Roulette table

This risks 144 chips for an 8-in-38 chance of reaching 1,504 immediately, just above the target. A miss leaves 856 chips and 19 spins for further attempts; the chosen numbers have no predictive significance.

These bets give an 8-in-38 chance of reaching exactly 1,500 chips this spin. The total stake is 184 chips, leaving 672 and 18 spins to pursue the target if none hits.

Any of these six pockets brings the bankroll to 1,512, reaching the target with a 6/38 chance this spin. The total stake is 168, leaving 504 chips if all six miss.

A 29-chip straight-up win raises the bankroll to 1,519, reaching the target with the smallest stake that can do so immediately. A loss leaves 475 chips for the remaining spins; every pocket has the same independent chance.

A 30-chip straight-up win raises the bankroll to 1,525, reaching the target immediately. This is the smallest straight-up stake that does so, preserving chips for further attempts if it loses.

A 31-chip straight-up win raises the bankroll to 1,530, reaching the target immediately. This is the smallest straight-up stake that does so, preserving chips for further attempts if it loses.

A 32-chip straight-up win reaches 1,534 chips, meeting the target immediately. This is the smallest straight-up stake that does so, preserving chips for later attempts if it loses.

A 32-chip straight-up win raises the bankroll to 1,502, reaching the target immediately. This is the smallest stake that can do so, preserving chips for further attempts if it loses.

A 33-chip straight-up win raises the bankroll to 1,505, reaching the target immediately. This is the smallest stake that can do so and preserves 317 chips for further attempts if it loses.

A win raises the bankroll to 1,507, meeting the target. This is the smallest straight-up stake that reaches the goal immediately, preserving chips for further attempts if it loses.

A 35-chip straight-up win raises the bankroll to 1,508, reaching the target immediately. This is the smallest stake that can do so on one number, preserving 248 chips for further attempts if it loses.

A hit raises the bankroll to 598, improving the chance of reaching 1,500 over the remaining spins. A miss leaves 238 chips, enough for six successive target-reaching straight-up attempts with appropriately adjusted stakes.

A 37-chip straight-up win takes the bankroll to 1,533, reaching the target without unnecessary overshoot. A loss leaves 201 chips for further attempts with seven spins remaining.

A 38-chip straight-up win reaches 1,531 chips, clearing the target immediately. This is the smallest stake that does so, preserving 163 chips for further attempts if it loses.

A 39-chip straight-up win reaches 1,528 chips, clearing the target immediately. If it misses, the remaining 124 chips can fund three further target-reaching straight-up attempts.

A 1-chip straight-up bet offers upside while preserving enough bankroll, even after a loss, for three subsequent straight-up attempts that could each reach 1,500. With five spins remaining, this uses the spare chip without sacrificing those chances.

A hit reaches 1,523 chips, clearing the target immediately. A miss leaves 83 chips, enough for two further straight-up attempts sized to reach the target.

A hit reaches 1,518 chips and secures the target. A miss leaves 42 chips, enough for another straight-up attempt that would also reach the target.

A winning 42-chip straight-up bet yields 1,512 chips, immediately reaching the target with probability 1/38. With only two spins remaining, this avoids needing multiple wins to qualify.

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