Card Counting Edge by True Count
We all know that the higher the True Count when using a Blackjack card
counting strategy, the higher the advantage. Genrally, the edge moves
to the player at a True Count of +1. The below chart displays the advantage
(expected value) for each True Count from 25 to +25. (Sim specifics:
HiLo strategy, Full set of card counting indexes, Flooring, 6Decks, S17,
DAS, LS, 5/6, 25 billion rounds.)
We can see that the edge tends to level off at low True Counts.
The above chart looks fairly linear. But let us look more closely at
how much gain exists as the count increases. The chart below displays
the increase in EV at each TC. You can ignore the extreme TCs as they
are rare and often involve strange card subsets. It is known that Blackjack
is not linear. The chart below indicates that the advantage tends to increase
by about .5% at each card count. But, the increase tends to accelerate
substantially as the count increases.
The two charts posted assumed a full set of Blackjack card counting indexes.
Suppose we use no indexes at all. I ran another 25 billion rounds and
the charts are very different. With full indexes, the advantage gain per
TC is larger at positive TCs. With no indexes, the gain per TC reduces
as the TC increases. The below charts are the same as the previous charts;
only they chart both full card counting indexes and no indexes.
What about the Illustrious 18 and Fab 4? These are the most useful card
counting indexes. I ran another 25 billion rounds. These charts include
the Ill18 & Fab4 Advantage by TC and Gain by TC:
All these charts displayed advantages by TC. But if you want to look
at the actual value of an index set; you need to bring True Count frequencies
into the equation since the larger the magnitude of the True Count the
fewer hands you will experience. So this is the same chart as the above
edge by true count, but in terms of dollars per hour won/lost instead
of edge:
On the right side of the chart, green indicates the $ won by TC with
no indexes. Red is the additional gain with the Illustrious 18 & Fab 4.
Blue is the additional gain using Full Indexes. There is barely any gain
with full indexes. On the left, you see the amount lost by removing indexes.
This last chart demonstrates something long known. Blackjack card counting
strategies realize most of their gain with a small number of important
indexes.
