Pip parity
Classic casino dice always have opposite faces summing to 7 (1 opposite 6, 2 opposite 5, 3 opposite 4) so pip counts stay balanced when painted.
Rolling a large pool of six-sided dice (D6) comes up in board games, tabletop wargames, and RPGs. If you’re rolling 10, 20, or even 100 dice, it’s useful to know the expected totals and how “swingy” the results can be. This guide explains the essentials in plain English so you can plan tactics, sanity-check outcomes, and talk probabilities with your gaming group.
Each D6 has an average (expected value) of 3.5. For n dice, the expected total is 3.5 × n. So 20 dice average 70, 50 dice average 175, and 100 dice average 350. The variability around that average is measured by variance and standard deviation. A single D6 has variance 35/12 ≈ 2.9167, so the sum of n dice has variance n × 35/12 and standard deviation ≈ 1.7078 × √n. With many dice, results cluster tightly near the average (the distribution looks bell-shaped by the Central Limit Theorem).
Example: with 20 D6, the mean is 70 and the standard deviation is about 7.63. Roughly 95% of rolls will land within two standard deviations (about 55–85). With 100 D6, the mean is 350 and the standard deviation is about 17.08, so totals are usually in the 316–384 range.
The minimum total for n D6 is n (all ones). The maximum is 6n (all sixes). Hitting either extreme becomes astronomically rare as n grows. Practically, the bigger the pool, the more consistent your totals feel—great for balancing scenarios or testing strategies.
In Warhammer 40,000 (and similar D6-based wargames), you often roll large pools for hit, wound, and save checks. If your unit needs “X+” on a D6, the success probability per die is (7 − X) / 6; for example, 4+ is 50%, 3+ is ~66.7%, and 2+ is ~83.3%. With rerolls, the math tweaks slightly:
p + (1/6)·p = (7/6)·p (capped below 1 since p ≤ 5/6).p + (1 − p)·p = p·(2 − p).Multiply per-die success by the number of dice to estimate expected successes. For example, 30 shots hitting on 3+ (p ≈ 0.667) yield ~20 hits on average; with “reroll 1s,” that bumps to about 22.2 hits. Your total will vary, but with large pools, it will be close to the expectation most of the time.
Keywords: roll many D6, multiple dice probability, Warhammer 40k dice math, D6 pool odds, expected value of dice, board game dice calculator, tabletop math (UK/EU).
Classic casino dice always have opposite faces summing to 7 (1 opposite 6, 2 opposite 5, 3 opposite 4) so pip counts stay balanced when painted.
The symbols ⚀–⚅ are real Unicode code points (U+2680…U+2685). That’s why this tool can show giant dice without any images or fonts.
Physical dice can drift in fairness if pips are drilled too deep. Casinos weigh finished dice to the milligram and replace them every 8 hours to stay true.
Roll 30 D6 and the total hovers near 105 most of the time—the Central Limit Theorem makes big dice pools behave like neat bell curves.
Pressing R here is faster than real dice: you can “roll” 100 dice ~10 times per second and log thousands of outcomes for testing or game prep.
This tool rolls standard six-sided dice (D6).
Yes. You can roll between 1 and 100 dice in a single roll and see the total.
Yes. All rolls are computed locally in your browser; no data leaves your device.
Each die result is drawn from a uniform distribution over {1,2,3,4,5,6} using JavaScript’s Math.random().