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

A note: The full version of SBA includes the "Explanation of Blackjack Statistics" document, which is not available in the demo version. However, you can see its content on the About SBA screen.

**I. TECHNICAL DETAILS**

If a simulation runs for more than the number of rounds you specify in the Number of Rounds (1000x) input line on the Simulation page, then SBA automatically creates a permanent Simulation Report. Otherwise the report is temporary and is given the name WorkFile.txt. This feature can save you the trouble of manually deleting dozens of unwanted ‘trial’ simulation results because these temporary reports are overwritten by the next similarly short report created in the same folder on your computer.

The filename of a permanent report consists of the name that you gave to the simulation, plus the name that you specified in the Simulation Report Suffix input line on the Simulation page, plus a three-digit number automatically added by SBA.

**II. THE CONTENT OF THE REPORT**

After the heading follows the time and date when the simulation started and finished. On the next line is the random seed that initiated the random number generator. Next, SBA gives a fully comprehensive list of rules and playing conditions etc. used in the simulation.

**Then follows the COUNT STATISTICS (PRIMARY) Table:**

This table contains the most valuable data from the simulation. A description of its components follows. All the data in this table are independent of your betting spread. For a full explanation of all SBA’s statistics, click **Help** in SBA’s menu bar, click **Blackjack Statistics** and then click the link **Explanation of Blackjack statistics**.

__Note__: The statistics in the initial and final row of the table are for, respectively, that Count plus all Counts below, and that Count plus all Counts above.

**1) TC and PERCEN (columns 1 & 2)**

**TC **is, depending on your Counting method, either the **True Count** or the **Running Count**, and is calculated at the beginning of each round.

PERCEN tells you the frequency (in %) with which you can expect to face that Count.

**2) AC and PERCEN (columns 3 & 4)**

**AC** (**Adjusted Count**) is the TC adjusted for the Ace Side Count, and is calculated at the beginning of each round.

PERCEN** **tells you the frequency (in %) with which you can expect to face that Count.

If you don’t use an Ace Side Count, then the data in these columns are copied from columns 1 & 2, so you should adjust your interpretation of the data accordingly.

All the following columns refer to the AC if you use an Ace Side Count. If you don’t, then they refer to the TC.

**3) ST. ERR. (column 5)**

This column tells you the Standard Error of the value in the preceding column.

**4) ADVANT and ST.ERR. (columns 6 & 7)**

ADVANT tells you the percentage advantage at each Count.

ST. ERR. tells you the Standard Error of the value in the preceding column.

**5) SDROUND (column 8)**

This tells you the Standard Deviation of each round, per unit bet, with respect to each Count, and is a very important statistic. If you know the advantage and the Standard Deviation at a particular Count, then you can calculate the optimal bet (based on maximizing Kelly's utility).

**6) ACTION (final column)**

This tells you what fraction of your initial bet you can expect your total bet to be. For example, if **Action** at a particular Count is 1.1, then this means that you can expect, on average, to put out around an extra 10% of your initial bet on splits and doubles.

**Then follows the section containing the PRIMARY STATISTICS:**

**1) Initial bet advantage (IBA)**

This is one of the most important statistics. It’s listed together with its Standard Error. **IBA** is your advantage with respect to your initial bet.

IBA = total units won or lost / the bets placed before you receive your initial two cards.

**2) Total bets advantage (TBA)**

This is your advantage with respect to your initial bet plus all split, double and side bets. The Standard Error for **TBA** is practically the same as for IBA.

TBA = total units won or lost / total bets placed.

Because the denominator in the formula for TBA is always greater than in the formula for IBA, the absolute value of TBA is always smaller than the absolute value of IBA. In other words, IBA shows greater advantage or disadvantage than TBA. The difference is, typically, around 14%. It is slightly more if you play using a typical Counting system, since in this case you almost invariably double more on positive Counts than on negative ones.

**3) SCORE**

The SCORE was defined for Blackjack purposes by Don Schlesinger in the book **Blackjack Attack II**. SCORE is the square of the Desirability Index (DI). DI is the ratio of expected profit per round and standard deviation per round, multiplied by 1000 to reach reasonable units. DI is analogous to the Sharpe ratio, which is a measure of the desirability of investment opportunities in financial markets.

The SCORE is more useful than the Desirability Index, in the sense that it provides an absolute comparison of the value of different games. It can be said that a game A, with twice the SCORE of game B, has twice the value. This is true provided that:

you bet optimally according to your utility function i.e. using the correct Kelly fraction.

in the case of the game of Blackjack, both game A and B are played at the same speed (same number of hands per hour). If the speed is different, then you should adjust according to the ratio of the speeds. For example, suppose that game A has a SCORE of 55, and game B is 20% faster with a SCORE of 50. Then the relative SCORE of game B is 50 + 20% = 60, thus making game B the more valuable game in the order of 10% (ratio 60/55).

