Roulette table

With a 500-chip deficit to the 1500 target and only 200 total stake allowed per spin, spreading 20 chips across 10 distinct numbers maximizes the count of winning outcomes (10/38) that each individually pay enough (35x20-200=500) to hit the target in one spin, which is the mathematically optimal single-spin coverage given the stake caps.

Need +700 to hit 1500; a 20-chip straight-up bet pays 35:1, exactly reaching 1500 on a win while risking only 20 chips, preserving bankroll for future spins if it misses.

With bankroll 780 and target 1500, a single straight-up hit at 35:1 needs only ceil((1500-780)/35)=21 chips staked to instantly reach the goal if it lands, while risking minimal capital each spin; this maximizes the probability of hitting the target across the remaining 16 spins given the per-bet stake cap.

With a large distance to the 1500 target and 15 spins left, the sub-fair house edge means grinding even-money bets is unlikely to get there; the mathematically sound approach is a bold, low-probability, high-payout single-number bet sized just enough (22 chips on 35:1 payout) to hit the target exactly if it wins, while preserving most of the bankroll for future attempts if it misses.

With 737 chips and 13 spins left, only a straight-up bet's 35:1 payout can close the 763-chip gap to the 1500 target in a single spin; staking the minimal 22 chips needed (737-22+22*36=1507) preserves bankroll for future attempts if this spin misses, mirroring the bold-play optimal single-bet policy.

With 715 chips and only 11 spins left, I need a single big win to reach 1500; spreading 196 chips across 7 straight-up numbers gives a ~18% per-spin hit chance and a payout of 36×28=1008 (net +812) if any hits, enough to clear the target while keeping total stake within the 200 cap.

With 519 chips and 10 spins left needing 1500, I spread near-max total stake across six straight-up numbers sized so any single hit (36x payout) pushes bankroll past the target immediately, maximizing per-spin success probability while staying within the 200-chip cap.

With only 9 spins left and needing to reach 1500 from 321, bold-play theory (Dubins-Savage) says the optimal sub-fair-game strategy is to bet the minimum straight-up stake that reaches the target immediately if it hits; 34 chips on a single number yields 321-34+34*36=1511 on a win, satisfying the goal in one spin, while preserving remaining bankroll for further bold bets if it misses.

With only 7 spins left and a bankroll of 287, no low-payout bet can reach 1500 in one spin due to the 100-chip cap; a straight-up bet at 35:1 can. Betting the minimum stake (35) that, if hit, pushes bankroll to at least 1500 preserves the rest of the bankroll for future attempts if this spin misses, following the bold-play principle for sub-fair games.

With only 252 chips and 6 spins left, the target of 1500 can only be reached via a high-multiplier straight-up hit; spreading the max 200-chip stake across 4 numbers at 50 each guarantees that any single hit (payout 36x) pushes bankroll to about 1852, clearing the target, while maximizing hit probability to ~10.5% this spin.

With only 52 chips and 4 spins left, the only path to 1500 is a high-variance straight-up bet (35:1); a single hit already exceeds the target, so I'm going all-in on one number.

Bankroll is 0 and no legal bets are available (max stake per bet and total stake are both 0), so no wager can be placed this spin.

Bankroll is 0 and no legal bets are available (max_total_stake is 0), so no wager can be placed this spin.

Bankroll is 0 and no legal bets are available (max stake and legal bet list are empty), so no action can be taken on this final spin.