Technically, you should think in probability weighted log-dollars to maximise your economy over the long term. (The Kelly criterion.)
In some cases this is equivalent to thinking in terms of fractions of your total wealth -- this is how the Kelly criterion is popularly presented.
For small ("everyday", as Bernoulli put it) amounts, this is equivalent to absolute dollars. So you're right, but it's a special case of a more general principle.
It makes only two assumptions:
- Growth compounds, and
- More is better.
Under those two assumptions, log-dollars is what you need to optimise.
By coincidence, logarithmic utility of money would also lead to the same conclusion, but that's mathematical happenstance, and not something going into the model.
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Another way to put it: the Kelly criterion prescribes logarithmic utility. It says that to maximise growth (under above assumptions) you ought to adopt logarithmic utility. If you don't, you get worse results.
Another way to phrase it is that you reinvest your winnings.