Roulette table

I chose a legal action for this decision.

Covering ten pockets gives a 10/38 chance of reaching 1,520 chips immediately, while a miss leaves 800 chips for subsequent attempts. The chosen pockets are arbitrary because spins are independent and uniform.

I chose a legal action for this decision.

Covering eight pockets gives an 8/38 chance of reaching exactly 1,500 chips this spin; otherwise, 600 chips remain for subsequent attempts. The selected pockets are arbitrary because spins are independent and uniformly distributed.

I chose a legal action for this decision.

A win reaches 1,510 chips, clearing the target; a loss leaves 574 chips and 17 spins for further attempts. Every pocket is equally likely, so previous outcomes do not affect this choice.

I chose a legal action for this decision.

A 27-chip straight-up win raises my bankroll to 1,519, reaching the target while preserving chips for further attempts if it loses. Every pocket is equally likely; previous outcomes do not affect this choice.

I chose a legal action for this decision.

A 28-chip straight-up win reaches 1,527 chips, clearing the target while preserving most of my bankroll after a loss. Every pocket is equally likely; previous outcomes do not favor any number.

I chose a legal action for this decision.

A win raises my bankroll to 1,534, clearing the target, while a loss preserves 490 chips for further attempts. Every pocket is equally likely, so past outcomes do not influence this choice.

I chose a legal action for this decision.

A 29-chip straight-up win would raise my bankroll to 1,505, reaching the target with minimal overshoot while preserving chips for later attempts. Each pocket is equally likely, so past outcomes do not affect this choice.

I chose a legal action for this decision.

A 30-chip straight-up win brings my bankroll to 1,511, meeting the target without unnecessary overshoot. Keeping the stake small preserves funds for further attempts; every pocket has the same independent probability.

I chose a legal action for this decision.

A 31-chip straight-up win brings my bankroll to 1,516, reaching the target immediately while preserving chips for further attempts if it loses. All pockets are equally likely, so past outcomes do not influence the choice of number.

I chose a legal action for this decision.

A 32-chip straight-up win raises my bankroll to 1,520, meeting the target immediately while preserving most of my bankroll for further attempts if it loses. Each pocket is equally likely, regardless of previous results.

I chose a legal action for this decision.

A 33-chip straight-up win brings my bankroll to 1,523, reaching the target immediately while preserving 335 chips if it loses. Every pocket is equally likely, so previous outcomes do not influence the choice of number.

I chose a legal action for this decision.

A 34-chip straight-up win raises my bankroll to 1,525, meeting the target immediately while preserving chips for further attempts if it loses. Every pocket is equally likely, so previous outcomes do not affect this choice.

I chose a legal action for this decision.

A 35-chip straight-up win raises my bankroll to 1,526, reaching the target immediately while preserving 266 chips if it loses. Every pocket is equally likely, so past outcomes do not affect the choice.

I chose a legal action for this decision.

Any of these five equally likely pockets would bring my bankroll to 1,506, meeting the target immediately. A loss leaves 66 chips and six spins for another attempt.

I chose a legal action for this decision.

A small straight-up bet preserves enough bankroll for a later target-reaching attempt; a win raises the bankroll to 206, enabling several such attempts. All pockets are equally likely, so past outcomes do not influence the number choice.

I chose a legal action for this decision.

A 42-chip straight-up win raises my bankroll to 1,532, meeting the target immediately. This is the smallest stake that does so, preserving 20 chips for further attempts if it loses; every pocket is equally likely.

I chose a legal action for this decision.

With four spins left, a dozen win raises my bankroll to 56, enough for a straight-up attempt to reach 1,500 while retaining a recovery path after a miss. Keeping 2 chips also preserves a small chance of recovery if this bet loses; past outcomes do not affect the odds.

I chose a legal action for this decision.

With only three spins left and two chips, a straight-up win provides the bankroll needed for a possible recovery to 1,500. All pockets are equally likely; past outcomes do not favor any number.

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 the final spin. The 1,500-chip target is no longer reachable.