Divisor-Count Cricket Demo: Rules and Math

Scoring each delivery

Each delivery independently draws one of eight equally likely codes: 0, 1, 2, 3, 4, 6, W, W. Each numerical result has probability 1/8; the two W codes together give a wicket probability of 1/4. The first non-wicket result adds no score. For each later non-wicket result, add the number of positive divisors of (previous non-wicket value + 1) × (current value + 1). A wicket does not erase the previous non-wicket value. This arithmetic score differs from ordinary cricket runs.

For example, results 1, W, 2 retain the non-wicket pair 1 and 2. Their product after adding one to each value is 2 × 3 = 6. The positive divisors of 6 are 1, 2, 3, and 6, so the contribution is 4 points, not the divisor sum of 12. The wicket still counts toward the two-wicket stopping rule.

Targets, stopping rules, and payout

Choose target 4, 12, or 16 before starting. The round stops when the score reaches or exceeds that target, when the second wicket arrives, or after six balls. There is no collection button during the round. Deliveries are scheduled 450 milliseconds apart. Stake selection, target selection, balance restoration, and starting another round remain locked until settlement.

For a target with hit probability P, a successful round returns a gross multiplier of 0.96 / P. Multiply that number by the captured stake to obtain the raw return in coins. Gross return includes the stake; it is not net profit. A missed target returns zero. The exact expected gross return is therefore 96% of the stake for each target, before the wallet distributes fractions through carry.

Expected return and saved samples

The saved simulation ran 1,000,000 rounds for each target. Its measured gross returns were 96.0054%, 96.0713%, and 96.1400% for targets 4, 12, and 16 respectively. These are sample observations, not the proof of the payout law or a promised session result. The exact hit probabilities and the multiplier 0.96 / P establish the 96% expectation. Hit probability and expected return are different quantities.

A larger target has a lower hit probability and a larger multiplier on success. This changes the distribution of individual results without changing the exact 96% expected gross return. A short run of wins or misses does not have to resemble that average.

Stakes and locked controls

The stake presets are 10, 20, 50, and 100 virtual coins, with 20 selected initially. Target 4 is selected initially. Starting captures the stake once; the game then delivers results without a mid-round collection option.

Wallet settlement and persistence

A new wallet starts with 1000 virtual coins. Starting a round deducts the selected stake once. At settlement, the wallet combines the raw return with any saved fractional carry, credits the whole-number part of that sum, and saves its fractional remainder. A missed target pays zero and preserves the carry. The balance, including zero, and the carry are saved in this browser’s localStorage.

When the game is idle and the balance is below 10, the manual restoration control sets the balance to exactly 1000 coins. It does not add 1000 to the old balance, and it preserves fractional carry. Restoration is never automatic.

Reloading an unfinished round leaves its stake deducted and gives no refund, payout, or continuation. The wallet and fractional carry remain saved, but the round does not resume. The controls return to stake 20, target 4, and an idle game. Stake and target selections are not saved settings.

A worked target-4 example

With target 4 and stake 10, a sequence of zero results scores 0 on the first ball and adds one point on each later zero, because 1 has one positive divisor. The score reaches 4 on ball five, so ball six is not played. The gross multiplier is about 1.20704027×, giving a raw return of about 12.0704027 coins. With no previous carry, 12 coins are credited and about 0.0704027 is retained as carry.

A score can also pass a target rather than land on it exactly. That still counts as success. The divisor function counts positive divisors; it does not add them together. The raw return must include the stake multiplication, so the multiplier by itself is not a coin payout.

Frequently asked questions