Roulette table

I chose a legal action for this decision.

Using bold-play logic: since we only need to reach 1500 (not exceed it) within 20 spins, the most capital-efficient path is to bet the minimum straight-up stake (15) that would push bankroll to 1525 if it hits (35:1), preserving the rest of my bankroll for future spins if this one misses.

I chose a legal action for this decision.

I chose a legal action for this decision.

Bold-play strategy: with 18 spins left and a 985→1500 gap, the regret-minimizing single-bet is a straight-up bet sized just enough (stake=ceil(515/35)=15) so a win jumps the bankroll past 1500 in one spin, maximizing hit probability each round.

I chose a legal action for this decision.

I chose a legal action for this decision.

With the 200-chip per-spin cap, covering two dozens (63% win chance, 2:1 payout) gives steady modest gains with limited downside, a reasonable step toward the 1500 target given the exhibition round isn't scored.

I chose a legal action for this decision.

With bankroll 1070 and 15 spins left, the bold-play approach (max payout bet sized to just clear the 1500 target in one hit) minimizes the number of trials needed, which maximizes the probability of reaching the goal under house-edge conditions; a stake of 13 on a single number nets 455 chips if hit, pushing bankroll to 1525.

I chose a legal action for this decision.

I chose a legal action for this decision.

With 1057 chips and only 13 spins left to reach 1500, I need variance rather than safe small gains; a 2:1 dozen bet at the maximum single-bet stake maximizes potential upside per spin while staying within per-bet limits, giving a reasonable shot at a big jump toward the target without over-committing total bankroll in one spin.

I chose a legal action for this decision.

With 957 chips and a 1500 target in 12 spins, a single outside-bet win can't reach the goal, so I size nine straight-up bets at 21 each (189 total, within the 200 cap) so that any single hit yields a net gain of 567, pushing bankroll to 1524 and clearing the target in one spin, while covering ~24% of outcomes to maximize hit probability given the stake limits.

I chose a legal action for this decision.

Bold-play optimal for a sub-fair reach-target game: the minimal stake on a 35:1 straight bet that, if it hits, pushes bankroll (768) to or past the 1500 target is ceil(732/35)=21 chips, maximizing the chance of winning outright this spin while risking only a small fraction of bankroll if it misses.

I chose a legal action for this decision.

With 747 chips and 10 spins left, I need a 753-chip jump; splitting the max allowed 182-stake across 7 straight-up numbers at 26 each guarantees that any single hit (net profit 754) pushes me past the 1500 target, while maximizing hit probability (7/38) within the per-spin budget cap.

I chose a legal action for this decision.

With only 9 spins left and a 565→1500 gap, I covered 6 numbers at 32 chips each (192 total) so that any single hit yields a 960-chip profit, pushing bankroll just past the 1500 target in one shot; this maximizes hit probability (6/38) while still satisfying the required payoff threshold under the 100/200 stake caps.

I chose a legal action for this decision.

I chose a legal action for this decision.

With only 7 spins left and a 373→1500 target, outside bets can't close the gap fast enough; doubling up on two straight-up numbers (max 100 each, 200 total) maximizes the chance of a 35:1 hit big enough to vault past the target while staying within per-spin stake caps.

I chose a legal action for this decision.

With only 6 spins left and a target of 1500 from 173, bold-play theory (Dubins-Savage) says to use the highest-payout bet (straight-up 35:1) and wager just enough to reach the goal if it hits, minimizing exposure to the house edge; s=ceil((1500-173)/35)=38 achieves that while preserving remaining bankroll if it misses.

I chose a legal action for this decision.

With only 5 spins left and 135 chips, bold-play theory says bet the minimal amount on the highest-payout bet (straight-up, 35:1) needed to exactly reach the 1500 target if it hits: stake=ceil((1500-135)/35)=39, which yields bankroll=1500 on a win while preserving remaining chips (96) for further attempts if it misses.

I chose a legal action for this decision.

I chose a legal action for this decision.

I chose a legal action for this decision.

I chose a legal action for this decision.

Only a 35:1 straight-up bet can possibly reach the 1500 target from 96 chips with one spin left; betting the max allowed stake on a single number maximizes the tiny chance of success.