The core question: Is physical randomization of pills in a jar actually uniformly random? Short answer: No. Physical lottery systems have well-documented bias. So... everyone getting Entropia for more RNG in their rolls. Or if you are using Dice. Read ahead. The Problems with Entropia. Physical Drawing Is NOT Uniformly Random This is the big one. Studies of lottery machines, bingo cages, and ball-drawing systems consistently show that physical randomization of objects in a container has measurable bias: Weight variance: If some pills are even 0.01g heavier (infill differences, excess material at layer seams), they settle to the bottom and are drawn less frequently Friction/static: PLA pills in a glass jar build up static charge. Pills that cling together get drawn in clusters Container geometry: Pills near the walls and bottom of the jar are statistically less likely to be drawn than ones near the top/center. The "well-mixed" assumption breaks down Human drawing bias: The person reaching into the jar unconsciously favors certain regions, depths, or pill orientations Side selection is not random: When you draw a pill, which side do you read? If you always read the "face up" side, or the side facing you, that's a systematic bias affecting ~50% of your entropy No Way to Verify the Entropy Quality You cannot prove after the fact that your draw was sufficiently random. If an adversary knows the bias distribution of your pills (e.g., from studying 3D-printed Entropia sets), they can reduce the keyspace they need to brute-force. Even a 10% bias on certain words dramatically shrinks the effective entropy. For perspective: a perfectly random 12-word seed has 128 bits of entropy (2^128 possibilities). If your physical draw has bias that effectively reduces this to, say, 100 bits, that's not catastrophic, but it's also not the 128 bits you think you have. And you'd never know. Without-Replacement Skews the Distribution Drawing 11 pills from 1,024 without replacement means: After each draw, the remaining distribution changes If pill weights aren't uniform, the bias compounds with each draw The paired word on the back of each drawn pill can never appear - this creates a subtle dependency between words that wouldn't exist in a true PRNG Manufacturing Variance Across Sets 3D-printed pills have layer-line artifacts, stringing, infill density variation, and dimensional tolerance differences. A set printed on a Bambu P1S at 0.2mm will have different physical characteristics than one printed at 0.16mm or on a different printer. Each set has its own unique bias fingerprint. ------------------------------------------------------- Entropy in information theory (Shannon entropy) is basically a measure of surprise, how unpredictable a single outcome is. A fair coinflip has 1 bit of entropy: two equally likely outcomes, so learning the result gives you 1 bit of new information. A fair die roll (d6) has about 2.58 bits - more entropy per roll, but not 6x more. That's the key insight: entropy scales logarithmically, not linearly. Each coinflip is 1 bit, each die roll is log2(6) ≈ 2.58 bits. So in what sense is a die roll "basically a coinflip"? 1. Per-outcome information gain - A die gives you ~2.58 bits per roll. That's roughly 2.5 coinflips worth of uncertainty packed into one event. It's the same kind of flat-uniform randomness, just with more faces. 2. Binary outcome framing - If you collapse any die roll into a yes/no question ("is it ≥4?"), you've literally turned it into a coinflip. A d6 split 3/3 gives you exactly 1 bit. Any source of randomness can be binarized this way. 3. Same source entropy - Both are uniform distributions. The "quality" of randomness is identical; a die just has a bigger alphabet. Six symbols instead of two, but each equally likely, so the shape of unpredictability is the same. 4. Practical equivalency - If you need, say, 128 bits of entropy for a crypto key, you could use 128 coinflips or ~50 die rolls (128/2.58). Same entropy budget, different granularity. Dice are just coins with more faces. The deeper point: all fair uniform sources are "the same kind of thing" - coins, dice, a shuffled deck, radioactive decay. The only difference is how many bits per draw. A coinflip is the atomic unit (1 bit), and everything else is just coins bundled together. #entropia #coinkite #coldcard #seedsigner #security