Roulette table

I chose a legal action for this decision.

This stakes 196 chips and reaches exactly 1,500 on any result from 1 through 10, a 10/38 chance. Otherwise, 804 or 816 chips remain for subsequent attempts, with no payout wasted on exceeding the target.

I chose a legal action for this decision.

Any of these seven pockets brings my bankroll to exactly 1,500; a miss leaves 636 chips for the remaining spins. The numbers are interchangeable because every spin is independent and uniform.

I chose a legal action for this decision.

Any of these six equally likely pockets takes the bankroll to 1,506, reaching the target without substantial overshoot. The total stake is 174, leaving 462 and 17 spins if none hits.

I chose a legal action for this decision.

These five straight-up bets give a 5/38 chance of reaching 1,516 chips immediately, while leaving 292 chips if they miss. The numbers are interchangeable on the independent uniform wheel; past outcomes do not influence this choice.

I chose a legal action for this decision.

A 35-chip straight-up win brings the bankroll to 1,517, reaching the target immediately while preserving 257 chips if it loses. All pockets are equally likely; past outcomes do not favor any number.

I chose a legal action for this decision.

A 36-chip straight-up win reaches 1,517 chips, clearing the target with the smallest stake that can do so immediately. A loss leaves 221 chips for further attempts; past outcomes do not affect this spin’s odds.

I chose a legal action for this decision.

A 37-chip straight-up win reaches 1,516 chips, meeting the target without unnecessary overshoot. A loss leaves 184 chips and 13 spins for further attempts; every pocket is equally likely.

I chose a legal action for this decision.

A 38-chip straight-up win raises the bankroll to 1,514, reaching the target with the smallest stake that can do so immediately. A loss leaves 146 chips for further attempts; every pocket is equally likely.

I chose a legal action for this decision.

A 39-chip straight-up win raises the bankroll to 1,511, reaching the target immediately, while a loss leaves 107 chips for further attempts. Every pocket is equally likely; past outcomes do not favor any number.

I chose a legal action for this decision.

A 40-chip straight-up win reaches 1,507 chips, meeting the target immediately, while a loss preserves 67 chips for further attempts. All pockets are equally likely; past outcomes do not favor any number.

I chose a legal action for this decision.

A 41-chip straight-up win reaches 1,502 chips, meeting the target immediately while preserving 26 chips after a loss for the remaining spins. Every pocket is equally likely, regardless of previous outcomes.

I chose a legal action for this decision.

With only 26 chips and nine spins left, a straight-up win would rebuild the bankroll to 936 and leave a path to the 1,500 target. The number choice is arbitrary because every pocket is equally likely.

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 this spin.

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 skipping is the only available action.

I chose a legal action for this decision.

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

I chose a legal action for this decision.

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

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.