The Allais Paradox, though not actually a paradox, was a classic experiment which showed that decisions made by humans do not demonstrate consistent preferences. If you actually want to accomplish something, rather than simply feel good about your decisions, this is rather disturbing.
When something like the Allais Paradox is presented all in one go, it's fairly easy to see that the two cases are equivalent, and ensure that your decisions are consistent. But if I clone you right now, present one of you with gamble 1, and one of you with gamble 2, you might not fare so well. The question is how to consistently advance your own preferences even when you're only looking at one side of the problem.
Obviously, one solution is to actually construct a utility function in money, and apply it rigorously to all decisions. Logarithmic in your total net worth is usually a good place to start. Next you can assign a number of utilons to each year you live, a negative number to each day you are sick, a number for each sunrise you witness...
I would humbly suggest that a less drastic strategy might be to familiarize yourself with the ways in which you can transform a decision which should make no difference unto decision theory, and actually get in the habit of applying these transformations to decisions you make in real life.
So, let us say that I present you with Allais Gamble #2: choose between A: 34% chance of winning $24,000, and 66% chance of winning nothing, and B: 33% chance of winning $27,000, and 67% chance of winning nothing.
Assume your decision matters:
The gamble, as given, contains lots of probability mass in which your decision will not matter one way or the other -- shave it off!
Two possible resulting scenarios:
A: $24,000 with certainty, B: 33/34 chance of $27,000
Or, less obviously: I spin a wheel with 67 notches, 34 marked A and 33 marked B. Choose A and win $24,000 if the wheel comes up A, nothing otherwise. Choose B and win $27,000 if the wheel comes up B, nothing otherwise.
Assume your decision probably doesn't matter:
Tiny movements away from certainty tend to be more strongly felt -- try shifting all your probabilities down and see how you feel about them.
A: 3.4% chance of winning $24,000, 96.6% chance of nothing. B: 3.3% chance of winning $27,000, 96.7% chance of nothing.
Convert potential wins into potential losses, and vice versa:
Suppose I simply give you the $24,000 today. You spend the rest of the day counting your bills and planning wonderful ways of spending it. Tomorrow, I come to you and offer you an additional $3,000, with the proviso that there is a 1/34 chance that you will lose everything.
(If 1/34 is hard to emotionally weight, also feel free to imagine a fair coin coming up heads five times in a row)
Or, suppose I give you the full $27,000 today, and tomorrow, a mugger comes, grabs $3,000 from your wallet, and then offers it back for a 1/34 shot at the whole thing.
I'm not saying that there is one way of transforming a decision such that your inner Bayesian master will suddenly snap to attention and make the decision for you. This method is simply a diagnostic. If you make one of these transforms and find the emotional weight of the decision switching sides, something is going wrong in your reasoning, and you should fight to understand what it is before making a decision either way.