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BjOdds: Blackjack Software to Calculate Precisely the Dealer Bust Odds, House Edge, House Advantage

By Ion Saliu, Founder of Blackjack Mathematics

Sale Withdrawn for Pricing and Patent Considerations

Blackjack software calculates mathematically dealer bust odds, bust probability, house edge.

BjBustOdds - High-Power Odds Calculator, Hands Generating Software for Blackjack

Published on August 19, 2010; last update June 2014.

Version 21, June 2014; New Software.
precisely generates all favorable cases (busted hands) and all possible cases (total blackjack actions). Thus, mathematically precise calculations of the blackjack odds and house edge are possible for the first time ever. The historic algorithms are here for everybody to see, read, comprehend, and fully verify. The old bust odds, as previously calculated by John Scarne, had a quite large margin of approximation.

A visual presentation of the BjBustOdds software follows. It can't be more intuitive and informative, especially given the intellectual level of the potential buyers!

Blackjack software: calculate correct odds, probability for casino dealer.

Generate all casino blackjack hands where the order of the cards counts.

BJ software generates all blackjack hands, including bust and blackjacks or natural 21.

This blackjack package does not need installation, if you downloaded BjBustOdds to a folder on your hard drive; e.g.: C:\BjBustOdds

The best method is to go to the Command Prompt (Windows 2000 and later). Create a directory (folder); e.g. C:\BjBustOdds. You can do that in Windows Explorer as well. Download BjBustOdds to C:\BjBustOdds. Click on BjBustOdds to decompress the file automatically.

To begin, navigate to the C:\BjBustOdds folder and click on BjMenu. If you right-click on BjMenu you can create a shortcut on your desktop.

For the best results, work at the Command Prompt in C:\BjBustOdds. Navigate to the C:\BjBustOdds folder in a Command Prompt and type at the C:\BjBustOdds prompt:


This is the recommended method as speed of execution is gained.

Let's stay in the GUI for a little longer. We need to create a few useful batch files to make the command prompt environment even more productive. Simply open that unheralded Notepad. The batch files must be in text format (plain vanilla formatting for computer files). I have this batch file named MA.BAT (MA indicates macros). Instead of typing, you can copy and paste the following lines (without any blank line):

doskey co=copy $1 $2
doskey d=dir /O:N /P
REM doskey da=dir A: /O:N /P
doskey dc=dir C: /O:N /P
doskey dh=dir H: /O:N /P
REM doskey de=dir E: /O:N /P
REM The following, re, is a replace utility
doskey re=xcopy $1 $2 /D /U /Y
doskey bk=attrib +A $1$Txcopy $1 $2 /M /-Y
doskey xc=xcopy $1 $2 /M /-Y
doskey x=exit
REM doskey bcg=bellcurvegenerator
REM doskey per=cd\$Tcd\bas$TPermuteCombine
REM doskey lex=cd\$Tcd\bas$TLexicographicSets
REM doskey sf=cd\$Tcd\bas$TSuperFormula
REM doskey fl=C:\bas\filelines
REM doskey bp=C:\bas\BirthdayParadox
REM doskey col=C:\bas\Collisions
REM doskey osp=C:\bas\OccupancySaliuParadox

PATH C:\;C:\BAT\;C:\BAS\;C:\LOTTERY\;C:\BjBustOdds\;%PATH% is the most important line in the batch file. The PATH was set via the AUTOEXEC.BAT prior to Windows 2000. Now, AUTOEXEC.BAT is no longer available to the computer user. Instead, Windows establishes the PATH automatically; it is the value %PATH%. Our batch file just adds more entries to the automatic Windows %PATH%. You can add your own folders in the main line of the batch file MA.BAT. For example: C:\BRIGHT3\;C:\BRIGHT6\; etc. But remember the \ and the ; separator.

Any time you start a command prompt session, you type MA (or ma) at the C: prompt. The batch file has also useful shortcuts created for the DOSKEY utility (automatically loaded by Windows). For example, the great utility PermuteCombine (generator of permutations, combinations and more) resides in a BAS folder. I just type per to start the application.

