Isotonic Path Repair: Game Mechanics and Types

This Demo’s Exact Mechanic

A path starts at signed position 0. Twelve independent fair left/right steps move the position by −1 or +1, producing thirteen positions including the origin. The system automatically finds a nondecreasing integer sequence that minimizes the sum of absolute differences from these thirteen positions. That minimum total error is the score. You do not choose a fitted sequence. It is an original plinko-family optimization demo, with 4096 equally likely complete paths; payout does not depend solely on the final position.

Three Powers of the Same Score

For score s and reward power p (1, 2 or 3), the gross multiplier is 0.96 × s^p divided by the exact mean of s^p across all 4096 paths. Each power therefore has 96% expected gross return. This is a mathematical expectation, not a promised session result or 96% profit. A zero score gives a zero multiplier. The whole chosen stake is deducted when the draw starts. At settlement the game adds previous fractional carry to stake × multiplier, returns the integer part and stores the remaining fraction. The displayed multiplier is rounded to four decimals; settlement uses the unrounded value.

Stakes and Controls

Select a virtual stake of 10, 20, 50 or 100 and reward power 1, 2 or 3, then start one draw. Only one ball is active at a time. Stake, mode and restoration controls are locked while the draw is active; sound remains adjustable. There is no Auto, Stop, pause or early cash-out control. The optimum is calculated automatically, so there are no additional decisions during the path.

Wallet and Persistence

The wallet starts with 1000 virtual coins. Settled balance, including zero, and fractional carry persist in localStorage. When idle with balance below 10, you may manually restore the balance to exactly 1000; this does not add 1000 or reset fractional carry. There is no automatic refill. Reloading an unfinished draw ends it without refund or resume. The already deducted stake remains deducted and the stored balance and previous carry remain available.

Storage Observations

The game source uses localStorage for settled balance and fractional carry. The template declares a Google Fonts stylesheet; a full network capture remains pending. These observations do not establish anonymity, absence of tracking or personal-data processing, or exclusive local processing. The demo has no registration, login or payment flow. That absence is not a complete privacy guarantee for this site or an outside service.

Comparison and Scope

This original plinko-family demonstration uses a whole path and an automatic fitting problem. It does not establish a conventional final-pocket paytable, a slot catalogue or a collection of outside games. Its three powers alter the payout distribution while retaining the same raw score and 96% expected gross return.

Frequently asked questions