Seven Check Bits FAQ: Syndromes and Saved Coins

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Seven independent fair bits occupy positions one through seven. XOR the position indices of every set bit to obtain the three-bit Hamming syndrome. Only syndrome zero qualifies: raw score is then the number of set bits, with the all-zero word also scoring zero. Other syndromes score zero. One whole captured stake prices the entire board, without row stake shares.

Set positions one, two and three have syndrome 1 XOR 2 XOR 3 = 0 and score three. Set positions one and two have syndrome three and score zero. All seven set positions have syndrome zero and score seven. Among 128 equally likely words, raw score counts are zero:113, three:7, four:7 and seven:1. A positive raw score is not necessarily a net virtual gain.

Select power one, two or three before drawing. Gross multiplier is 0.96 times raw score raised to that power divided by the corresponding exact unconditional mean. The means are 0.4375, 1.75 and 7.65625. Zero stays zero. Each mode has 96% exact unrounded expected gross credit of captured stake, not winning frequency or a session promise. No external game’s mathematics is established by this calculation.

One whole captured stake is debited once. Settings and refill lock during settlement and an active Auto queue. Auto schedules at most ten rounds. Stop cancels future rounds while the active round settles; there is no early cashout. Choose the next settings after the queue is idle. The complete sampled board is not redrawn during its animation.

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