Save it as MA.BAT (at the C:\ prompt). Save the file in Notepad (you may need sometimes to surround the name by “ “ to be sure it saves a text file with the BAT extension): Name: "MA.BAT" in drive C: (root directory); Save as type: All files; Encoding: ANSI.

Copy and paste now an example batch file to abbreviate the start of the BjOdds package. Again, simply copy and paste the 4 lines:


Save this file in Notepad as BJ.BAT, but this time in the C:\BAT\ folder. The REM command does one thing only: Disables the DOS command that follows it; that is, the rest of the line will have no effect.

You can create similar batch files for Bright6 (L6), or any other LotWon software package. After you start the Command Prompt session, type ma (and press Enter); then type bj (and press Enter); you will navigate automatically to the C:\BjOdds\ folder.

You can navigate anywhere at the command prompt by using the CD command (Change Directory). For example, you are at the C: prompt. If you want to navigate to C:\BjBustOdds\, type:


If you want to go back to the root directory C:\ from C:\BjBustOdds\ type:


This blackjack probability, odds software is a first-timer ever and ready to buy.

The source code was compiled with: PowerBasic Console Compiler (PBCC), version 4.04. Older or newer versions of PBCC may or may not work with the source code in this package without modifications.

You, the programmer, assume full responsibility for such tasks.

The source code is adequately commented for the average programmer. You should be at least an average programmer who worked with PBCC for around five years.

There is NO programming support offered whatsoever. If your programming language is different, you need help from PBCC programmers to translate my source code to your programming language of choice.

Generate all possible blackjack hands as combinations where the card order does not count.

The files in this package - BjBustOdds:

1. BjBustOddsCombos  
generates all possible blackjack hands as COMBINATIONS
source code: BjDealerCombos.bas.

2. BjBustOddsOrder generates all possible blackjack hands as ARRANGEMENTS. source code: BjDealerOrder.bas.

3. BjBustOdds the menuing of this blackjack software package source code: BjMenu.bas.

4. BjDeck1.TXT a layout file consisting of deck of cards (52), arranged lexicographically from the 4 2's to the 4 Aces (11).

5. BjDeck2.TXT a layout file consisting of deck of cards (48), arranged lexicographically from the 4 2's to the 4 Aces (11); *** this deck has only 12 Ten-value cards (Double-Attack or DABJ).

6. BjDeck1-11.TXT a layout file consisting of deck of cards (13), with only one suit for each card (from one 2 to one Ace).

7. BjDeck4-11.TXT a layout file consisting of deck of cards (16), with only one suit for each card (from one 2 to FOUR Aces).

8. BjDeck1Shuf.TXT a layout file consisting of deck of 52 cards, by shuffling the regular BjDeck1.TXT deck of cards.

9. BjDeck1Rev.TXT a layout file consisting of deck of 52 cards, by reversing the regular BjDeck1.TXT deck: from Aces to 2's.

10. BjAllHands1Combos.TXT all possible blackjack hands generated by BjDeck1.TXT as COMBINATIONS.

11. BjAllHands2Combos.TXT all possible blackjack hands generated by BjDeck2.TXT as COMBINATIONS (for Double Attack Blackjack).

12. BjAllHands1-11Ord.TXT all possible blackjack hands generated by BjDeck1-11.TXT as ARRANGEMENTS.

13. BjAllHands4-11Ord.TXT all possible blackjack hands generated by BjDeck4-11.TXT as ARRANGEMENTS.

14. EULA-Saliu-Software.pdf END-USER LICENSE AGREEMENT accompanying Ion Saliu's software -- the document PDF format to be viewed in the free Adobe Reader.

15. EULA-Saliu-Software.htm END-USER LICENSE AGREEMENT accompanying Ion Saliu's software -- the HTML file to be viewed in a browser, such as Internet Explorer 8.

Apply dealer rules to different hit stand limits to get closer to player bust odds.

