Roulette table

Any of these eight pockets reaches 1,504 chips, giving an 8/38 chance of meeting the target immediately with little overshoot. A miss leaves 856 chips and 19 spins for further attempts.

These eight bets total 184 chips, and any covered pocket brings the bankroll to exactly 1,500, giving an 8/38 chance of reaching the target immediately. A miss leaves 672 chips and 18 spins for further attempts.

Any of these four pockets brings the bankroll to 1,504, just above the target. The 104-chip total stake leaves 568 chips for subsequent attempts if this spin misses.

A 27-chip straight-up win brings the bankroll to 1,513, reaching the target without unnecessary overshoot. This is the smallest single straight-up stake that succeeds immediately and preserves most chips for further attempts if it loses.

Any of these six equally likely pockets brings the bankroll to 1,501, reaching the target without meaningful overshoot. A miss leaves 349 chips and 15 spins for further attempts.

A 33-chip straight-up win brings the bankroll to 1,504, reaching the target without unnecessary overshoot. A loss leaves 316 chips for further attempts with 14 spins remaining.

A 34-chip straight-up win raises the bankroll to 1,506, reaching the target without unnecessary overshoot. This is the smallest single wager that can reach the target immediately and leaves 282 chips for further attempts if it loses.

A 35-chip straight-up win reaches 1,507 chips, meeting the target without unnecessary overshoot. A loss leaves 247 chips for further attempts; every pocket is equally likely.

A 36-chip straight-up win brings the bankroll to 1,507, meeting the target immediately. This is the smallest stake that can do so, preserving 211 chips for further attempts if it loses.

A 37-chip straight-up win raises the bankroll to 1,506, reaching the target with minimal overshoot. A loss leaves 174 chips for further attempts during the remaining spins.

A 38-chip straight-up win reaches 1,504 chips, just above the target. This is the smallest stake that can reach the target immediately, while leaving 136 chips for further attempts if it loses.

A 39-chip straight-up win raises the bankroll to 1,501, meeting the target immediately. This is the smallest stake that can do so, preserving 97 chips for later attempts if it loses.

A hit raises my bankroll to 1,532, reaching the target immediately. A miss leaves 56 chips, preserving another direct attempt with spins remaining.

A 42-chip straight-up win reaches 1,526 chips, clearing the target immediately. It is the smallest stake that does so and preserves 14 chips for another attempt if this spin loses.

A dozen win raises the bankroll to 42, enough for a subsequent all-in straight-up win to reach 1,512. This provides a direct two-spin route to the target with about a 0.83% success probability.

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 I must skip this spin.

With a zero bankroll and no legal bets available, skipping is the only legal choice.

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

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