Die & Card Probability Game

Roll a six-sided die and draw from a 10-card deck. Every outcome is one of 60 equally likely combinations — see which events it matches, earn points based on rarity, and watch your results settle toward the real probabilities the longer you play.

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Your Experiment — Observed vs. Theoretical
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Dice Roller See the Law of Large Numbers in action. Roll two six-sided dice and watch your observed sums move toward the theoretical distribution.

The experiment

Each round is one die roll (1–6) plus one random draw from 10 possible card values (1–10). The card values reset for each round, so every round has the same 6 × 10 = 60 possible outcomes. Every individual outcome, like rolling a 3 and drawing a 7, has exactly a 1-in-60 chance.

The four events

Each round is checked against four events, from rarest to most common:

  • Both numbers are 5 — only (5,5) qualifies. 1 outcome, 1.67% chance, worth 60 points.
  • Sum is 3 — (1,2) or (2,1). 2 outcomes, 3.33% chance, worth 30 points.
  • At least one number is 3 — the die is 3, the card is 3, or both. 15 outcomes, 25% chance, worth 4 points.
  • Neither number is 5 — 45 outcomes, 75% chance, worth 1 point.

Points are based on the inverse of each event's probability: 60 ÷ the number of matching outcomes. That means rarer events are worth more — landing (5,5) is exciting precisely because it's only 1 in 60.

Why events overlap

These four events aren't mutually exclusive. Rolling (1,2) satisfies both "sum is 3" and "neither number is 5" at the same time — the game shows you every event a roll matches, then scores you on the rarest one, since that's the more interesting fact about that outcome. This is also why the "no match" category exists: 12 of the 60 outcomes (20%) satisfy none of the four events at all. That's not a bug — it's simply the set of outcomes that don't meet any of the four conditions.

Why "both numbers are 5" is rarer than "sum is 3"

This mirrors a classic probability question: of the 60 possible outcomes, exactly one — (5,5) — has both numbers equal to 5. But two outcomes, (1,2) and (2,1), sum to 3, because the die and the card are two separate parts of the experiment: rolling 1 and drawing 2 is a different outcome from rolling 2 and drawing 1, even though they add up the same way. Order matters here precisely because the die and the card aren't interchangeable.

Frequently asked questions

Why did I get "No Match" and zero points?

Your roll didn't satisfy any of the four defined events because it had exactly one 5 and no 3. This happens on 12 of the 60 possible outcomes, or 20% of rounds, so roughly 1 in 5 rounds will land here. It's a normal, expected part of the sample space, not a failure.

Why does my roll sometimes match more than one event?

The four events aren't designed to be mutually exclusive, so a single outcome can genuinely satisfy more than one at once — for example, (1,2) satisfies both "sum is 3" and "neither number is 5." Your score is always based on the single rarest event you matched, but the game shows you every event that applies, since that's part of what's interesting about probability.

Why are points based on rarity instead of a fixed amount?

Each event's point value is 60 divided by how many of the 60 outcomes satisfy it, so the math directly reflects how hard that event is to hit. A 1-in-60 outcome is worth 60 points; a 45-in-60 outcome is worth 1. Flattening this out would make the score feel nicer round to round, but it would stop teaching the actual lesson — that rare things are worth more precisely because they're rare.