Questions About Our Original Weighted Drift Area Demo

Each ball starts at position zero and takes twelve independent fair steps, left minus one or right plus one. All 4096 paths have equal probability. Let x_i be the signed position after step i. The raw reward is the sum, over i from one to twelve, of i times the absolute value of x_i. Every visited prefix position contributes with its step index as weight. A whole captured stake prices one ball; it is not split into row stakes, and credit does not depend only on the final endpoint.

The first position is always minus one or one, and odd-numbered steps cannot end at zero. The minimum weighted reward is thirty-six, achieved by a path alternating away from zero and back. Twelve steps all in the same direction give the maximum 650, the sum of i squared for i from one to twelve. No legal path scores zero. Positive gross credit is therefore certain for a completed valid ball, but a credit can be smaller than its charged stake and reduce the wallet. A positive reward is not a guaranteed profit.

Choose linear, squared or cubed weighting. Gross credit is the whole captured stake times 0.96 times raw reward raised to that power, divided by its exact mean over all 4096 paths. The three means are 175.95703125,42797 and 13076147.390625 respectively. Each mode has exact unrounded expected gross credit of 96% of stake. A square or cube is an exponent, not multiplication by two or three. All modes use the same always-positive raw-path distribution, while their normalized credit sizes differ. Expected credit is not a session guarantee or a winning frequency.

The wallet begins with 1000 free virtual coins. Settled wallet and fractional-credit carry persist in browser localStorage. Manual refill is available only after all active balls have settled and the automatic queue is empty, with idle balance below ten. It sets balance to 1000 and preserves carry; it does not add 1000. Reloading does not reset saved settled values. Unfinished balls are not resumed or refunded on reload and pending credits can be lost. Keep active play open until settlement. Ordinary cache deletion may leave localStorage intact.

At most six priced drops can be active at once. Each captures its own whole stake and weighting at launch. Changing controls affects future balls only, including future automatic launches, rather than balls already in flight. A seventh concurrent launch cannot charge a new stake. Automatic play schedules at most ten drops. Stop cancels future launches while active balls still settle. Refill remains locked until every ball has settled and the queue is empty. Concurrency and automatic scheduling do not improve the normalized expectation.