Two Readings and a Coprime Count
Draw two independent uniform integers a and b from zero through twelve. Score counts integer pairs (x,y) with 1 ≤ x ≤ a and 1 ≤ y ≤ b whose greatest common divisor is one. It does not count every point or simply take gcd(a,b). For readings two and three the score is five: all six points except (2,2) qualify. If either reading is zero there are no qualifying points and score is zero.
Three Complete Score Bands
There are 169 equally likely ordered reading pairs. Sort the distinct attainable scores, then partition that sorted list into three consecutive groups with nearly equal numbers of distinct values. Every attainable score belongs to exactly one band. Gaps such as 24 or 28 are unattainable scores, not additional losing outcomes. The selected band wins when it contains the resulting score; the other two selections lose for that same draw.
- 1: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17; 81/169
- 2: 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 35, 36, 38, 39, 40, 42; 51/169
- 3: 43, 44, 46, 47, 49, 52, 54, 55, 57, 59, 60, 63, 68, 71, 73, 76, 83, 87, 91; 37/169
Probability and Gross Credit
The three band probabilities are 81/169, 51/169 and 37/169. A matching selected band returns captured stake × 0.96 divided by that band probability, including stake. Gross multipliers are approximately 2.002963, 3.181176 and 4.384865. A miss returns zero. Probability multiplied by gross multiplier equals 0.96 for each band. This is exact unrounded expected gross credit, not a promised wallet result, winning frequency or an external product’s odds.
Saved Wallet and Optional Refill
The wallet starts with 1000 free virtual coins. Settled balance and fractional payout carry persist in browser localStorage. Manual refill is available only while idle and balance is below ten. It sets balance to 1000 and preserves carry; it does not add 1000. Reload preserves the saved debited wallet and carry, but an unfinished round is not resumed or refunded. Free coins cannot be deposited, withdrawn or exchanged for money or prizes.
Frequently asked questions
How is the score calculated?
Count coprime integer points in the rectangle from (1,1) to the two drawn readings. A zero reading gives score zero.
What are the three hit probabilities?
They are 81/169, 51/169 and 37/169 for the lower, middle and upper score bands.
Are gaps in the band lists losing outcomes?
No. Such gaps are unattainable scores. Every attainable score belongs to one band; a miss means it belongs to another band.
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