
Effect of Blackjack True Count Methods
How
do different manners of True Counting differ?
There exist different methods of calculating a true count. (This
page will not be of interest to runningcount players.) You can
estimate the remaining decks in different manners, round the results
differently or include or exclude cards on the table among other
variations. We will look at a couple of these variations here.
First, we must estimate the number of remaining cards. This chart
shows three levels of accuracy in this estimate: remaining cards
estimated to the nearest full decks, half decks or exact cards.
All data are based on six decks. The blue line indicates an exact
calculation of cards in the discard tray (not counting the cards
on the table). As you can see the higher the accuracy, the higher
the advantage at high counts. These counts generally occur late
in the shoe where accuracy is more important. However, the important
counts are +1 through +5 as this is where most of the money is bet.
At these counts there is not a large difference. Therefore the overall
gain in better accuracy is not that high unless the penetration
is very deep. Charts on overall gain by penetration are available
in later pages of this site.


What
about division rounding methods?
Another area of variability in true count calculation is the method
of integerization after dividing the running count by remaining decks.
Nearly all Blackjack card counters use integer true counts. When you
divide 5 by 3, how do you turn this into an integer? (Most Blackjack
books give easy examples like 6/3 and fail to touch on the question.)
Some people round to the nearest integer (rounding), some always round
down (flooring) and some round towards zero (truncation). Truncation
is a bit less accurate because it greatly increases the number of
zero counts. This reduces the resolution of the count. Rounding and
flooring have about the same overall accuracy. As the chart shows,
flooring and truncating have the same advantages at positive counts
because they both round down at positive counts. But this changes
below the zero count since truncation now rounds up. This means that
truncated counts below zero will have a lower advantage. See the follwing
graph for the details. 

How
does this affect count frequencies?
If you integerize True Counts in different manners, the frequencies
of those true counts will change. This chart provides the frequencies
for the three methods of integerization. The green and red lines (flooring
and truncation) are identical for counts of +1 and higher. The red
line indicates a very large percentage (42%) of counts of zero for
truncation. This is because all counts between .999 and .999 will
truncate to zero. Truncation is a bit inferior due to this large peak
at TC zero. When you have so many hands all identified as a count
of zero, the count is less precise and an index of zero less valuable.
However, the overall effect on advantage is not high. 

Sim details
 Six decks, S17, DAS, LS, 4.81/6, HiLo max indexes, trunc, halfdeck
 Six decks, S17, DAS, LS, 4.81/6, HiLo max indexes, trunc, fulldeck
 Six decks, S17, DAS, LS, 4.81/6, HiLo max indexes, trunc, exact
cards
 Six decks, S17, DAS, LS, 4.81/6, HiLo max indexes, round, halfdeck
 Six decks, S17, DAS, LS, 4.81/6, HiLo max indexes, floor, halfdeck
 Ten billion rounds for six and two decks, five billion rounds
for singledeck
 

