When looking at Risk Aversion vis a vis variance reduction — look at it this way:
Let’s say you have a hand where you have a small advantage. The opportunity
to split or double is present. You have an advantage so you need to press that advantage
by doubling your bet. So far so good. Now lets imagine that you
have a nice little advantage — lets say 2%. So you double.
Now lets look at that hand again. IF the hand matchup is to your advantage, then it is
always MORE advantageous (in terms of winning the hand) to refrain from doubling.
We can hit, retaining the right to draw further cards.
What if by doubling (a one card draw) ?
Your advantage drops from 2% to 1.25% ? So … If you double you gain 1.25% of two units,
which is more (by 0.5%) than 2.0% of one unit. SO … Why not double ?
Because you are risking twice as much for a modest increase in profit.
Now where/when/how does this make sense.
The answer resides within your Risk of Ruin.
If your risk is high (whatever that means to you), e.g.> 13%,
every time you have extra money at risk, your bankroll may
get seriously dented. You may soon have to resize your betting ramp.
If your risk of ruin is very low, e.g. < 1.0% than this issue of “money at risk” is hardly even an issue at all.
In my experience training Card Counters, (as “lone wolf“ players),
R I S K should be the paramount concern, when all too often it isn’t.