Blackjack Running Count, True Count, and
Player Advantage Simulator
The following Excel spreadsheet simulates the
dealing of 6 decks of cards at random. It graphs the running
count, true count, and player advantage as the cards are
dealt. When counting cards, you should make your minimum
waiting bet when the player advantage is zero or negative.
When the player advantage goes positive, you should bet a
percentage of your bankroll equal to your player advantage,
according to the Kelly
If necessary, bring the two
graphs into view using the scroll bar:
Running count / True count
Player advantage %
To deal another 6 decks and update the graphs, first click to select
any cell (such as K4), then press the F9 key. Press F9 again for
another 6 decks. If you don't have an F9 key,
click the Refresh icon
below the spreadsheet, or
reload the page.
To see graphs for a single-deck or double-deck game,
click the "Single" or "2 decks" tab at the bottom of the
If you accidentally modify a cell value or formula, you
might ruin the graph. To fix it, reload the web page.
The running count (grey graph line) keeps track of the number
of high vs. low cards using the classic Hi-Lo count strategy,
where cards 2-3-4-5-6 have a value of +1, cards 7-8-9 have a
value of 0, and cards 10-J-Q-K-A have a value of -1. The count
at the beginning is zero. The count at the end is also zero,
because the numbers of low and high cards are balanced.
As the cards are dealt, the count randomly varies between
positive and negative values, depending on whether more low or
high cards are dealt out. The graph is equally likely to be
above or below zero.
The true count (blue graph line in top graph) is the running
count divided by the number remaining decks to be dealt. This
adjusts the running count to determine the true effect,
fraction-wise, on the probability of dealing out high or low
cards from the remaining decks. For this reason, I prefer to
call this the "true-effect count" or "one-deck
Player Advantage Graph
The player advantage graph shows your advantage as a
percentage of your bet. For example, when your advantage is
1.00 percent and you make a $20 bet, your average win on that
bet will be 20 cents. Not a huge advantage by any means!
You have an advantage when the graph goes above zero, as
indicated by the solid black horizontal line. The dashed
horizontal purple line - - - - - -
- represents the basic strategy player edge for a
typical good 6-deck game, -0.6 percent. The player advantage
graph is centered on the dashed purple line; it is equally
likely to be above or below this line. Thus, you play at a
disadvantage more than half the time.
The player advantage graph is shown solid for the first 4.5
decks and dashed for the remaining 1.5 decks. This is because
most casinos shuffle when there are 1.5 decks remaining. That
means you will not have any opportunities to make bets in the
dashed portions of the graph.
You can place a bet only at the end of each round. At an
uncrowded table, maybe 12 or so cards are dealt in each round,
on average. Therefore, I've spaced the card number labels at
the bottom at intervals of 12. These represent (approximately)
the intervals at which you can place bets.
Cell N2 contains the basic strategy player advantage at the
start of the game, -0.60 percent by default. For a game
that pays only 6:5 on blackjack, the player advantage is worse
by 1.4 percent. To see the effect of a 6:5 payoff, enter -2.00
into cell N2.
Player Advantage Pie Chart
The pie chart shows the relative amounts of time that you play
at an advantage, at a disadvantage, and even with the casino. A player edge
between -0.25 and +0.25 percent is considered even. The pie chart applies only to
the part of the graph before the shuffle.