This works because of what I found in my reward analysis post, specifically the fact there are only six possibilities of cash rewards.

The first step is to attack a character twice, and record the cash rewards for each battle. If you get the same number twice, or if they are only a dollar or two off, you'll need a third battle.

Then Take the higher of your two values and divide it by the lower.

If you get 2.25,2,1.75 or 1.25, multiply the lower cash value by 13/8 to get your average cash reward.

If you get 1.8,1.6,1.4 or 1.2, multiply the lower cash value by 13/10 to get your average cash reward.

If you get 1.333 or 1.667, multiply the lower cash value by 13/12 to get your average cash reward.

If you get 1.286 or 1.143, multiply the lower cash value by 13/14 to get your average cash reward.

If you get 1.125, multiply the lower cash value by 13/16 to get your average cash reward.

If you get 1.5, there are two possibilities for what your average cash reward can be - low*13/8 or low*13/12. You can look at both and guess which is right, or you can fight another battle and try again, or you can find a nice quiet corner and cry.

Once you've figured out your average cash reward, you can look at the ratios in my analysis post to get more info about your rewards.