Show us. Use maths.

The distinction already exists in the natural language used to describe the two scenarios.

In one scenario, we are told that a certain amount of money will become ours, but we do not yet possess it. In the other, we consider ourselves to already possess the money and are given opportunities to risk some of it.

Hypothetical money is not treated as equivalent to possessed money. (Well, hypothetical hypothetical vs. possessed hypothetical in the experiment discussed, but you know what I mean.)