Roulette table

With 20 spins available and a 500-chip gap, a 100-chip dozen bet offers a 200-chip gain while preserving 900 chips if it loses. This balances progress toward the target with room for subsequent attempts.

A winning dozen bet brings the bankroll to 1,400, leaving just 100 chips to reach the target, while a loss costs 100 with 18 spins left to recover. Previous outcomes do not affect this spin’s odds.

A 100-chip dozen bet offers a 200-chip gain toward the 400-chip shortfall while retaining room to recover after a loss. With 18 spins remaining, this balances progress toward the target against bankroll preservation.

Covering eight pockets gives an 8/38 chance of reaching 1,504 chips immediately, with little wasted overshoot. A miss leaves 856 chips and 16 spins for further attempts.

Covering eight pockets gives an 8/38 chance of reaching exactly 1,500 chips this spin, with no wasted overshoot. A miss leaves 672 chips and 15 spins to pursue the target.

Any of these four pockets brings the bankroll to 1,504, just above the target. The 104-chip total stake gives a 4/38 chance of reaching the goal immediately while leaving 568 chips for further attempts if it misses.

A 27-chip straight-up win reaches 1,513 chips, clearing the target without paying for unnecessary overshoot. The small stake preserves bankroll for further attempts if this spin loses; every pocket is equally likely.

Any of these six equally likely pockets leaves 1,501 chips, immediately reaching the target. The 192-chip total stake preserves 349 chips for further attempts if none hits.

Any of these four pockets brings the bankroll to 1,501, reaching the target immediately with probability 4/38. A miss leaves 205 chips for further attempts during the remaining spins.

A 37-chip straight-up win reaches exactly 1,500 chips, while a loss leaves 168 chips for further attempts. Every pocket is equally likely; past results do not affect this choice.

A 39-chip straight-up win reaches 1,533 chips, clearing the target immediately. This is the smallest stake that can do so in one spin, while leaving 129 chips for further attempts if it loses.

Any of these three equally likely pockets would bring the bankroll to 1,515, meeting the target immediately. This gives a 3/38 immediate success chance while retaining 3 chips if all three miss.

With only 3 chips and eight spins remaining, a straight-up win would raise the bankroll to 108 and preserve a possible route to 1,500. This risks elimination, but smaller-payout bets offer little scope to reach the target in time.

With a zero bankroll 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 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 legal bets are available, so 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 I must skip the final spin.