fix(provably-fair): use rejection sampling in computeDiceRoll to eliminate modulo bias#4
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computeDiceRoll() computed raw % 10000 on a uint32. Because 2^32 (4,294,967,296) is not evenly divisible by 10,000, values 0–7,295 appear slightly more often than values 7,296–9,999 — a systematic bias of ~1.7 per million per value in the favoured range. In a high-volume casino context this is not negligible: over millions of rolls the house retains a hidden edge on top of the declared house edge. Replace modulo with rejection sampling over successive 4-byte HMAC windows using a rejection threshold of floor(2^32 / 10000) * 10000 (4,294,960,000). Values at or above the threshold are discarded; the next 4-byte window is used. Average iterations per roll < 2.
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Bug
computeDiceRoll()maps a uniform uint32 to [0, 9999] with a simple modulo:Because 2³² = 4,294,967,296 is not evenly divisible by 10,000, values 0–7,295 are each produced by 429,497 possible inputs while values 7,296–9,999 are each produced by only 429,496 — a systematic bias of ~1 in 429,496 per value.
Impact: In a high-volume casino context this is exploitable. Over millions of rolls, the house retains a hidden edge on top of the declared house edge for outcomes in the biased range (0–7,295). Players who bet consistently on those values receive slightly worse expected returns than the published odds imply.
Fix
Replace the modulo with rejection sampling over successive 4-byte HMAC windows. A rejection threshold of
floor(2³² / 10000) × 10000 = 4,294,960,000is used; values at or above the threshold are discarded and the next 4-byte window is tried. Average iterations per roll is less than 2. The output distribution is exactly uniform.