How can we apply the new programming to determine the bust odds for the blackjack Player? After heated debates in forums in 2014, I simply modified my software. The hit-stand limits can be set by the user. Initially, it was fixed — the ubiquitous hit all 16s and under, stand on all 17s or greater.

The software user can set the hit-limit to any value. The choices are, obviously, from 12 to 16. I tried, for example, the hit limit to 11 — that is, hit anything 11 or under, stand on anything 12 or higher. Evidently, there is no bust in such situations. That's another proof that my programming is 100% correct.

I believe that setting the hit limit to 14 or 13 reflects pretty closely the bust odds for the Player. That is, stand on 15 or greater (as arrangements):

 Total BJ Actions:                274254 
 Hits to 1st 2-Cards:             136789 
 Total Non-Bust Hands:            75809 
 Total Player Bust Hands (*):     61656 

 Percentage Player Bust:          61656 / 274254 = 22.48%

 Natural Blackjacks (10+A):       64 / 1326 = 4.83%

Or, stand on 14 or greater (as arrangements):

 Total BJ Actions:                3702 
 Hits to 1st 2-Cards:             1804 
 Total Non-Bust Hands:            1328 
 Total Player Bust Hands (*):     570 

 Percentage Player Bust:          570 / 3702 = 15.40%

 Natural Blackjacks (10+A):       8 / 156 = 5.13%

 Total Complete BJ Hands:         1898 

Now, the house edge goes between something like .3355 * .2248 = 8.3% and something like .3355 * .1978 = 6.6%. It averages out to 7.5%. It is a far cry from the intentionally false house advantage (HA) of 1%, or even .5%! The overwhelming majority of blackjack players lose their bankrolls quickly, because this is NOT a 50-50 game or so much close to that margin! And always be mindful that blackjack is strongly sequential: The Dealer always plays the last hand. Otherwise, the casinos would go bankrupt!

Generate all possible blackjack hands to calculate player bust odds.

There are plenty of text files for you to take a good look at. They are absolutely FREE to view and even download to your PC. For viewing, I recommend a great text editor (also free): Notepad++. The text files show how the odds vary for different hit-limit settings. If you right-click a link, you can download it to your computer. If you just click, the text files open directly in the browser.


  • the typical 52-card blackjack deck


  • a modified deck, with one suit of each card; 13 cards from 2 to Ace, written as 11


  • the modified deck; hit-limit=12; stand on everything 13 or larger


  • the modified deck; hit-limit=13; stand on everything 14 or larger


  • the modified deck; hit-limit=14; stand on everything 15 or larger


  • the modified deck; hit-limit=15; stand on everything 16 or larger


  • the modified deck; hit-limit=16; stand on everything 17 or larger; the ubiquitous Dealer's rule


  • statistical summary only of all possible hands as arrangements; the typical 52-card blackjack deck; hit-limit=16; stand on everything 17 or larger; the ubiquitous Dealer's rule


  • the modified deck; hit-limit=17; stand on everything 18 or larger; just an example


  • the modified deck; hit-limit=11; stand on everything 12 or larger; the “rule” with no bust!


  • combinations from the typical 52-card deck; hit-limit=13; stand on everything 14 or larger; size: 1.4 MB


  • combinations from the typical 52-card deck; hit-limit=14; stand on everything 15 or larger; size: 2.3 MB


  • combinations from the typical 52-card deck; hit-limit=16; stand on everything 17 or larger; size: 5.5 MB.

    Get excellent resources in blackjack, including articles, books, pages, links, software.

    Free blackjack software generates 2-card hands to show accurate programming algorithms for BJ odds.

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    Read essentials of blackjack, software, calculator, odds, probability, dealer bust, house advantage.

    “Arrange, arrangement,
    Where is your regiment?”
    “It's at war against them odds
    That mightily scare the gods!”

    A blackjack deck of cards arranged lexicographically from the 4 deuces to the 4 Aces.

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    This BJ deck has only 12 Ten-value figures or paint cards as in Double-Attack Blackjack.