Roulette table

A dozen bet offers a 12-in-38 chance to gain 200 chips, making substantial progress toward the 1,500-chip target while retaining bankroll for the remaining spins. All dozens have identical odds on this independent, uniform wheel.

A 100-chip dozen bet offers a 200-chip net gain on a win, making meaningful progress toward the 1,500-chip target while preserving funds for the 18 subsequent spins. Previous outcomes do not affect this spin’s probabilities.

A win adds 700 chips, reaching the 1,500-chip target exactly, while a loss preserves most of the bankroll for the remaining spins. Every pocket is equally likely; previous outcomes do not affect this choice.

Any of these seven pockets takes the bankroll to 1,505, giving a 7/38 chance of reaching the target immediately. A miss leaves 605 chips for the remaining 16 spins; previous outcomes do not affect these odds.

Any of these five pockets brings the bankroll to 1,504 chips, reaching the target without paying for unnecessary overshoot. A miss leaves 460 chips for the remaining 15 spins; all pockets are equally likely.

Any of these five hits raises the bankroll to 1,514, meeting the target immediately with probability 5/38. A miss leaves 290 chips for the remaining 14 spins; all pockets are equally likely.

A 35-chip straight-up win brings the bankroll to 1,515, meeting the target immediately. This is the smallest single straight-up stake that reaches the target while preserving chips for further attempts if it loses.

A 36-chip straight-up win reaches 1,515 chips, meeting the target immediately. This is the smallest stake that can do so in one spin and preserves 219 chips after a loss for further attempts.

A 37-chip straight-up win reaches 1,514 chips, meeting the target immediately. A loss leaves 182 chips for further attempts; every pocket is equally likely.

A 38-chip straight-up win raises the bankroll to 1,512, meeting the target immediately. If it loses, 144 chips remain for further attempts; all pockets are equally likely.

A 39-chip straight-up win reaches 1,509 chips, meeting the target without unnecessary overshoot. A loss leaves 105 chips for further attempts; every pocket is equally likely.

A win brings the bankroll to 1,505 chips, reaching the target with the smallest single-number stake that can do so. A loss leaves 65 chips for further attempts; every pocket is equally likely.

A win brings the bankroll to exactly 1,500 chips, meeting the target immediately. A loss preserves 24 chips for the remaining seven spins; every straight-up number has the same probability.

With only 24 chips and seven spins left, a straight-up win would rebuild the bankroll to 864 and create a viable path to 1,500. Every pocket is equally likely; this wager prioritizes recovery over preserving a bankroll far below the target.

With a bankroll of zero and no legal bets available, skipping is the only legal action.

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

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

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

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

The bankroll is zero and no bets are legal, so I must skip the final spin. The 1,500-chip target is no longer reachable.