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Keep the faces until the rule is finished

Part C · L11 · Prerequisite: L10 · One modelling idea

Situation, question, and prediction

A Blades-style highest-die component reads the highest of three d6, not their sum. Can a total of 13 tell you whether two sixes were rolled? Predict how a sum and a maximum differ.

Build

dice_pool(3, 6) is a pool: three separate dice. .sum() reduces their faces to a total. .order_stat(1) selects the largest face: this API counts ranks from 1, unlike list indexing introduced later. Neither call mutates the original pool. .p_any(6) asks whether at least one die shows 6; L14 explores that query and its complement.

pool = dice_pool(3, 6)
output("Sum of three d6", pool.sum())
output("Highest of three d6", pool.order_stat(1))
output("Any six", pool.p_any(6))

Sum of three d6 · DieRoll · mean 10.500

outcome	%	frac	X/216
3	0.46	1/216	1
4	1.39	1/72	3
5	2.78	1/36	6
6	4.63	5/108	10
7	6.94	5/72	15
8	9.72	7/72	21
9	11.6	25/216	25
10	12.5	1/8	27
11	12.5	1/8	27
12	11.6	25/216	25
13	9.72	7/72	21
14	6.94	5/72	15
15	4.63	5/108	10
16	2.78	1/36	6
17	1.39	1/72	3
18	0.46	1/216	1

Highest of three d6 · DieRoll · mean 4.958

outcome	%	frac	X/216
1	0.46	1/216	1
2	3.24	7/216	7
3	8.80	19/216	19
4	17.1	37/216	37
5	28.2	61/216	61
6	42.1	91/216	91

Any six · Prob

outcome	%	frac	X/216
Any six	42.1	91/216	91

Run, read, and check

The sum ranges 3–18 with mean 10.5. The highest ranges 1–6. Any six has probability 1 − (5/6)^3 = 91/216. A total alone loses information: (6, 6, 1) and (5, 4, 4) both total 13 but have different numbers of sixes.

Change one thing

Use two dice. Any six becomes 11/36, the sum has mean 7, and the highest still cannot exceed 6.

Try it yourself

Choose representations for: add damage dice; detect two sixes; name result bands. Answer: summed distribution; unsummed pool until the count is known; named outcomes after classifying. A total of 12 on three dice can be (6,5,1) or (4,4,4), not evidence of a critical.

Rules and model notes

Blades in the Dark, core system. Position describes consequences and is separate from the number of dice. No stress, resistance, or effect-level calculation here. This is deliberately not the complete action roll: criticals and zero dice arrive in L23.

What you now know / where next

Keep the faces until the rule is finished is the reusable idea. Follow the generated previous/next links below, or return to the course index. For a complete self-contained application, see blades-in-the-dark.

Content ID: L11 · Review status: pilot

Prerequisites: L10