Roulette table

I chose a legal action for this decision.

Reaching 1500 requires +500; betting two straight-ups sized so any hit clears the target (1000-30+540=1510) and repeating with stakes growing to cover prior losses gives ~64% success over 20 spins, far better than even-money grinding.

I chose a legal action for this decision.

Need +530 with 19 spins left; even-money bets can't close that gap reliably, so I buy five straight-up numbers at 18 each (any hit nets 18*31=558, clearing the target) while keeping budget to repeat this across many spins for a higher cumulative hit chance.

I chose a legal action for this decision.

Reaching 1500 from 880 in 18 spins is far more likely via straight-up shots than even-money grinds; 19 on each of three numbers is the cheapest per-shot stake that still clears 1500 on a hit (880-57+19*36=1507), maximizing total shots over the session.

I chose a legal action for this decision.

Need +677 with 17 spins; three straight-ups at 21 each yield net +693 on any hit (reaching 1516), and this sizing lets the bankroll fund ~9 such spins, giving roughly 52% success versus ~36% for single-number or even-money grinding.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only finishing above the target counts, so the optimal action is to place no bets and lock in the result for the remaining spins.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only reaching it counts; any bet has negative expectation and risks dropping below target, so skipping is optimal.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only finishing above it counts, so any further wager adds only downside risk; skipping locks in success.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only finishing at or above target counts, so the optimal policy is to place no further bets and lock in the result.

I chose a legal action for this decision.

Bankroll is already above the 1,500 target and only finishing at or above it counts, so skipping every remaining spin locks in success with zero variance.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only finishing above it counts, so any wager adds downside risk with no benefit; skipping locks in success.

I chose a legal action for this decision.

Bankroll is already above the 1,500 target with 10 spins left; skipping is allowed and locks in success, while any bet only adds downside risk.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target; any wager only risks dropping below it, so the optimal action is to skip and preserve the result.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target with 8 spins left; every bet has negative expectation and only risks dropping below target, so skipping is optimal.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only finishing above target counts, so skipping all remaining spins locks in success with zero variance.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target and only finishing above it counts, so any bet introduces downside with no upside; skipping locks in success.

I chose a legal action for this decision.

Bankroll is 1516, already above the 1500 target; only reaching the target counts, so skipping all remaining spins guarantees success while any bet risks dropping below.

I chose a legal action for this decision.

Bankroll is already 1516, above the 1500 target; skipping is allowed and unpenalised, so any bet only risks dropping below target with no upside.

I chose a legal action for this decision.

Bankroll of 1516 already exceeds the 1500 target with 3 spins left; any wager only risks dropping below it, so the optimal action is to not bet.

I chose a legal action for this decision.

Bankroll 1516 already exceeds the 1500 target with 2 spins left; any bet risks dropping below target while margin gives no credit, so skipping is optimal.

I chose a legal action for this decision.

Bankroll is already above the 1,500 target with one spin left and margin doesn't count, so any wager only adds downside risk; skipping locks in the win.