The Probability Calculator computes the distribution of outcomes for dice pools, deck draws, and similar randomness in your game. Use it to answer questions like "what's the chance of rolling 12+ on 3d6?" or "in a 60-card deck with 4 copies of a card, what's the chance of drawing one in my opening hand of 7?".

What this page helps you do

Set up a probability question.
See the full outcome distribution.
Tune your design based on the math.

Open the tool

Tools → Designing → Probability Calculator.

Set up the question

The tool supports several question types:

Dice pool

How many dice of each size (e.g. 3d6–2d10).
Modifiers (constant added or subtracted).
Reroll rules (reroll all 1s, drop lowest, etc.), limited to common patterns; complex custom logic may not be supported.
Target threshold (≥ 10, exactly 7, etc.), calculates probability of meeting it.

Deck draw

Deck size (e.g. 60 cards).
How many "hits" in the deck (cards you're hoping to draw).
Hand / draw size (you draw N cards).
Question: probability of drawing at least 1 hit, exactly 2 hits, etc.

This is hypergeometric distribution, relevant for any "chance of seeing this card by turn N" calculation.

Custom

For anything more complex, define discrete probabilities and combine, the advanced mode lets you build a small table of outcomes and combine them.

Read the results

The tool shows:

Full distribution: bar chart of every possible outcome's probability.
Cumulative probability: chance of getting at least X.
Mean and standard deviation: average outcome and spread.

Common design uses

Combat resolution. "On 2d6, what's the chance of beating defense 8?" → tune defense numbers based on the answer.
Card draw timing. "Of 60 cards, how many copies of the silver bullet card should I include for it to show up by turn 3?" → run the hypergeometric.
Comparing dice systems. d20 + modifier vs 3d6 + modifier vs step-die system. The probability curves are very different.
Encounter design. "What's the chance of a TPK if 4 monsters each have a 30% hit chance?", combine probabilities.

Limits

Very complex custom mechanics (e.g. probability that depends on game state two turns ahead) are out of scope. For those, simulate in code or Anydice.
Continuous distributions (rare in board games) are not supported.

Tips & common questions

This isn't on my Tools list, why? The Probability Calculator is currently in preview / roadmap state in some workspaces. The tool route works directly, but the discoverability in the Tools list may not be enabled yet.

The result doesn't match what I get rolling actual dice. Real-world rolls are random, small samples diverge from the theoretical distribution. The calculator shows the true distribution; physical testing approximates it. If you roll 100 times and the average is far from the calculator's mean, something is off (loaded dice, miscount).

I want to compare two dice systems side by side. Set up question A, save the result, set up question B, save. The tool can overlay distributions for comparison.

Why does this matter for design? Math doesn't replace playtesting, but it complements it. Math tells you "the d20 + skill system has a 25% chance of failing every roll, no matter the player's skill." Playtesting tells you whether that 25% feels fair.