Overlapping roulette bets: coverage and net profit

When several roulette wagers share a number, that result can win more than one position. Calculate coverage using unique pockets, then calculate money using every individual wager. The same covered set can produce different net returns when chips are placed differently.

Use one settlement formula

For each possible winning pocket, add the total returns from all wagers covering it. Include each winning stake's return. Subtract the entire amount staked in the round once, including every losing position.

Net result for a pocket = sum of winning total returns − total round stake.

This method also handles a covered outcome that still loses money overall.

Red plus one number

Place 2 chips on red and 1 straight up on 1. Total stake is 3.

There are 18 covered pockets, not 19: number 1 already belongs to red. On a single-zero wheel, hit probability is 18/37. Expected profit is (37 + 17 × 1 − 19 × 3)/37 = −3/37 chips, the ordinary edge applied to three staked.

A winning wager can leave a round loss

Place 1 chip on a dozen and 3 on red. Total stake is 4. If a black number in the selected dozen wins, the dozen returns 3 and red loses. The round's net result is −1 even though the dozen won. “At least one bet wins” and “the round earns a profit” are different events.

Equal coverage can hide unequal weights

Orphelins covers eight pockets with either eight straight-up chips or a five-chip straight-and-split package. Both have an 8/37 hit chance. Their stakes and winning returns differ, with 17 winning two splits in the five-chip version.

Build a pocket table when auditing a collection: one row per possible result, one column per wager, then a total-return and net-result column. The bet builder offers a practical way to inspect coverage. The payout reference supplies standard payments, and roulette probability explains unique-set counting.