Final answer:
Comparing the two roulette strategies, the first is a higher risk but quicker resolution, while the second involves extended play with a variable-ratio reinforcement schedule making it addictive and unpredictable.
Step-by-step explanation:
In considering the two gambling strategies at roulette, we should assess the probabilities and potential outcomes. If the man bets all $20 on evens at once and wins, he will immediately have his desired $40, with a 48.6% chance of success (due to the presence of zero and double zero in American roulette which are neither even nor odd). However, if he loses, he loses everything immediately.
The alternative strategy of betting $1 at a time gives him more plays, but it also subjects him to the house edge more times. While he may seem to have more control and can stop if he's ahead, the same house edge that applies to the larger one-time bet also applies to each $1 bet, reducing the overall likelihood of reaching $40. Each $1 bet on evens also has a 48.6% chance to win, but the extended play could lead to more wins or more losses due to the variable-ratio schedule of reinforcement described by Skinner, making it addictive and unpredictable.
Ultimately, the first strategy has a higher risk but a quicker resolution, while the second offers prolonged play with multiple risks of small losses adding up, making both strategies unfavorable in the long run due to the house edge.