Dice Roll Probability Simulator
Calculate exact dice probabilities, keep the highest dice, compare advantage or disadvantage, simulate 100,000 rolls and roll once.
About this dice roll probability simulator
Calculate exact dice probabilities, keep the highest dice, compare advantage or disadvantage, simulate 100,000 rolls and roll once Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
Evaluates statistical metrics, linear regression models, and probability distributions in compliance with NIST engineering statistics standards. Computes sample variance ($s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2$) using Bessel's correction for unbiased estimation, alongside population variance. Normal distribution tools compute Z-scores ($z = (x - \mu)/\sigma$) and cumulative distribution functions (CDF) via the Gauss error function (erf). Evaluates Binomial ($P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$) and Poisson ($P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$) discrete distributions.
Worked numerical calculation
Scenario: Calculate probabilities
Sample input:
Processing: Fractions are reduced and exact for fair independent dice. Percentages and plot coordinates are rounded binary64 approximations. Every action replaces the previous result; editing inputs clears stale results and errors.
Illustrative output:
Domain range & precision boundaries
Use NdS or NdSkhK: N dice with S sides, keeping the highest K. Example: 4d6kh3. N=1–20 per pool, S=2–100, K=1–N; omitting kh keeps all dice. Up to 64 UTF-16 units; ASCII digits, d/kh case insensitive, whitespace between tokens. No modifiers, mixed dice, exploding dice or rerolls. Advantage rolls two independent pools of the whole expression and takes the higher total; disadvantage takes the lower. Thus 1d20 with advantage is two d20s, keeping one. For ties the first pool is selected. Each pool has at most 20 dice; these modes use up to 40 dice across both pools. Local dice-count and face limits bound the workload; time depends on the device. One-click rolls display original faces, retained highest faces, both pool totals when applicable, and the selected total. No game-specific success threshold or critical-hit rules are applied. No download is required or offered. Rolls use crypto.getRandomValues in 16 KiB requests. A uint32 value x is accepted only below floor(2³²/S)×S, then mapped to x mod S + 1, avoiding modulo bias. A failure or 4096 consecutive rejected words stops the action without a Math.random fallback. Browser CSPRNG, no hardware entropy certification, seed control or cryptographic-key use. Theory needs no random source. All calculations stay in this browser and work offline after loading. No added calculation dependencies, external service, fees or usage quota.
Calculations in Dice Roll Probability Simulator use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Dice Roll Probability Simulator run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
Dice Roll Probability Simulator verification · Audit standards
How to use it
- Enter a dice expression and choose the mode.
- Calculate exact probabilities, simulate 100,000 rolls or roll once.
- Inspect the curve, frequency bars, exact table and individual roll details.
Frequently asked questions
Which expressions are supported?+
Operational requirements for "Which expressions are supported?" are verified in local memory during execution of Dice Roll Probability Simulator.
How are advantage and disadvantage defined?+
Boundary constraints concerning "How are advantage and disadvantage defined?" prevent invalid parameter state mutations client-side.
Are probabilities exact?+
For ordinary dice, coefficients of (x+x²+…+xˢ)ᴺ count ordered outcomes with denominator Sᴺ. For khK, a descending-face combinatorial dynamic program counts assignments using binomial coefficients and sums over discarded lower faces. BigInt preserves integer counts. If F is the pool cumulative probability, advantage uses F(t)²−F(t−1)²; disadvantage uses (1−F(t−1))²−(1−F(t))².
How do simulations and single rolls work?+
The purple curve joins the discrete point probabilities. Blue bars show empirical relative frequencies from exactly 100,000 trials, with the same vertical probability scale. All sums are shown; wide plots scroll horizontally. Full exact probabilities and integer frequencies are in the table. Random runs vary and do not prove convergence or certify randomness.