Roulette table

I chose a legal action for this decision.

Target of +500 in 20 spins is best pursued with straight-up bets sized so any single hit clears 1500 (34*15=510 >= 500); two numbers per spin spreads the 1000 budget across all 20 spins for roughly a 63% success chance, far better than even-money or dozen grinding.

I chose a legal action for this decision.

Need +530 with 19 spins; a hit on any of 9 straight-up numbers at 20 each nets +520... actually 36*20-180=+540, reaching 1510 in one spin, giving a ~24% chance per spin and a bold-play ladder that outperforms even-money grinding over the remaining spins.

I chose a legal action for this decision.

At 790 needing 1500, even-money grinding has ~25% success; straight-up bets sized so a single hit (23*36=828) clears the target maximize success probability (~50%) by minimizing total house-edge paid across attempts.

I chose a legal action for this decision.

Reaching 1500 from 698 via even-money bets needs an unlikely +5 win streak; a 24-chip straight-up hit nets +816 (to 1514), and two numbers per spin spreads ~30 cheap 1/38 chances across the remaining 17 spins for roughly a 50% target probability.

I chose a legal action for this decision.

Needing +850 in 16 spins, even-money grinding is hopeless; two straight-up bets at 25 each hit 1500 exactly on a win (650-50+900) and leave enough bankroll for ~9 more attempts, maximizing the chance of reaching the target.

I chose a legal action for this decision.

With 600 chips and 15 spins, even-money bets can't realistically climb 900 under the 200 cap; a 27-chip straight-up hit nets 918 which clears the target in one spin, and two numbers per spin at this cost gives roughly a 45% chance of at least one hit before chips run out, better than one number per spin.

I chose a legal action for this decision.

At 546 with 14 spins, even-money grinding to 1500 is nearly hopeless; a 29-chip straight hit (546+34*29=1532) clears the target in one shot, so I spread minimal qualifying stakes across two numbers to maximize the number of winning tickets over the remaining spins.

I chose a legal action for this decision.

At 488 with 13 spins left and a 1500 target, only straight-up hits can realistically get there; 5 numbers at 33 each is the maximum coverage where a single hit (488-165+1188=1511) clears the target, giving ~13% this spin and ~30% over the next three spins.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only finishing above the target matters, so skipping every remaining spin locks in success with zero variance.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target, so any wager only risks dropping below it; skipping every remaining spin locks in success.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only finishing at or above target counts, so any wager only adds downside risk; skipping locks in success.

I chose a legal action for this decision.

Bankroll is already 1511, above the 1500 target; skipping all remaining spins locks in success with zero risk since margin doesn't matter.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target; any wager only risks dropping below it, so skipping is optimal for the remaining spins.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only finishing at or above it counts, so any wager can only risk dropping below; skipping locks in success.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only reaching it counts, so skipping all remaining spins locks in success with zero risk.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only success counts, so betting nothing eliminates any risk of dropping below it.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only success counts, so skipping all remaining spins locks in the objective with zero risk.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target and only finishing above it matters, so any wager adds downside risk with no upside; skipping is the optimal action.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target with two spins left; any wager only adds risk of dropping below the threshold, so skipping is optimal.

I chose a legal action for this decision.

Bankroll of 1511 already exceeds the 1500 target with one spin left, and only reaching the target counts; any bet risks dropping below, so skipping locks in success.