Roulette table

A 100-chip dozen bet offers a 12-in-38 chance to gain 200 chips, making meaningful progress toward the target while retaining enough bankroll for later attempts. All dozens have identical probabilities on this independent, uniform wheel.

Covering eight pockets gives an 8/38 chance of reaching 1,516 chips immediately, exceeding the target. The 176-chip total stake leaves 724 chips and 18 spins to recover if this bet loses.

Any of these seven pockets would bring the bankroll to 1,507, reaching the target with a 7/38 chance this spin. The 189-chip total stake leaves 535 chips to pursue the target if all seven miss.

A 28-chip straight-up win raises the bankroll to 1,515, reaching the target. This is the smallest stake that can reach the target in one spin, preserving chips for further attempts if it loses.

Any result from 1 through 6 brings the bankroll to 1,501, giving a 6/38 chance of reaching the target immediately. The total stake is 200, leaving at least 307 chips for later spins if these bets miss.

A 35-chip straight-up win raises my bankroll to 1,532, reaching the target. This is the smallest single-pocket stake that reaches the target immediately, preserving chips for further attempts if it loses.

A win raises the bankroll to 1,532, reaching the target. This is the smallest straight-up stake that reaches 1,500 immediately, preserving chips for further attempts if it loses.

A win raises my bankroll to 1,496, just four chips short of the target with 12 spins left. This stake preserves funds for additional high-payout attempts if it loses; every pocket is equally likely.

A 38-chip straight-up win brings the bankroll to 1,530, reaching the target immediately. This is the smallest stake that can do so, preserving chips for further attempts if it loses.

A hit raises my bankroll to 1,527, reaching the target. This is the smallest straight-up stake that succeeds immediately and preserves enough chips for three more target-reaching attempts if it loses.

A 40-chip straight-up win reaches 1,523 chips, satisfying the target immediately. A loss leaves 83 chips, enough for two further straight-up attempts sized to reach the target.

A hit raises the bankroll to 1,518, reaching the target immediately. A loss leaves 42 chips, enough for another straight-up attempt that can still reach 1,500.

A winning 42-chip straight-up bet raises the bankroll to 1,512, immediately meeting the target. Every pocket is equally likely, so choosing 0 gives the same 1-in-38 chance as any other number.

With a bankroll of 0 and no legal bets available, I must skip this spin.

The bankroll is zero and no bets are legal, so I must skip this spin.

The bankroll is zero and no bets are legal, so skipping is the only available action.

The bankroll is zero and no bets are legal, so the only valid action is to place no bets.

The bankroll is zero and no bets are legal, so the only available action is to skip.

The bankroll is zero and no bets are legal, so I must skip this spin.

The bankroll is zero and no bets are legal, so the only available action is to place no bets.