Roulette table

This combination reaches exactly 1,500 chips on any of ten pockets, giving a 10/38 chance of securing the target immediately. Otherwise, it preserves at least 804 chips for the remaining 19 spins.

Any of these seven pockets brings the bankroll to exactly 1,500, giving a 7/38 chance of reaching the target immediately. The total stake of 168 preserves 636 chips if none hits, leaving funds for subsequent attempts.

A win adds 875 chips, taking the bankroll to 1,511 and meeting the target immediately. The small stake preserves chips for further attempts if this spin loses; every pocket is equally likely.

Either covered pocket would raise the bankroll to 1,529, meeting the target immediately. The 54-chip total stake preserves enough bankroll for further target-reaching attempts if both bets lose.

A 27-chip straight-up win reaches 1,502 chips, meeting the target without unnecessary overshoot. The small stake preserves bankroll for further attempts if this spin loses; all pockets are equally likely.

A 28-chip straight-up win reaches 1,510 chips, meeting the target immediately. The minimum target-reaching stake preserves enough bankroll for further attempts if this spin loses; every pocket is equally likely.

A 29-chip straight-up win raises the bankroll to 1,517, reaching the target immediately. This is the smallest stake that does so, preserving chips for further attempts if it loses.

A win raises the bankroll to 1,523, reaching the target immediately. The 30-chip stake is the smallest straight-up wager that does so, preserving funds for further attempts if it loses.

Either winning pocket takes the bankroll to 1,531 chips, meeting the target without unnecessary overshoot. The 64-chip total stake preserves 379 chips for further attempts if both bets lose.

Either covered pocket raises the bankroll to 1,501 chips, meeting the target immediately. The 66-chip total stake preserves 313 chips for subsequent attempts if both bets lose.

A 34-chip straight-up win raises the bankroll to 1,503, meeting the target immediately. This is the smallest stake that can do so, preserving chips for further attempts if it loses; all pockets are equally likely.

A 35-chip straight-up win would bring the bankroll to 1,504, reaching the target. This is the smallest stake that can reach the target in one win, preserving chips for further attempts if it loses.

Any of these four hits raises my bankroll to 1,524, clearing the target immediately. If all miss, I retain 84 chips for further attempts; every pocket is equally likely.

A 41-chip straight-up win raises the bankroll to 1,519, reaching the target immediately. A loss leaves 43 chips for another attempt during the remaining spins; all pockets are equally likely.

A hit raises the bankroll to 1,513, reaching the target immediately. Staking 42 rather than all 43 preserves one chip for a remaining attempt if this bet loses.

With one chip and five spins left, a straight-up bet offers a chance to rebuild enough bankroll to pursue the 1,500-chip target. All straight-up numbers have the same probability; past outcomes do not affect this spin.

The bankroll is zero and no legal bets are available, so I must place no bets.

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

The bankroll is zero and no legal bets are available, so I must place no bets.

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