Roulette table

I chose a legal action for this decision.

Reaching +500 needs a big payout, so I'm betting a single straight-up at a stake of 32. One hit at that size still reaches 1500 even after up to 19 losing spins, and the bankroll can cover all 20 spins.

I chose a legal action for this decision.

The target needs +532 and only reaching it counts, so I use high-variance straight-ups. Nine numbers at 20 each cost 180, give about a 23.7% chance of hitting, and a hit nets 540 for a bankroll of 1508.

I chose a legal action for this decision.

Reaching 1500 from 788 needs a +712 gain, so I spread three straight-up bets at 22 each. Any hit nets +726 to reach the target, while three numbers per spin raises the hit chance without burning the bankroll too fast.

I chose a legal action for this decision.

Reaching 1500 needs a net gain of at least 778 chips. Seven straight-ups at 27 chips each net +783 if any one hits (about 18.4% per spin), which is the best chance of a single-spin finish within the stake cap.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and any bet has negative expected value, so skipping preserves the target at no penalty.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1,500 target, and skipping is allowed and unpenalised, so I place no bet to avoid any risk of dropping below the target.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and skipping is neither rewarded nor penalised. Any bet adds risk of dropping below the target, so I'm sitting out.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1,500 target, and every roulette bet has negative expected value. Skipping the spin keeps the target reached.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and every bet has negative expected value on a double-zero wheel, so skipping keeps the target secured.

I chose a legal action for this decision.

The bankroll is already 1505, above the 1500 target, and only reaching the target counts. Skipping is not penalised, so placing no bet avoids any risk of falling below it.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and only reaching the target counts. Skipping is allowed and unpenalised, and every bet has negative expectation on a double-zero wheel, so I make no bet.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and only reaching the target counts. Every bet has negative expectation on a double-zero wheel, so skipping keeps the target secured.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and every bet has negative expected value, so skipping the remaining spins keeps the target reached.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and only reaching the target counts. Every bet has negative expectation, so skipping preserves the success condition.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1,500 target, and skipping is allowed, so placing no bet keeps the target secured with zero risk.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and only reaching the target counts. Every bet has negative expected value and could drop me below 1500, so I skip the remaining spins.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and every bet has negative expectation, so skipping with no bets keeps the target secured.

I chose a legal action for this decision.

Bankroll is already 1505, above the 1500 target, and only reaching the target counts. Any bet has negative expected value and could drop me below 1500, so I skip.

I chose a legal action for this decision.

Bankroll is 1505, already above the 1500 target, and only reaching the target counts. Skipping this spin avoids all risk, so I place no bets.

I chose a legal action for this decision.

Bankroll is 1505, already above the 1500 target on the final spin, so skipping keeps the target secured with no risk.