Roulette table

Two straight-up bets of 15 each: a hit nets +510 and reaches the 1500 target in one spin, while the low cost (30/spin) keeps this 2/38-per-spin shot sustainable across all 20 spins for roughly a 65% overall success chance, near the fair-game bound.

Need +530 with 19 spins left; even-money grinding at the 200 cap only reaches +3 net wins ~30% of the time, whereas repeated small straight-up bets sized so a single hit clears 1500 (35*17-34=+561) give roughly 60% cumulative hit probability over the affordable spins.

Deficit is 581; two straight-up bets at 18 each net +612 on a hit (reaching 1531) while costing only 36 per spin, so this can be sustained for ~15 spins at 2/38 per spin, giving a higher overall chance of crossing 1500 than even-money grinding or a single straight bet.

Need +617 in 17 spins; three straight-up bets at 19 each is the minimum stake where a single hit reaches 1500 (883-57+684=1510), and the bankroll sustains ~10 such attempts for roughly a 56% chance of success, better than even-money or single-number plans.

Need +674 with 16 spins left; covering 8 numbers at 25 each gives a 21% chance per spin to jump straight to 1526 (25*35 - 175 = +700), and this ladder of straight-up coverage over the next few spins gives roughly a 48% overall chance of hitting the target, better than grinding even-money bets.

Need +874 in 15 spins; only a straight-up hit can reach 1500. Staking 44 per spin on one number gives 14 independent 1/38 chances (~31%) where any hit clears the target, better than larger stakes with fewer spins.

Need +918 with 14 spins left; only straight-up hits can realistically get there. 27 on a number pays 945 net, so one hit from two numbers lands exactly on 1500 while keeping enough bankroll to repeat sized bets for many more spins.

Need +972 with 13 spins left; a 28-chip straight-up win pays 980, reaching exactly 1508. Single-number bets sized to just clear the target are the cheapest per trial, letting me take one shot each spin and keep bankroll for later attempts (ending with a multi-number shot).

Needing +1000 in 12 spins, even-money bets are near hopeless (~5%), so I use straight-up bets sized so any single hit (30x35=1050) clears the 1500 target, spreading two numbers per spin to maximize independent hit chances (~30% overall) within the bankroll.

At 440 with 11 spins left, only a straight-up hit can reach 1500; staking 44 per number lets me buy 10 independent 1/38 shots (any hit lands at least 1584), maximizing the chance of hitting the target versus fewer larger stakes.

At 264 chips needing 1500 with 10 spins left, only straight-up hits can reach the target; 40 on a number returns 1440 net which clears 1500, so five 40-chip tickets maximize hit probability this spin while leaving 64 for one more ticket next spin.

At 64 chips with 9 spins left, only a straight-up hit can reach 1500; a 42-chip stake is the minimum that gets there in one hit (64+35*42=1534), while keeping 22 chips for another two-hit attempt if it misses.

With 22 chips and 8 spins left, only straight-up hits can reach 1500; spreading 21 chips over three numbers gives a 3/38 shot at ~253 chips, from which repeated 42-chip straight bets can still close the gap in one hit.

With 1 chip and 7 spins left, the only path to 1500 is a chain of straight-up hits (1→36→1296→beyond), so I bet the single chip on a straight-up number; every pocket is equally likely.

Bankroll is 0 and no legal bet ids are available, so the only legal action is to place no bets.

Bankroll is 0 and no legal bet ids are available, so the only legal action is to place no bets.

Bankroll is 0 and there are no legal bet ids with max total stake 0, so no bet is possible; skipping is the only legal action.

Bankroll is 0 and no legal bet ids are available, so the only legal action is to place no bets.

Bankroll is 0 and there are no legal bet ids or stake capacity, so the only legal action is to place no bets.

Bankroll is 0 and no legal bet ids are available, so the only legal action is to place no bets.