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Six Row Ledger: Probabilities and Returns

The Six Row Ledger is a simple Plinko-style game where a ball drops through six rows of left or right choices. This guide explains the exact mathematical probabilities and how gross and net returns are calculated.
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Game Mechanics and Probabilities

Players select a whole-coin stake of 5, 25, or 100, with 5 as the default. A single ball is dropped through six independent rows, each offering a fifty percent chance of moving left or right. The final position is determined by the number of right turns, ranging from zero to six. This distribution follows a binomial pattern with probabilities of 1/64, 6/64, 15/64, 20/64, 15/64, 6/64, and 1/64 for the seven possible outcomes.

Gross versus Net Returns

The game uses multipliers of 8, 2, 0.5, 0.36, 0.5, 2, and 8 for the seven buckets. Gross return is calculated by multiplying the stake by the bucket multiplier, which includes the original stake. Net profit is the gross return minus the initial stake. For example, a 5-coin stake landing in a 0.5x bucket yields a gross return of 2.5 coins, resulting in a net loss of 2.5 coins. The exact expected gross return is 97.1875 percent, indicating the long-term theoretical payout.

Wallet and Settlement Rules

The chosen stake is deducted immediately upon starting a round. Settlement occurs automatically after 700 milliseconds, with controls disabled during this period. Fractional hundredths are saved in a carry value and combined with gross returns to credit whole coins. A manual balance restoration to 1000 is available only when idle and the balance is below five coins. Reloading the page does not resume an unfinished round, nor does it refund the previously deducted stake.

Questions and answers

What is the difference between gross and net returns?

Gross return includes the original stake multiplied by the bucket multiplier. Net result is the gross return minus the initial stake, representing actual profit or loss.

How is the wallet balance restored?

You can manually set the balance to 1000 coins when idle and the balance is below five. This sets the balance to that amount rather than adding it, while preserving any fractional carry.