A six is more common than one in six: a useful backgammon dice check
You leave a checker exposed and think, “They need a six.” How often does a six actually appear when two dice are rolled? The answer is 11 out of 36, or about 30.6%. One in six describes a single die. Backgammon uses two. Count the rolls before trusting the percentage Imagine the dice are different colours. There are 36 equally likely ordered results: six choices for the first die, multiplied by six for the second. Six results have a six on the first die. Another six have a six on the second. But 6–6 belongs to both groups, so counting both groups gives it two places. Subtract that extra count: 6 + 6 − 1 = 11. The same result applies to any one named face. At least one three, for example, also appears in 11 of the 36 ordered rolls. Three questions that sound similar but have different answers “Will at least one die show a six?” gives 11/36. “Will the dice total six?” gives 5/36: 1–5, 2–4, 3–3, 4–2 and 5–1. “Will it be double six?” gives 1/36. Confusing those questions can cha...