Roulette table

Any of these eight pockets reaches 1,504 chips immediately, giving an 8/38 chance of reaching the target this spin. The 144-chip total stake preserves 856 chips for subsequent attempts if none hits.

These bets give an 8-in-38 chance of reaching exactly 1,500 chips this spin, with no wasted overshoot. A miss leaves 672 chips and 18 spins for further attempts.

A hit raises the bankroll to 1,512, meeting the target with the smallest sufficient straight-up stake. A miss preserves 648 chips for the remaining 17 spins; every pocket is equally likely.

A hit raises the bankroll to 1,523, clearing the target, while a miss costs only 25 chips and preserves funds for further attempts. Every pocket is equally likely, so previous outcomes do not affect this choice.

Either hit brings the bankroll to 1,507 chips, just above the target. The combined 52-chip stake covers two equally likely pockets while preserving 571 chips for later attempts if both miss.

A 27-chip straight-up win brings the bankroll to 1,516, reaching the target without excessive overshoot. This small stake preserves funds for further attempts if it loses; every pocket is equally likely.

Either covered pocket reaches 1,530 chips, satisfying the target without excessive overshoot. If both miss, the remaining 486 chips can fund target-reaching straight-up attempts on all 13 remaining spins.

A win raises the bankroll to 1,501, meeting the target with the smallest possible straight-up stake. A loss preserves 457 chips for further attempts; every pocket is equally likely.

Any of these five pockets brings the bankroll to 1,511, reaching the target with a 5/38 chance this spin. A miss leaves 287 chips for further attempts; past outcomes do not affect these probabilities.

Any of these four pockets brings the bankroll to 1,503, reaching the target immediately. A miss leaves 135 chips for the remaining ten spins; previous outcomes do not affect the odds.

A 39-chip straight-up win reaches exactly 1,500 chips, while a loss leaves 96 chips for further attempts. This is the smallest single straight-up stake that reaches the target immediately.

A hit brings the bankroll to 1,531 chips, reaching the target immediately. This is the smallest straight-up stake that does so, preserving 55 chips for later attempts if it misses.

A 42-chip straight-up win raises the bankroll to 1,525, immediately reaching the target. This is the smallest stake that can do so in one spin, while preserving 13 chips for another attempt if it loses.

With 13 chips and seven spins left, reaching 1,500 requires high-payout wins. A 2-chip straight-up bet would raise the bankroll to 83 on a hit while preserving 11 chips for further attempts if it misses.

A hit raises the bankroll to 221, enough to fund five subsequent straight-up attempts to reach 1,500. A miss preserves 5 chips for another recovery attempt; every pocket is equally likely.

With only 5 chips and five spins left, a straight-up win would raise the bankroll to 180 and leave four spins to pursue the 1,500-chip target. Smaller-payout bets cannot build the bankroll quickly enough without several additional wins.

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

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