**4) Risk of Ruin**

For a given bankroll, betting and playing strategy, the Risk of Ruin measures the probability of ever losing the player's
bankrol. It is based on a formula, which was for Blackjack purposes first published by Don Schlesinger in the book **Blackjack Attack**.
This number has a close connection to the percentage of won and lost sessions (see also 13)) and it is possible to calculate one from the other.

**5) Estimated payoff per 100,000 rounds played with estimated Standard Deviation**

The** estimated payoff per 100,000 rounds played** and the **estimated Standard Deviation **are** **very important statistics. They can be used to derive the payoff for any number of rounds. Please note that if you bet zero on some rounds, then those rounds are excluded from these statistics.

**6) Estimated payoff per 100,000 rounds observed with estimated Standard Deviation**

If you bet zero on some rounds (Back Counting), then these statistics include those rounds. If you don’t make zero bets, then these statistics are superfluous and SBA doesn’t list them.

**7) Average Standard Deviation per round**

The **Average Standard Deviation per round** increases with the betting spread. This statistic allows you to calculate a Confidence Interval for your winnings for any number of rounds.

**8) Average Standard Deviation per round per unit bet**

This statistic is the __quadratic__ average of the weighted Standard Deviations (the weight being with respect to how often, and how much, you bet at each AC). Using the quadratic average is essential if you want to derive the closest possible approximation to your winnings for any number of rounds. The Statistic more commonly used (but giving a less accurate result) is the ‘linear average’ version of the above, which SBA avoids using.

**8) Average bet per round (ABR)**

This is your average initial bet for each round.

ABR = total of all bets placed before you receive your initial two cards / total number of rounds.

If you play multiple hands, then, for this statistic, each initial bet for these hands is added together and regarded as a single initial bet. Therefore the ABR when playing multiple hands is, typically, larger than the ABR for when playing only a single hand.

**10) Average bet total (ABT)**

This is the average of your initial bet plus all split, double and side bets.

ABT = total of all bets / total number of rounds

ABT is greater than ABR because the total of all bets is greater than the total of initial bets.

**11) Insurance contribution**

This statistic tells you how much your Insurance side bet contributes to your initial bet advantage (IBA).

**12) Insurance contribution to TBA**

Similar to the above, except with respect to TBA rather than IBA.

**13) Number of sessions won / lost / total, and Percentage of sessions won with Standard Error**

A session is won immediately you reach or exceed your Aim Bankroll (specified on the Betting Strategy page). A session is lost when your Bankroll (specified on the same page) is less than or equal to zero at the start of a round. You can end a session with a negative amount because SBA always makes the full initial bet(s) if your bankroll is greater than zero, and always splits, doubles and makes side bets even if your bankroll is negative.

**Percentage of sessions won **= 100 * # sessions won / total sessions. **St. Err.** (Standard Error) tells you the accuracy of this percentage.

__Note__: If you want to analyze the probability of, for example, double your real Blackjack bankroll with fixed betting, then it’s best to make the simulation Bankroll around 1% of this real bankroll. This allows SBA to quickly acquire a statistically large sample of sessions. And there is a simple formula at your disposal that allows you to take the result from this simulation and derive the probability that you are seeking. Using this technique you can expect a much more accurate result than you would get from running an equally long (time) simulation with Bankroll equal to your real Blackjack bankroll. If you want to see this formula now, then click **Help** in SBA’s menu bar, click **Blackjack Statistics** and then click the link **Explanation of Blackjack statistics** and see section VII. RISK OF RUIN CALCULATION.

**14) Surplus bank**

Typically a session ends slightly off zero Bankroll or Aim Bankroll. At the end of every session SBA puts this residual (negative and positive) into your Surplus bank. You need the Surplus bank if you want to calculate how many units you actually won.

**15) Number of shoes played**

The total number of shoes SBA played.

**16) Number of dropouts**

If you use the **Leaving Disadvantageous Counts **feature on the Betting Strategy page, then Number of dropouts tells you how many shoes you walked away from before the cut-card came out. If you don’t use leaving, then this statistic is superfluous and isn’t listed.

**17) Percentage of dropouts and Standard Error**

**Percentage of dropouts** = 100 * # dropouts / # shoes played. **St. Err.** tells you the statistical precision (Standard Error) of this percentage. If you don’t use leaving, then this statistic is superfluous and isn’t listed.

**18) Number of rounds played**

This tells you how many rounds you played with a non-zero bet.

**19) Number of rounds observed**

If you sometimes bet zero, then SBA disregards these occasions for most of the reported statistics. However, Number of rounds observed is the total number of **all** rounds. If you never bet zero, then this statistic is superfluous and isn’t listed.

