Out of 6 × 6 = 36 ordered two-dice outcomes, how many contain at least one 6? Six rolls on Die 1 plus six rolls on Die 2 minus the shared 6-6 double equals 6 + 6 - 1 = 11 rolls (30.6%)!
A blot 6 pips away can be hit by any 6 (11 rolls) plus 1-5, 5-1, 2-4, 4-2, 3-3, 2-2 (6 rolls) = 17/36 (47.2%). Once a blot is 7 pips away, only two-dice sums hit it (6/36 = 16.7%)—a massive 30.5% drop in danger!
When doubled from 1 to 2 in a gammonless race, passing loses 1 point while taking risks 2 points to gain 2. Setting expected value 2p - 2(1-p) = -1 yields p = 1/4 = 25%!
l
In sans-serif fonts, lowercase l (ASCII 108), uppercase I (ASCII 73), and numeral 1 (ASCII 49) look nearly identical. On Linux servers (Apache/Bluehost), URLs after the / are strictly case-sensitive—so we standardize on CameLcase (/LearningLab, SLog, FlippingDice, TopHat).
Every LearningLab in the Twisted23 Parlour stamps events using the 38-character alphabet (0-9, A-Z, |, ^—capital L only, zero lowercase ls!) counting seconds since March 18, 2020:
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