Ten-Ace Density and Betting efficiency.

I have a question about the relative density of hi to low cards, which most counting strategies attempt to measure.

Let us assume one uses Hi-Lo or Wong Halves for example, which require a true count.

It appears that (within certain limits, which cover the vast majority of card situations encountered) increases in true count result in a roughly linear increase in expected win rate.

But in my measurements, as the number of decks remaining decreases, a given true count, say X, actually reflects a higher density of high to low cards.

The sims I have seen do not address this issue. (If they do, I'd like to see where.) (It suggests a slight adjustment to the true count for betting accuracy.)

To address it properly, you would have to run a sim for each true count X, with N decks remaining (fixed) and starting with K decks (e.g., 6 decks). Then one would look at the different player advantages at count X, for N = 1, 2, 3.... K.

This information would be appreciated. I think it would increase betting efficiency.

I have a separate question about aces, but I will wait to see if I get a good answer to this question

You might want to look into a concept known as "Floating Advantage," which I investigated nearly 20 years ago.

See BJA3, Chapter 6.

Don

It appears my rough calculations had validity. (I saw a bar graph showing floating advantage.) Now I just need to figure out a simple adjustment (which may be your book's subject).

So what is "true count" exactly if it's not "true." Just a good first order approximation to work with?

the "floating advantage" is real but largely insignificant.

There are no excuses for failing to own and study:

"Blackjack Attack, 3rd ed." and
"Theory of Blackjack, 6th ed."

But in my measurements, as the number of decks remaining decreases, a given true count, say X, actually reflects a higher density of high to low cards.

This statement is not true.A given true count DOES reflect the same card distribution regardless of penetration. That's why we divide by the number of remaining decks.
If you had said that a given true count doesn't reflect the same edge as the number of decks decreases (floating advantage)then I could agree.

Francis Salmon

I have never liked the expression "floating advantage" but I wouldn't call it insignificant.Unlike the $-exchange rate it's not actually floating but steadily increasing as the shoe is depleted.This effect is accelerated towards the end.
Its real extent can be seen when we compare the house edge for different number of decks but otherwise identical rules.We all know that single deck is 0.5% better than 6-decks.
That means if we have a 6-deck-shoe with -0.3% off the top we can raise our bets even in a neutral count when there is just one deck remaining (+0.2%).
Generally speaking, I think we should integrate FA into our bet sizing, especially in games with deep penetration.

Francis Salmon