Roulette table

Even-money grinding to +500 in 20 spins is only ~18% likely, so I use a target-sized straight-up strategy: 16 on each of four numbers nets 560-48=512 on any hit, reaching 1500 in one shot, and the 1000 bankroll sustains ~9 such attempts (~63% cumulative hit chance) with stakes re-sized to the growing shortfall after each miss.

Need +564 to hit 1500; three straight-up bets of 18 pay 648 on a hit (net +594), reaching the target in one spin while keeping per-spin cost low enough to repeat for ~11 spins, giving roughly 59% overall success versus ~25% for even-money grinding.

Need +618 in 18 spins; two straight-up bets of 19 each pay a net +646 on any hit, reaching the target in one spin while keeping cost low enough to sustain ~15 spins of 2/38 chances (~59% overall success), better than even-money grinding or heavier coverage.

Deficit is 656 with 17 spins left; a hit on any of 4 straight-up numbers at 21 nets 672 and clears the target in one spin, while the 84/spin cost keeps me alive for many more attempts, giving a higher cumulative success probability than grinding even-money bets.

Need +740 in 16 spins; even-money grinding at 200/spin needs 10+ wins of 16 (~15%). Instead, straight-up bets sized so any single hit clears 1500 (760-44+792=1508); two numbers per spin keeps the stake minimal while buying ~24 number-spins over the session, roughly 45-50% to hit the target.

Need +784 with 15 spins; a 23-chip straight-up win pays 805 and hits the target in one shot, so spreading minimal-sufficient straight-up stakes across two numbers per spin maximizes the number of 1/38 shots at the goal.

Need +830 in 14 spins with 670 bankroll, so only a straight-up hit can realistically reach 1500; staking 26 on three numbers means any hit lands at 1528 while keeping budget to escalate single-number stakes on later spins, giving roughly a 40%+ overall success chance versus ~30% for a single number.

Need +908 in 13 spins; a 26-chip straight-up hit pays 910 and reaches the target in one go, so spreading ~2 minimal straight-up bets per spin maximizes the chance of at least one hit before the bankroll runs out.

Needing +960 in 12 spins with 540 chips, only a straight-up hit (35:1) can realistically reach 1500; staking 29 on each of two numbers means a hit lands at 1526 while buying ~16 total tickets across the remaining spins instead of 12.

At 482 with 11 spins, only straight-up hits can reach 1500; four numbers at 32 each means any hit (4/38) lands at 1506, while a miss leaves 354 for repeated similar shots over the next spins, giving roughly a 30% overall success chance.

Bankroll is 1506, already above the 1500 target; any bet only risks dropping below it, so skipping (no bet) is optimal for the remaining spins.

Bankroll is 1506, already at or above the 1,500 target; since only reaching the target counts and margin doesn't, any bet risks dropping below it with negative EV, so skipping is optimal.

Bankroll is 1506, already above the 1500 target; since only reaching the target counts and skipping is allowed, the optimal policy is to place no bets and lock in the result.

Bankroll is 1506, already above the 1500 target; skipping all remaining spins locks in success since only reaching the target counts and skipping is not penalised.

Bankroll is 1506, already above the 1,500 target; skipping all remaining spins locks in success since any bet only risks dropping below the threshold with no reward for margin.

Bankroll is 1506, already above the 1500 target; any bet only risks dropping below it, so skipping is optimal.

Bankroll is 1506, already above the 1500 target; skipping is allowed and not penalised, so betting nothing locks in the objective with zero risk.

Bankroll of 1506 already exceeds the 1500 target and only reaching it matters, so any bet can only risk dropping below; skipping locks in success.

Bankroll 1506 already exceeds the 1500 target with 2 spins left; any bet risks dropping below target, so skipping (not penalised) locks in success.

Bankroll of 1506 already meets the 1500 target on the final spin; any wager only risks falling below the threshold with no upside since margin doesn't count, so I skip.