Roulette table

Covering eight pockets gives an 8/38 chance of reaching 1,504 chips immediately, with little target overshoot. A miss costs 144 chips, leaving 856 chips and 19 spins to pursue the target.

These eight bets give an 8/38 chance of reaching exactly 1,500 chips this spin, with no payout wasted above the target. A miss leaves 672 chips and 18 spins for further attempts.

Any of these four pockets brings the bankroll to 1,504, reaching the target with little overshoot. The total stake is 104, leaving 568 chips and 17 spins to continue if none hits.

A 27-chip straight-up win would bring the bankroll to 1,513, reaching the target with the smallest sufficient stake. This preserves most chips for further attempts if it misses; every pocket is equally likely.

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

A 30-chip straight-up win raises the bankroll to 1,534, meeting the target immediately. This is the smallest stake that can do so, preserving chips for further attempts if it loses.

Any of these five pockets finishes this spin with 1,508 chips, reaching the target without substantial overshoot. A miss leaves 284 chips for further target-reaching attempts.

A 35-chip straight-up win brings the bankroll to 1,509, reaching the target. This is the smallest single straight-up stake that does so, preserving 249 chips for later attempts if it loses.

A 36-chip straight-up win raises the bankroll to 1,509, reaching the target without unnecessary overshoot. A loss leaves 213 chips for further attempts; all pockets are equally likely.

A 37-chip straight-up win brings the bankroll to 1,508, reaching the target without unnecessary overshoot. A loss leaves 176 chips for further attempts during the remaining spins.

A 38-chip straight-up win raises the bankroll to 1,506, reaching the target immediately. This is the smallest stake that can do so, preserving 138 chips for later attempts if it loses.

A 39-chip straight-up win reaches 1,503 chips, meeting the target without unnecessary overshoot. A loss leaves 99 chips for the remaining seven spins; all pockets are equally likely.

A 41-chip straight-up win reaches 1,534 chips, clearing the target immediately. A loss leaves 58 chips and six spins for further attempts; every pocket is equally likely.

A 42-chip straight-up win raises the bankroll to 1,528, reaching the target immediately. This is the smallest stake that does so, leaving 16 chips for the remaining five spins if it loses.

With five spins left, this gives a 12/38 chance to increase my bankroll to 48, enough to fund a straight-up bet that could reach 1,500. I am prioritizing a viable path to the target over preserving a bankroll far below it.

A 42-chip straight-up win reaches 1,518 chips, meeting the target immediately. This is the smallest stake that can do so, leaving 6 chips for another attempt if it loses.

A straight-up win raises the bankroll to 111, creating a path to 1,500 within the final two spins. Staking only 3 preserves another chance after a loss.

With only two spins left, a straight-up win is necessary to keep the target reachable. Betting all 3 chips would produce 108 on a win, enough to cover two target-reaching straight-up bets on the final spin.

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