SBA Report File Description

Following is a part of report file help provided with Statistical Blackjack Analyzer. The text should help you to understand the statistics in SBA's report files.

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A note: The "Statistics Explanation" text is not available in the demo version.

  Explanation of the Report File
  ------------------------------

I. TECHNICAL DETAILS

After finishing a simulation, SBA creates a report file. If the simulation
was "short "(shorter than a predefined number of rounds), the name of the
report file is WORKFILE.000. The WorkFile is considered to be a temporary
file, which is overwritten by next "short" simulation. (This way the
directory with report files will not be overfilled with hundreds of mostly
worthless report files, when most of them were just short trials.) 

If the simulation is long enough, a unique report file is created. The
name of the report file is specified in the Configuration/Other
Configuration dialog box. These report files are numbered 001 through 999.
They are all stored in the "Report files directory" which is set in the
Options/Directories... dialog box. 


II. THE CONTENT OF A REPORT FILE

A) BASIC LISTING

After the heading follows the time and date when the simulation started
and finished. On the very next line is the random seed that initiated the
random numbers generator. 

Next, SBA describes the rules, counting system, and conditions that were
used in the simulation. If you used any odd rules, like blackjack payoff
different than 3:2, SBA reports this too. In case a non-standard deck has
been used (either removed or added cards), SBA fully lists the deck --
card values with corresponding occurrence. 


B) COUNT STATISTICS

The following report file table provides a probability distribution of
each count. Note, that all the data in that table are independent on your
betting spread. All numbers are in percentages. A description of table
columns follows. 

1) 1st & 2nd columns: TC & PERCEN
(True count with its probability distribution.)
The first two columns show the distribution of the true count (TC) WITHOUT
ace side count adjustment. The TC is calculated at the beginning of each
round. 

2) 3rd & 4th columns: AC & PERC
(True count adjusted for ace side count with its probability
distribution.)  The next two columns show the distribution of the true
count ADJUSTED for ace side count (further referred to as adjusted count,
or AC), calculated at the beginning of each round. 

If you do not keep ace side count, the distribution will be exactly the
same as the distribution of the true count in the second column. Note,
that in the 'ADDITIONAL STATISTICS' section you can find another AC
distribution - that includes all splits and doubles. That distribution
will be slightly different. 

All the following columns are related exclusively to the AC.

3) 5th column: ST.ERR.
Standard error of the previous column (PERCEN).
This number tells us, how exact the estimate of the percentage of each AC
(in the PERCEN column) is. For an explanation of what exactly standard
error means, press Ctrl+F1 or go to Help/Statistics to open the
"Statistics explanation." 

4) 6th & 7th columns: ADVANT & ST.ERR.
Player's advantage on each AC (column ADVANT) with corresponding standard
error (column ST.ERR.) These columns provide very important information. 
The standard error tells how exact the estimate of the advantage per each
AC is. 

5) 8th column: SDROUND
Standard deviation of each round (per unit bet) with respect to each AC. A
very important statistics. If you know the advantage of each AC and the
standard deviation of a hand played on this AC, you can calculate the
optimal bet on this count (based on maximizing Kelly's utility). For more
information to this topic, see the "Statistics explanation." 


C) MAIN STATISTICS

In this section you will find most of the information you are looking for.

1) Number of winnings, losses, etc.: relates to your sessions.
"Number of winnings" is the total of won sessions. A session is considered
won as soon as you reached the AIM BANKROLL (specified in the "Player's
Strategy" dialog box.) 
"Number of losses" is the total of lost sessions. A session is considered
lost if you lost your session BANKROLL (specified, again, in the "Player's
Strategy" dialog box.) 
"Number of sessions" is the total of won and lost sessions.

2) Sessions won: what percentage of your sessions you won.
(Number of winnings / number of sessions). Provided together with standard
error.

Note, that if you want to analyze the probability of doubling your whole
bankroll for fixed betting (no proportional betting) you do not have to
run the simulation for the whole bankroll (which might be for example
10000 units). Rather, you can run it for 50 or 100 units, and than
recalculate the probability of doubling your bankroll for 10000 units. You
might want to do this since for 10000 units you probably would not get
good (reasonably exact) results even after running an extremely long
simulation. 