**Then follow the SECONDARY STATISTICS:**

This final part of the report provides some less important, but nevertheless very interesting, statistics about the game.

**1) Main Table**

The first column lists the entire range of **AC**’s (Adjusted Count) for the Secondary statistics. The AC (Adjusted Count) is calculated at the beginning of each round.

Columns 2 to 8 list, for each AC, how frequently you: got Blackjack (BLJACK), pushed (PUSH), Hard Doubled (HDOUBL), Soft Doubled (SDOUBL), Split (SPLIT), Surrendered (SURREN) and made the Insurance side bet (INSUR).

Column 9 lists, for each AC, the average profit from the Insurance side bet (INSADV).

The final column (ACDIST) lists, for each AC, the percentage of the** total** **bets** made across the entire range of AC’s listed in the Secondary statistics. And please Notice that there is a difference between this distribution and the similarly named AC distribution discussed in the PRIMARY STATISTICS section. There, the AC distribution is with respect to **initial** **bets** only. These two distributions usually differ slightly, because on some Counts you put out additional bets more frequently than on others (Insurance being a classic example).

**2) Insurance**

If you don’t make the Insurance bet, then this table is superfluous and isn’t listed.

Here you can find detailed information about the Insurance bet with respect to the TC (True Count or Running Count). The TC, unlike the AC, is critical for the Insurance decision. Listed is the probability distribution (INSUR), the advantage you gained (INSADV) and the Standard Error (ST. ERR.). The TC for Insurance decisions (InsTC) is calculated immediately before the Insurance decision is taken.

**3) Over/Under 13 bet**

If you don’t make these bets, then this table is superfluous and isn’t listed.

This table lists the advantage gained from the Over 13 bet (OVER ADV) and the Under 13 bet (UND. ADV) at each TC together with the Standard Error. The TC is calculated every round before the cards are dealt.

**4) Cumulative frequency of occurrence**

This table lists the overall frequency with which various events occurred. The one exception is the advantage of Insurance (INSADV), which tells you the average profit for that bet. Below are the calculation methods used:

**BLJACK**= 100 * # of** Blackjacks**/ # of** rounds**

**PUSH** = 100 * # of** pushes**/ (# of** rounds** + # **splits**)

**HDOUBL** = 100 * # of** Hard Doubles**/ (# of** rounds** + # **splits**)

**SDOUBL** = 100 * # of** Soft Doubles**/ (# of** rounds** + # **splits**)

**SPLIT**= 100 * # of** splits**/ # of** rounds**

**SURREN** = 100 * # of** Surrenders**/ # of** rounds**

**INSUR**= 100 * # of** Insurances**/ # of** rounds**

**INSADV**= 100 * (2 * # of** won** - # of** lost Insurances**)/ # of **Insurances**

**OVER**= 100 * # of **Overs**/ # of** rounds**

**UNDER**= 100 * # of **Unders**/ # of** rounds**

**5) Correlation Coefficients**

This table appears only if you checked **Include the correlation coefficients between simultaneous hands in the report** on the Simulation page.

The table lists the correlation coefficients between simultaneously played hands with respect to each Adjusted Count (AC). However, if you only played single hands at a given AC, then **N/A** appears in the table for that AC. This correlation coefficient is vital for correct calculation of bet size when playing multiple hands. For example, with two simultaneous hands, for the same risk, the total of the bets for both hands is more than the bet placed when playing only a single hand, but it isn’t twice as much. The reason it isn’t twice as much is because the two hands aren’t entirely independent i.e. they face the same dealer’s cards.

For a detailed explanation of this topic, together with the formula necessary for making the calculation, click **Help** in SBA’s menu bar, click **Blackjack Statistics** and then click the link **Explanation of Blackjack statistics** and see: section VI. Correlation Coefficient and Optimal Multiple Hands Betting.

**6) Dealer’s Statistics**

This table appears only if you check **Include supported dealer’s statistics in the report** on the Simulation page.

This table lists the probabilities of the dealer making 17, 18, 19, 20, 21, Blackjack or a bust from each first card. Please note that these statistics are based on the dealer always finishing his hand, regardless of whether this would occur in real play - the hand is finished artificially to increase the sample size. This artificial play has no effect on the validity of these statistics.

**7) Distribution of the final number of cards in Dealer's hand**

Here you can see the total number of cards that the dealer held at completion of play for the round, and the frequency with which he held this number. With this information it’s easy to calculate the average number of cards that the dealer takes. Please note that these statistics are based on the dealer playing his hand exactly as in real play i.e. he doesn’t always finish his hand.

**8) Distribution of cards drawn to Dealer's initial two cards**

This tells you the frequency with which the Dealer draws the various value cards (9, 10, ace etc.) to his initial two cards. Please note that these statistics are based on the dealer playing his hand exactly as in real play i.e. he doesn’t always finish his hand.