Games & strategy · course 10 of 105

Dice Odds From 2d6 to d20 Advantage

Know the chances behind the dice at your game table: totals on two dice, d20 rolls with advantage and disadvantage, average damage, drop-the-lowest and rerolls, and which attack does more.

4 modules

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Runs in Claude (claude.ai, the Claude apps or Claude Code) with your own Claude account. A course opens there as soon as your payment goes through; nothing is shipped.

Preview

What it teaches

The chances behind the dice you roll at a game table. One die and two dice (the chance of a total on two dice, “at least one 6” in several rolls), d20 rolls (needing a target number with a bonus, advantage, disadvantage, advantage and disadvantage cancelling, a 20 that always hits and a 1 that always misses), and averages and choices (the average of a roll like 2d6+3, “roll four dice and drop the lowest”, rerolling low dice, a +5 bonus against advantage, which attack does more damage per swing). The AI asks 3 questions, places you, shows a short card per module, then gives you one question at a time and checks your answer against keys computed by counting every outcome (in M1 to M3; the M0 word questions are checked against answers backed by quotes).

For board-gamers and tabletop role-players who want to know the numbers, not guess them. Not a rules reference and not a betting course: it can’t tell you what to play or bet, and it doesn’t cover casino games (see the Craps & Roulette course for those).

How long

41 items. About 12-35 rounds for a confident player (a quick student who already knows it needs 12-20) up to about 60-75 for a beginner, plus a 12-item final: 2 sessions (estimate, not timed with a real student). The tutor gives a one-line save code at the end of each session.

The modules

4 modules, drilled one item at a time.

M0
The words and rules
The words and rules: dice notation, advantage and disadvantage, meeting a DC, a 1 or a 20 on an attack, fair dice
M1
One die and two dice
Chances on one die and two dice: a total, and at least one of something in several rolls
M2
d20 chances
d20 chances: a target number with a bonus, advantage, disadvantage, both cancelling, a 20 that always hits and a 1 that always misses
M3
Averages and choices
Averages and choices: the average of 2d6+3, drop the lowest, rerolls, a +5 bonus against advantage, which attack does more damage

Before it teaches, it asks

1
Which do you play most (board games, a d20 tabletop role-playing game, both, neither yet), and do you use a calculator for dice maths?
2
Roll two fair six-sided dice and add them. What is the chance the total is 7?
3
An ability check against DC 15 with no modifier, rolled with advantage: what is the chance of success?

What’s exact, and what isn’t

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Straight from the course’s own notes.

Computed by script: Every M1, M2 and M3 key, by listing every outcome of the dice (up to 8,000 outcomes for three d20 rolls) with exact fractions, never by a formula. Every number in a Working comes from the same count, and every listed wrong answer is computed by the slip it names and checked to differ from the key. Percents are rounded to 1 decimal, halves up; a script refuses any item that would land exactly on a half.
Quoted, checked word for word: 27 quotes: 14 from the System Reference Document 5.1 (the official PDF, pages 1, 24, 76, 77, 94 and 251, read 2026-10-12) and 13 from four Wikipedia pages (“Dice”, “Dice notation”, “Probability”, “Expected value”, read 2026-10-12). For each M0 Answer, its key facts are paired with fragments of a cited quote, and a script checks that each paired fragment is in the Answer and in the quote; it does not catch a claim added to the Answer, so whether an Answer is a fair paraphrase of its quote is a human check.
One outside check on a Key: Wikipedia’s “Dice notation” prints the chance of an 18 and of a 3 when you roll four six-sided dice and drop the lowest (21/1,296 = 7/432 and 1/1,296). The count is checked to give the same numbers. No other key has a published twin; they rest on the count.
Honest limits: Every die is fair. The damage items ignore critical hits (each question says so), so they are not the full damage story. The rules quoted are the SRD 5.1's, and your table’s rules or edition may differ. The course can’t tell you what to play or bet, or whether your dice are fair.
Not in it yet: Critical-hit damage, saving throws and conditions, dice pools that count successes, exploding dice, percentile dice, the spread of results (variance, the bell curve), and casino dice bets.