I provide the formula which I derived for the recalculation. See the
"Statistics explanation", section VI. (Risk of Ruin Calculation) for the
formula and more details to the topic. 

3) Initial bet advantage (IBA):

IBA is one of the most important results. It is provided together with
standard error. IBA is advantage with respect to the 'initial' bet.

Definition of IBA:

IBA = total units won (lost) / total of initial bets
                      (without splits, doubles, insurance, etc.)

4) Advantage per total bets (ATB):

ATB is advantage with respect to all bets pulled out. ATB tells us what
the return on total investment (wager) is. Unlike the IBA, we include
addition bets for split hands, doubled hands, and any side bets. The
standard error for ATB is practically the same as for IBA. 

ATB is defined as:

ATB = total units won (lost) / total bets
                      (including splits, doubles, insurance, etc.)

Since the denominator in the formula for ATB is always greater than in the
formula for IBA, the absolute value of ATB will always be SMALLER than
absolute value of IBA. In other words, if we play on an advantage, IBA
will show greater advantage than ATB. If we play on disadvantage, IBA will
show greater disadvantage than ATB. The difference will typically be
around 13 to 15 percent. It will be a little more if you range your bets
and deviate from basic strategy, since in this case one doubles more on
positive counts than on negative ones. 

5) Estimated payoff for 100,000 rounds played with standard deviation:  A
very useful statistics, which provides the expected win together with
standard deviation for 100,000 rounds. You can recalculate the same for
any other number of rounds, of course. See the "Statistics explanation"
for a formula and detailed explanation on the recalculation. 

6) Estimated payoff for 100,000 rounds observed with standard deviation: 
In the case you bet zero on some true counts (backcounting), this
statistics includes also the rounds where you bet zero bets. (Unlike the
previous one -- number 5).) If you do not use zero bets, this statistics
is ommited since it would be the same as 5). 

7) Average standard deviation per round:  An important statistics which
provides average standard deviation per round for a given betting spread.
The higher the bets and betting spread, the higher will this number be.
This standard deviation allows us to calculate confidence interval and
standard deviation for player's winnings after any number of rounds. For
more information, see the "Statistics explanation." 

8) Average standard deviation per round per unit bet (SDRB):  This
statistics says: if you wanted to use only one standard deviation for all
true counts, this is the appropriate number. SDBR is (quadratic)  average
of standard deviations for each AC from the Count Statistics table,
appropriately weighted by each AC occurence and bet on each AC. SDRB
depends slightly on your betting spread, since different betting spreads
mean different weights for each AC in SDRB calculation. 

Using this number you can recalculate a rough approximation of player's
winnings after any number of rounds. It is a common (incorrect) approach
to take standard deviation of a blackjack hand (for one unit bet), and
multiply by average bet to get a standard deviation per round. However,
you can take the standard deviation of a blackjack hand and multiply by
the "quadratic average bet", which is calculated a little differently than
"standard"  average bet. 

If you multiply SDRB by quadratic average bet, you get exactly average
standard deviation per round.

9) Average bet per round (ABR):
The average bet calculated at the beginning of each round. No split,
doubled, and side bets included. The definition is: 

sum of initial bets / number of rounds

If you play multiple hands, ABR will be correspondingly higher. (For
example, if you play always two hands, ABR is twice as big than if you
played only one hand.) 

10) Average bet total (ABT):
The average bet considering ALL bets including splits, doubles, and side
bets. The definition is:

total bets pulled out / number of rounds

Since total bets are always more than initial bets only, ABT will always be
greater than ABR.

11) Surplus bank
If you end one session (lose your session bankroll, or reach your aim
bankroll), you not always end exactly on zero or reach exactly the aim
bankroll, unless you bet flat 1 unit. Most of the time you end several
units above your aim bankroll (if won), or below zero (if lost). A sum of
these 'residuals' is the surplus bank. The surplus bank will usually be
positive.  You need the surplus bank if you want to calculate how many
units you actually won. 

12) Insurance contribution
The insurance contribution says exactly how much insurance contributes to
your overall initial bet advantage (IBA). If you did not buy insurance,
IBA would be smaller exactly by the 'Insurance contribution' amount. 

13) Insurance contribution to ATB:
Similar to 10), only with respect to ATB rather than IBA.

