Roulette table

I chose a legal action for this decision.

Bold-play under the 200/spin cap: 13 straight-ups at 15 each (195 total) gives a 13/38 chance to jump from 1000 to 1525 in one spin, which beats grinding even-money bets; if it misses I re-size stakes so any single hit still clears 1500.

I chose a legal action for this decision.

Reaching 1500 from 805 in 19 spins requires high variance; a 21-chip straight-up hit nets 1519 even after the other number loses, and spreading two numbers per spin uses the bankroll over ~13 spins for roughly a 50% chance of at least one hit, better than one number per spin.

I chose a legal action for this decision.

Need +737 in 18 spins; outside bets cannot realistically get there, so a single straight-up hit at 22 chips (net +748 with two numbers covered) reaches the target, and spreading 44 chips per spin across two numbers maximizes total number-spins over the remaining bankroll (~47% overall success).

I chose a legal action for this decision.

From 719 I need +781; a straight-up hit at 23 chips with two numbers covered returns 719-46+828=1501, exactly reaching the target, so I take many cheap 1/19-per-spin shots rather than grinding even-money bets that require ~4 net wins.

I chose a legal action for this decision.

Need +827 in 16 spins with a 200 cap per spin, so even-money grinding is unlikely to reach 1500; a straight-up hit at 33 chips nets 990 and clears the target in one spin, and covering 6 numbers gives ~15.8% per spin while leaving bankroll for two more similar shots.

I chose a legal action for this decision.

At 475 with 15 spins left, even-money grinding almost never reaches 1500; 35 on each of 5 numbers (175 total) hits the target in one spin on any hit (35*35+300=1525), giving ~13% this spin and a structured ~28% path over the next few spins.

I chose a legal action for this decision.

At 300 chips needing 1500 with 14 spins left, only a straight-up hit can realistically reach the target; 5 numbers at 40 each is the widest coverage (5/38) where a single hit (+1400-160=+1240) still clears 1500, leaving 100 for one more 2-number shot if it misses.

I chose a legal action for this decision.

With 100 chips and 1500 target, only straight-up hits can get there; 42 on a straight number (win = 1512) plus 58 on a column not containing it (win = 174, enabling four more qualifying straight shots) maximizes the probability of reaching the target versus a single 100-chip straight bet.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target and only finishing above target counts, so skipping (allowed, not penalised) locks in success with zero variance.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target; every bet has negative expectation and only adds risk of dropping below the threshold, so skipping is optimal.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target with 10 spins left; any bet only risks falling below the threshold, so skipping maximizes success probability.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target and only reaching the target counts, so the optimal policy is to stop betting and preserve the margin; skipping is allowed and not penalised.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target with 8 spins left; any wager only adds risk of dropping below the threshold, so skipping maximizes success probability.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target with 7 spins left; any bet has negative expectation and only risks dropping below the target, so skipping is optimal.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target with 6 spins left; any bet only adds risk of dropping below the threshold, so skipping is optimal.

I chose a legal action for this decision.

Bankroll is 1686, already above the 1500 target with 5 spins left; skipping is allowed and not penalised, so betting nothing locks in success without risking a drop below target.

I chose a legal action for this decision.

Bankroll 1686 already exceeds the 1500 target with 4 spins left; skipping is allowed and unpenalised, so any bet only risks dropping below the target with no benefit.

I chose a legal action for this decision.

Bankroll 1686 already exceeds the 1500 target with 3 spins left; skipping is allowed and unpenalised, so the optimal policy is to not bet and lock in the objective.

I chose a legal action for this decision.

Bankroll of 1686 already exceeds the 1500 target with two spins left; placing no bets guarantees finishing above target, while any wager only adds downside risk.

I chose a legal action for this decision.

Bankroll 1686 already exceeds the 1500 target with one spin left; skipping is allowed and guarantees success, so no bet.