Roulette table

I chose a legal action for this decision.

Under the Dubins-Savage theorem for subfair games, reaching the target in a single win minimizes the house edge. A 15-chip straight-up bet pays 525 chips at 35:1, which immediately achieves the 1,500 bankroll target.

I chose a legal action for this decision.

A 15 chip straight-up win pays 525, bringing bankroll from 985 to 1,510 to reach the objective in one spin while minimizing house edge exposure.

I chose a legal action for this decision.

To reach the 1,500 target from 970 within 18 spins, a single straight-up bet of 16 chips reaches 1,530 on a win (35:1 payout), maximizing target probability under the single-bet constraint.

I chose a legal action for this decision.

Spreading 189 chips across 9 straight-up numbers gives a 23.7% chance to hit the 1,500 target immediately on this spin.

I chose a legal action for this decision.

Betting 21 chips on a straight-up number yields a profit of 735 upon winning, reaching the 1,500 chip target immediately while preserving bankroll for future attempts across the remaining 16 spins.

I chose a legal action for this decision.

With a bankroll of 744 and a target of 1500, we need 756 chips. A straight-up bet pays 35:1, so a stake of 22 chips nets 770 chips upon a win (reaching 1514 chips), matching the single-bet optimal policy to reach the target.

I chose a legal action for this decision.

Applying bold play to cover the 778-chip deficit: hitting any of the three straight-up bets pays 24 * 35 - 48 = +792 chips, reaching the 1,500 target immediately while maximizing overall hit probability across available spins.

I chose a legal action for this decision.

With 650 chips and 13 spins remaining to hit 1,500, placing two straight-up bets of 25 chips each reaches exactly 1,500 on a win (850 net profit) while leaving enough bankroll to sustain repeated attempts across future spins.

I chose a legal action for this decision.

With a 900 chip deficit to reach the 1,500 target across 12 remaining spins, betting 26 on a single straight-up number yields 910 profit on a hit, reaching the objective immediately with optimal target probability.

I chose a legal action for this decision.

We need 926 chips to reach 1,500. Betting 31 chips on 6 straight-up numbers yields a net profit of 930 if any hit, reaching the target bankroll immediately while preserving bankroll for multiple attempts.

I chose a legal action for this decision.

We need to gain at least 1,112 chips in 10 spins to reach 1,500. Betting 33 chips on two straight-up numbers hits the 1,500 target on a win while giving multiple opportunities across the remaining spins.

I chose a legal action for this decision.

With 322 chips and 9 spins remaining, staking 35 on a straight-up number yields a net gain of 1,225 on a hit, reaching 1,547. Betting 35 gives 9 full attempts within the remaining bankroll.

I chose a legal action for this decision.

With a current bankroll of 287 and a target of 1500, hitting any 40-chip straight-up bet yields 1,440 chips, bringing the total to 1,527 and hitting the goal immediately with a 5/38 probability.

I chose a legal action for this decision.

Bankroll is currently at 1,527, which already exceeds the target of 1,500. Placing zero bets safely preserves the winning bankroll through the remaining spins.

I chose a legal action for this decision.

Bankroll is 1,527, which already exceeds the target of 1,500; skipping bets preserves the bankroll and guarantees reaching the objective.

I chose a legal action for this decision.

Bankroll is currently at 1,527 chips, which already meets the 1,500 target. Placing no bets preserves the target through the remaining spins.

I chose a legal action for this decision.

Bankroll is currently at 1,527 chips, which exceeds the target of 1,500. Skipping bets preserves the winning total across the remaining spins.

I chose a legal action for this decision.

Bankroll is currently at 1,527, exceeding the target of 1,500. Skipping bets preserves the winning state.

I chose a legal action for this decision.

Bankroll is already above the 1,500 target with 2 spins remaining, so skipping bets guarantees reaching the objective.

I chose a legal action for this decision.

Our current bankroll of 1,527 already exceeds the 1,500 target on the final spin. Placing no bets locks in the objective.