Roulette table

I chose a legal action for this decision.

These bets risk 144 chips and reach 1,504 if any of eight covered pockets hits, giving an 8/38 chance of reaching the target immediately. A miss leaves 856 chips for the remaining 19 spins.

I chose a legal action for this decision.

These eight bets give an 8/38 chance of reaching exactly 1,500 chips this spin, while a miss leaves 672 chips for the remaining 18 spins. Every pocket is equally likely; past outcomes do not affect this choice.

I chose a legal action for this decision.

A winning dozen bet would raise the bankroll to 872, making progress toward 1,500 while preserving funds for the remaining spins if it loses. Every dozen has the same probability; past outcomes do not affect this choice.

I chose a legal action for this decision.

Covering eight pockets gives an 8/38 chance of reaching 1,516 chips immediately, while retaining 688 chips if all miss. The pocket choices are arbitrary because spins are independent and uniform.

I chose a legal action for this decision.

These bets give a 7/38 chance of reaching exactly 1,500 chips this spin, with no unnecessary overshoot. A miss leaves 492 chips and 15 spins to continue pursuing the target; previous outcomes do not affect the odds.

I chose a legal action for this decision.

A 29-chip straight-up win raises my bankroll to 1,507, meeting the target with minimal overshoot. A loss leaves 463 chips for further attempts; all pockets are equally likely regardless of past results.

I chose a legal action for this decision.

A 30-chip straight-up win would raise my bankroll to 1,513, reaching the target with minimal overshoot. This limits the cost of a miss and preserves chips for later attempts; every pocket is equally likely.

I chose a legal action for this decision.

A 31-chip straight-up win raises the bankroll to 1,518, meeting the target, while a loss leaves 402 chips for the remaining spins. Every pocket is equally likely; past results do not affect this choice.

I chose a legal action for this decision.

A 32-chip straight-up win would bring the bankroll to 1,522, reaching the target immediately while preserving 370 chips after a loss. Every pocket is equally likely; prior outcomes do not affect this choice.

I chose a legal action for this decision.

Any of these four pockets brings the bankroll to 1,522, meeting the target immediately; a miss leaves 226 chips for the remaining ten spins. The selected pockets are equally likely, regardless of previous outcomes.

I chose a legal action for this decision.

Any of these three pockets brings my bankroll to 1,513, meeting the target immediately. A miss leaves 109 chips for further attempts; all pockets are equally likely regardless of past results.

I chose a legal action for this decision.

A 40-chip straight-up win brings the bankroll to 1,509, meeting the target with the smallest stake that can do so immediately. A loss leaves 69 chips for the remaining eight spins; every pocket is equally likely.

I chose a legal action for this decision.

A hit raises the bankroll to 279, enough to fund several subsequent attempts to reach 1,500; a miss preserves 63 with seven spins left. The pocket choice is arbitrary because spins are independent and uniform.

I chose a legal action for this decision.

A 21-chip even-money bet leaves either 42 or 84 chips, preserving one or two target-reaching straight-up attempts within the remaining spins. Past outcomes do not affect the odds.

I chose a legal action for this decision.

Either covered pocket returns 1,512 chips, reaching the target with a combined probability of 2/38. This risks the remaining bankroll without paying for an unnecessary margin above the target.

I chose a legal action for this decision.

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

I chose a legal action for this decision.

With no chips remaining and no legal bets available, skipping is the only legal action.

I chose a legal action for this decision.

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

I chose a legal action for this decision.

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

I chose a legal action for this decision.

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