14) Number of shoes played
The total number of shoes SBA played.

15) Number of dropouts
Number of dropouts is the number of shoes SBA left because the true count
(adjusted count) was negative. This number is greater than zero only if
you leave on negative counts. 

16) Percentage of dropouts
Percentage of dropouts is the percentage of shoes left on a negative
count.  percentage of dropouts = number of dropouts / number of shoes
played * 100

The percentage of dropouts is provided together with standard error.

17) Number of rounds played
The total number of rounds SBA played and bet non-zero.

18) Number of rounds observed
If you bet zero on some counts, SBA disregards these counts for most of
the reported statistics. However, this number here says what the total
number of rounds is included the rounds where you bet zero. If you never
bet zero, this statistics is ommited since it would be the same as the
previous one -- 17). 


D) ADDITIONAL STATISTICS

The last part of the report file, additional statistics, provides some
more information and statistics about the game. This statistics is usually
not as much important as the statistics from the previous section. 

1) the first table provides distributions (percentages) of blackjack
(first column), pushes (second column), hard doubles (third column), soft
doubles (fourth column), splits (fifth column), surrender (seventh
column), percentage of insurance (eight column), and advantage of
insurance (ninth column). All this information is given with respect to
the adjusted count (AC). If you want to see how exactly these percentages
are calculated, just continue reading. 

The last (tenth) column called ACDIST gives the distribution of ALL bets
with respect to the AC. Note, that this is not exactly the same as the AC
distribution in the very first table from part A) COUNT STATISTICS. The AC
distribution from the first table considered only initial bets, while this
AC distribution considers all bets -- including splits, doubles, and side
bets.  For example, if SBA splits a hand, one additional bet is counted
for this AC distribution, while only the original one was considered for
the AC distribution in the first table. There is a tiny difference between
the two, since on some counts you double (and split) more than on others,
you insure only on positive counts, etc. The AC is calculated at the
beginning of a round. 

2) The second table provides detailed information of insurance with
respect to the TC (if you do not buy insurance, this table is missing.)
The TC, unlike the AC, is decisive for insurance decisions. Provided is
the probability distribution, advantage, and standard error. The TC for
insurance decisions is calculated immediate before the insurance decision. 

3) Following are overall percentages of blackjack, pushes, hard and soft
doubles, splits, insurance, and insurance advantage. 

To have a full understanding what each number from 1), 2), and 3) above
means, look carefully at the exact definitions: 
% of BJ     = # of BJs    /  # of rounds                   * 100
% of push   = # of pushes / (# of rounds + # of splits)    * 100
% of hdoubl = # of hdoubl / (# of rounds + # of splits)    * 100
% of sdoubl = # of sdoubl / (# of rounds + # of splits)    * 100
% of split  = # of splits /  # of rounds                   * 100
% of surren = # of surren /  # of rounds                   * 100
% of insur  = # of insur  /  # of rounds                   * 100

For example, the percentage of blackjack at AC zero is calculated as:
number of blackjacks at AC zero / number of rounds at AC zero * 100 (percent)

I used the definitions above, since I found them most logically consistent.

4) If you set the correlation option on (it is set in the
Configuration/Other Configuration dialog box), then the next table
provides correlation coefficients between two simultaneously played hands
with respect to each AC. However, if you did not play at least two hands
on a given adjusted count, the correlation coefficient could not be
calculated for this count, and N/A appears in the table.

The correlation coefficient is very important for ranging your bets on
multiple hands. For example, if you play two hands, your total bet on the
two hands can be higher than if you played only one hand, in order to be
on the same level of risk. However, the total bet should NOT be twice as
much as you would bet when playing only one hand. The reason is that the
two hands are not independent -- they face the same dealer's cards. 

To determine how much more in total you should bet when playing more than
one hand, you need the correlation coefficient, which is a measure of
dependence.  For a detailed explanation to this topic, together with a
formula and some examples on calculating the optimal bet for more
simultaneously played hands, see the "Statistics explanation." 

5) If you checked the Up Card Statistics in the Configuration/Other
Configuration dialog box, then the last table in the report file provides
you with information about the probability of dealer drawing to 17, 18,
19, 20, 21, blackjack, and busting, given his up card. For example, you
can see the probability of dealer busting if he has a 6 up.