Roulette table

Ten straight-ups at 20 each use the full 200 limit. A hit nets +520 and reaches 1500 immediately, with about a 26% chance per spin, which is far better odds of reaching the target than outside bets.

A single straight hit at 21 chips pays 735, which covers the net 700 needed to reach 1500 even after the other 21-chip bet is lost. Two numbers per spin with minimal stake gives the best chance of reaching the target over the remaining spins.

Need +742 from 758 in 18 spins, so I spread straight-up bets sized so a single hit reaches 1500 (31*24=744 net) while keeping enough bankroll for several more tries.

Reaching 1500 from 638 needs about +862, so I use two straight-ups at 26 each. One hit pays 910 and loses 26 on the other number, for a net of +884 and a bankroll of 1522, while a miss costs only 52 and keeps later spins available.

Reaching 1500 needs +914 in 16 spins, so I'm using four straight-up bets of 29 chips. If one hits, the net win is 928 (1015 payout minus the other three stakes), enough to reach the target, and the 116 chips per spin allows about five attempts.

Reaching 1500 needs +1030, and a 30-chip straight-up bet pays 1050 on a hit, which does it. With 470 chips I can afford about 15 such bets, one per remaining spin, which maximizes the chance of hitting at least once.

Needing 1060 more chips, only a straight-up hit can reach the target. Five straights at 35 each (175 total) mean any single hit takes the bankroll to at least 1500, with about 13% chance per spin.

Reaching 1500 from 265 needs about +1235, so only a 35:1 straight hit can do it. A 36-chip stake on a straight pays enough to reach the target, and covering five numbers at once gives about 13% this spin while leaving 85 chips for a later attempt.

With 85 chips, reaching 1500 needs a straight-up hit. Two straights at 42 each (84 total) double the hit chance this spin, and either one pays enough to clear 1500.

With a bankroll of 1 and a target of 1500, the target is nearly unreachable. The highest-variance bet, a 1-chip straight-up at 35:1, gives the best chance of growing the bankroll.

Bankroll is 0 and no legal bet ids or stake are available (max_total_stake is 0), so the only legal action is to place no bets.

Bankroll is 0 and legal_bet_ids is empty with max total stake 0, so no bet is legal; placing no bet is the only valid action.

Bankroll is 0 and legal_bet_ids is empty with max_total_stake 0, so no bet is legal; the only valid action is to place no bets.

Bankroll is 0 and max stake is 0 with no legal bet IDs, so the only legal action is to place no bet.

Bankroll is 0 and no bet ids are legal (max stake 0), so the only legal action is to place no bets.

Bankroll is 0 and legal_bet_ids is empty with max total stake 0, so no bet is legal; the only valid action is to place no bets.

Bankroll is 0 and legal_bet_ids is empty with max total stake 0, so no bet is legal; the only valid action is to place no bets.

Bankroll is 0 and legal_bet_ids is empty with max_total_stake 0, so no bet is possible; the fallback is no_bet and an empty bet list is the only legal action.

Bankroll is 0 and legal_bet_ids is empty with max total stake 0, so no bet is legal; the only valid action is to place no bets.

Bankroll is 0 and no legal bet ids or stake are available (max_total_stake is 0), so the only legal action is to place no bets.