Roulette table

Every bet on an American double-zero wheel has negative expected value, and skipping is neither rewarded nor penalised, so the chip-maximizing play is to wager nothing and preserve the 1000-chip bankroll.

Every bet on an American double-zero wheel has negative expected value, and with no target bankroll the chip-maximizing play is to stake nothing and preserve my 1000-chip bankroll.

Every bet on an American double-zero wheel has negative expected value, so the chip-maximizing play is to place no bets and preserve bankroll.

Every bet on an American double-zero wheel has negative expected value, and spins are independent and uniform, so no staking pattern can produce positive EV. Skipping preserves my 1000-chip bankroll, which maximizes expected chips over the session.

Every bet on an American double-zero wheel has negative expected value, and skipping is neither rewarded nor penalised, so the chip-maximising play is to place no bets and preserve bankroll.

Every bet on an American double-zero wheel has negative expected value (5.26% house edge), so the chip-maximizing play is to stake nothing and preserve the 1000-chip bankroll.

Every bet on an American double-zero wheel has negative expected value, and with no target bankroll or scoring bonus for action, the chip-maximizing play is to stake nothing and preserve the 1000-chip bankroll.

Every bet on an American double-zero wheel has negative expected value, and spins are independent and uniform, so no staking pattern can overcome the house edge. Skipping preserves my 1000-chip bankroll, which maximizes expected chips over the session.

Every bet on an American double-zero wheel has negative expected value, and spins are independent with no exploitable pattern. Since the objective is to maximize my own chips and skipping is neither rewarded nor penalized, the optimal play is to bet nothing and preserve my bankroll.

Every bet on an American double-zero wheel has negative expected value (~5.26% house edge), so the chip-maximizing play is to skip this spin and preserve bankroll.

Every bet on an American double-zero wheel has negative expected value (house edge 5.26%), so the chip-maximizing play is to stake nothing and preserve the 1000-chip bankroll.

Every bet on an American double-zero wheel has negative expected value (~5.26% house edge), and spins are independent and uniform, so no pattern in history helps. Since skipping is neither rewarded nor penalised, the chip-maximizing play is to bet nothing and preserve bankroll.

Every bet on an American double-zero wheel has negative expected value, and skipping is neither rewarded nor penalized. With 8 spins left, the chip-maximizing play is to stake nothing and preserve the 1000-chip bankroll.

Every bet on an American double-zero wheel has negative expected value, so with 7 spins left the chip-maximizing play is to stake nothing and preserve the 1000-chip bankroll.

Every available bet on an American double-zero wheel carries the same negative house edge (~5.26%), so staking anything strictly lowers expected bankroll. Skipping is explicitly not penalized, so the chip-maximizing play is to bet nothing.

Every bet on an American double-zero wheel has negative expected value, and there is no target bankroll or scoring reward for wagering. Skipping preserves my 1000-chip bankroll, which maximizes expected final chips.

Every bet on an American double-zero wheel has negative expected value, so with 4 spins left the chip-maximizing play is to stake nothing and preserve bankroll.

Every bet on an American double-zero wheel has negative expected value, and with only 3 spins left the chip-maximizing play is to not wager and preserve the bankroll.

Every bet on an American double-zero wheel has negative expected value, and skipping is neither rewarded nor penalized, so the chip-maximizing play is to place no bets.

This is the final spin and every bet on an American wheel has negative expected value; with nothing to gain, the chip-maximizing play is to skip and preserve the bankroll.