Roulette table

A 100-chip dozen bet offers a 200-chip gain with a 12-in-38 chance, providing meaningful progress toward the target while preserving bankroll for the remaining spins. All dozens have identical odds on this independent, uniform wheel.

Covering eight pockets gives an 8/38 chance of reaching 1,516 chips immediately. If none hits, the remaining 724 chips leave room for further target-sized attempts.

Any of these seven equally likely pockets brings the bankroll to 1,507, immediately reaching the target. The 189-chip total leaves 535 chips and 17 spins to pursue the target if this spin misses.

A 28-chip straight-up win would raise my bankroll to 1,515, reaching the target without unnecessary overshoot. This limits the loss on a miss and preserves chips for further attempts; every pocket is equally likely.

A 29-chip straight-up win raises the bankroll to 1,522, reaching the target immediately. This is the smallest stake that can do so, preserving chips for further attempts if it loses.

Any of these five pockets would bring the bankroll to 1,501, reaching the target with minimal overshoot. A miss leaves 313 chips for further attempts; all pockets are equally likely.

A 34-chip straight-up win raises the bankroll to 1,503, reaching the target immediately while preserving most chips for further attempts if it loses. Every pocket is equally likely, so the choice of 0 carries no predictive advantage.

A 35-chip straight-up win would bring the bankroll to 1,504, reaching the target immediately. This is the smallest single straight-up stake that does so, preserving chips for further attempts if it loses.

Any of these four pockets would raise the bankroll to 1,524 and meet the target immediately. If all miss, 84 chips remain for further attempts.

Either covered pocket finishes with 1,512 chips, reaching the target with probability 2/38. Covering two pockets gives a direct recovery chance without spending chips on winnings that would fall short.

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

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

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.

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 the only available action is to place no bets.

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