Roulette table

I chose a legal action for this decision.

Reaching +500 needs a big payout, so I'm using straight-up bets of about 40 per number. One hit at that size reaches 1500 while leaving enough bankroll to cover about 23 number-spins, and I'm starting with two numbers to use them all.

I chose a legal action for this decision.

Need +580 from 920 in 19 spins, so I'm spreading straight-up bets (4 x 20) where a single hit pays about +640 net and reaches the target; I'll rescale stakes as the bankroll changes.

I chose a legal action for this decision.

Needing +660 with a 200-chip per-spin cap, eight straight-ups at 24 each (192 total) give a 21% chance that a single hit reaches 1500 (profit 672), which beats grinding outside bets that carry a negative edge.

I chose a legal action for this decision.

Need +852 from 648 with 17 spins left. Six straight-ups at 29 chips each risk 174 and give a win chance of 6/38 (about 16%) per spin, and a single hit pays 870 net, which reaches the 1500 target.

I chose a legal action for this decision.

I need +1026 from 474 with 16 spins left. Five straight-ups at 34 each (170 total) net 1054 if any one hits, which reaches 1500, and that is about a 13% chance per spin.

I chose a legal action for this decision.

Reaching 1500 from 304 needs a straight-up hit, and a 35-chip straight win gets there. I spread 5 numbers at 35 each to maximise hit chance this spin and keep about 129 chips for a follow-up.

I chose a legal action for this decision.

Starting from 129 chips, three straight-up bets of 43 chips each mean any single hit pays 43*36=1548, which reaches the 1500 target. That gives about a 7.9% chance this spin, close to the best available odds of reaching the target.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target, and skipping is allowed with no penalty, so placing no bet preserves the success condition.

I chose a legal action for this decision.

Bankroll of 1548 already meets the 1500 target and every bet has negative expectation on a double-zero wheel, so I skip this spin to avoid risking the target.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target, and skipping is allowed with no penalty. Every bet has negative expected value on a double-zero wheel, so I skip to protect the target.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target, and only reaching the target counts. Every roulette bet has negative expected value, so skipping each remaining spin is the safest way to finish at or above 1500.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target. Skipping is allowed and unpenalised, and every bet has negative expected value, so I place no bet to protect the target.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target, and skipping is allowed, so placing no bet keeps the target secured with no risk.

I chose a legal action for this decision.

Bankroll is 1548, already above the 1500 target, and skipping is allowed with no penalty, so placing no bet keeps the target secured.

I chose a legal action for this decision.

Bankroll is 1548, already above the 1500 target, and every roulette bet has negative expectation, so skipping every spin preserves success.

I chose a legal action for this decision.

Bankroll 1548 already meets the 1,500 target, and only reaching the target counts. Every bet has negative expected value and could drop me below 1,500, so I skip this spin and keep the bankroll.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target, and skipping is allowed with no penalty. Placing no bets locks in success, since any wager only adds risk of dropping below the target.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1,500 target, and only reaching the target counts. Any bet has negative expected value and could drop me below 1,500, so I skip.

I chose a legal action for this decision.

Bankroll is already 1548, above the 1500 target, and skipping is allowed and not penalised. Any bet carries negative expected value and could only lower the chance of finishing at or above 1500, so I place no bet.

I chose a legal action for this decision.

Bankroll is 1548, already above the 1500 target on the final spin, and only reaching the target counts. Skipping keeps the target secured with certainty, while any bet only adds risk.