Both kinds of scenarios should happen equally often
Not in real life, they don’t.
People planning future actions prefer the certainty of having the necessary resources on hand at the proper time. Crudely speaking, that’s what planning is. If the amount of resources that will be available is uncertain, people often prefer to create that certainty by getting enough resources so that the amount at the lower bound is sufficient—and that involves paying the price of getting more (in the expectation) than you need.
Because people do plan, the situation of “I’ll pick the sufficient and certain amount over a chance to lose and a chance to win” occurs much more often than “I certainly have insufficient resources, so a chance to win is better than no chance at all”.
Not in real life, they don’t.
People planning future actions prefer the certainty of having the necessary resources on hand at the proper time. Crudely speaking, that’s what planning is. If the amount of resources that will be available is uncertain, people often prefer to create that certainty by getting enough resources so that the amount at the lower bound is sufficient—and that involves paying the price of getting more (in the expectation) than you need.
Because people do plan, the situation of “I’ll pick the sufficient and certain amount over a chance to lose and a chance to win” occurs much more often than “I certainly have insufficient resources, so a chance to win is better than no chance at all”.