Every TTRPG check comes down to a probability question — what are the real odds behind that d20, that dice pool, that advantage roll? This calculator answers it exactly, using the same convolution math that powers tools like AnyDice, so you can see the full distribution behind any notation rather than guessing from a gut feel.
How the distribution is built
Every die contributes a small probability distribution of its own — a d6 has a 1-in-6 chance of landing on each face. Rolling multiple dice and summing them means convolving those distributions together: for every possible sum, the calculator adds up the probability of every combination of individual die results that produces it. For a plain roll like 2d6+3, that's a straightforward sum-of-two-dice convolution shifted by the flat modifier. Keep-highest and keep-lowest pools (like 4d6kh3) need a more careful calculation — an exact dynamic-programming pass over each possible face value, tracking how many dice remain and how many "keep" slots are still open — because simply enumerating every outcome gets slow once the dice or sides get larger. Either way, the result is an exact answer, not a Monte Carlo estimate.
Advantage, disadvantage, and what they're really worth
Advantage and disadvantage are two of the most common house rules and official mechanics in modern TTRPGs, and they're easy to misjudge by feel. Advantage rolls two dice and keeps the higher; disadvantage keeps the lower. On a d20, that turns a flat 30% chance to hit DC 15 into 51% with advantage, or drops it to 9% with disadvantage — a swing worth roughly +3 to +4 on your effective roll near the middle of the range, but noticeably less extreme near the very top or bottom of the die (you can't push past a natural 20 no matter how many times you roll). The calculator's Advantage/Disadvantage tab lets you see all three outcomes side by side for your exact target.
Exploding dice and dice pools
Systems like Savage Worlds and Shadowrun let a die 'explode' — rolling the maximum face triggers another roll that gets added on top, chaining as long as you keep hitting the max. That turns a bounded die into one with a long, thin tail of huge results, which this calculator models by tracking the chain out to a vanishingly small residual probability rather than a fixed number of re-rolls. Dice pools with keep-highest or keep-lowest notation (4d6kh3, 3d6kl1) work differently again: instead of summing everything, you only count the best or worst few dice, which shifts the average up or down from what a plain sum would give you.
Named dice event comparison
Compare two named finite dice expressions under the same named events. Each die independently draws one equiprobable position from its face list; repeated face values retain their multiplicity. The modifier is added once to the total and never to maxima or individual-face conditions. At least one means that any die face satisfies the chosen comparison.
The comparison supports two expressions, up to 8 dice and 100 faces per die, at most 2000 ordered outcomes per expression, and 12 events. Excess work is rejected before enumeration. Decimal totals and event comparisons are exact; original face positions and every ordered outcome are reported. Nonrepresentable plotted totals and exploding rules are unavailable in this finite comparison. The original ordinary and custom total modes remain separate.