Do you agree that –
For any two occurrences A and B, you will either prefer A to B, or prefer B to A, or be indifferent between them?
If you prefer A to B and B to C, then you'll prefer A to C?
If you're indifferent between A and B, and between B and C, then you'll be indifferent between A and C?
If you prefer A to B and B to C, then there is some probability p such that you'd be indifferent between B, and a “lottery” that gives you a chance p of getting A and a chance 1-p of getting C?
If you're indifferent between occurrences A and B, and if A is one possible outcome of a lottery, then substituting B for A as an outcome of the lottery will not affect your preferences?
The preferences of a rational decision-maker can be represented by a utility function (the choice of origin and scale is arbitrary - all else is then determinate); decisions can be evaluated in terms of the expected utility of the outcome. If the utility curve is linear over the range of possible outcomes, this is equivalent to evaluating decisions in terms of expected payoff; if the curve is upward-sloping but downward-bending over the range of outcomes, the decision-maker is “risk averse.” (Over a wide range of possible outcomes this is typically the case; e.g., for most people, the increase in utility in moving from their current wealth level to a level $1,000,000 higher is greater than the increase in moving from +$1,000,000 to +$2,000,000.)
Here's a spreadsheet to help you determine your own utility function.
A question, another question, and an observation.