it (advanced): 1 divided by the probability, the average wait for the first success. For a 12 on 2d6 that is 36 rolls, though half of all tables see one sooner and a few wait far longer.
- Full table (advanced): every total with its combinations and exact, or-higher and or-lower percentages, the same table hobby tools draw for homebrew mechanics. Household dice carry small manufacturing bias at the margins; casino dice are machined and retired regularly.