Mb99: Last Return Plinko Exact Rules

Last Return to the Starting Position

Last Return Plinko gives each ball twelve independent fair left/right steps, forming 4096 equally likely paths. Starting at horizontal position zero, a left step subtracts one and a right step adds one. The score is the last row from 1 through 12 whose cumulative position is zero, or zero if no row returns to the start. A return earlier in the path still counts even if the final position is not zero. The endpoint bucket alone does not determine the score.

Twelve left steps never return to the starting position and give score zero. Alternating left and right steps return at every even row, so the score is 12. A path that returns at row two and then takes ten right steps has score two, despite ending away from zero. In Linear mode, stake 20 and score zero give gross20×0.96/7, approximately 2.742857 coins; score 12 gives approximately 35.657143 coins.

Linear, Squared and Cubed Returns

The displayed payout modes are Linear, Squared and Cubed. They use weights (score+1) raised to powers 1, 2 and 3. The exact mean weights over all 4096 paths are 7, 70 and 784 respectively. The gross return is captured stake × 0.96 × weight divided by the selected mode’s exact mean. It includes the stake. Score zero still has weight one and a positive gross return; it is not a zero-payout event, though that return is less than the stake.

Expected Return and Its Limits

Each mode has exact unrounded expected RTP96% over the 4096 equally likely paths. The modes change the payout weights without changing path probabilities or scoring. This is an expectation over completed balls, not a guarantee for a session or a winning percentage. Signals, previous paths and launch timing do not increase expected return. There is no mid-path collection; unfinished balls abandoned on reload do not settle.

One Captured Stake per Ball

A new local wallet starts with 1000 virtual coins. Stakes are 10,20,50 or100, initially20. Each released ball captures and charges one stake and its current payout mode. At most six balls can be active. Stake, mode and restoration lock while any ball remains active; further balls use the captured current settings and are charged individually. A seventh ball is refused without an additional charge.

The settled wallet, including zero, and fractional payout carry persist in localStorage. Whole coins are credited on settlement and the fractional remainder is kept for later payouts. Reloading ends every unfinished ball without refunding its charged stake or continuing its path. Settings return to their defaults. Another device, browser or cleared site storage can have different counters. Clearing cache alone may leave localStorage. When no ball is active and the wallet is below 10, Restore balance sets it to exactly 1000 virtual coins, rather than adding 1000. Saved fractional carry remains. Restoration requires pressing its button and is not an automatic consequence of losing. These counters have no cash or prize value and cannot be withdrawn.

Uniform Binary Directions

Each independent direction is selected by an exact half-range threshold on a uniformly sampled 32-bit integer. Both halves contain the same number of values. Twelve choices produce the 4096 equiprobable paths used in the calculation. This original outcome law does not establish the mathematics, licence or audit status of an external product.