Roulette table

Any of these eight pockets takes the bankroll to 1,504, reaching the target with little overshoot. A miss leaves 856 chips and 19 spins for further attempts.

These eight bets total 184 chips and give an 8/38 chance of reaching exactly 1,500 this spin. A miss leaves 672 chips for further attempts; previous outcomes do not affect the odds.

Any of these four pockets brings the bankroll to 1,504, reaching the target with little overshoot. The total stake is 104, leaving 568 for further attempts if this spin misses.

A 27-chip straight-up win raises the bankroll to 1,513, reaching the target without paying for unnecessary upside. The small stake preserves funds for further attempts if this spin loses; every pocket is equally likely.

A 28-chip straight-up win raises the bankroll to 1,521, meeting the target. This is the smallest straight-up stake that succeeds immediately, preserving chips for further attempts if it loses.

A 29-chip straight-up win raises the bankroll to 1,528, reaching the target. This is the smallest single straight-up stake that succeeds immediately, preserving chips for further attempts if it loses.

Any of these four pockets brings the bankroll to 1,508, meeting the target without substantial overshoot. A miss leaves 356 chips and 13 spins for further attempts; all pockets are equally likely.

Any of these five pockets finishes the spin at 1,503 chips, giving a 5/38 chance of reaching the target immediately. A miss leaves 171 chips for further attempts; all pockets are equally likely.

A 38-chip straight-up win reaches 1,501 chips, meeting the target immediately. This is the smallest stake that can do so, preserving 133 chips for further attempts if it loses.

A 40-chip straight-up win brings the bankroll to 1,533, reaching the target immediately. This is the smallest stake that can do so, preserving 93 chips for further attempts if it loses.

A 41-chip straight-up win raises the bankroll to 1,528, reaching the target immediately. A loss leaves 52 chips for further attempts over the remaining nine spins.

A 42-chip straight-up win raises the bankroll to 1,522, reaching the target immediately. A loss leaves 10 chips for the remaining eight spins; every pocket has the same chance.

With only 10 chips and eight spins left, a straight-up win offers a plausible route back toward 1,500. Staking five preserves another attempt after a loss while a win raises the bankroll to 185.

A hit raises the bankroll to 75 chips, enough to reach 1,500 with a subsequent straight-up win. Keeping 3 chips preserves another recovery attempt if this bet loses.

With only 3 chips and six spins left, a straight-up win would rebuild the bankroll to 108 and leave a possible path to 1,500. I accept the risk of immediate elimination because only reaching the target counts.

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 skipping is the only available action.

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 skipping is the only available action.

With zero chips and no legal bets available, skipping is the only legal action.