Blackjack House Advantage Calculator

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This guarantees the house a 25.71% advantage over the player in these situations. Second, a no-bust player will only hit a hand of eleven or less, or a soft (hence unbreakable) hand of 12 to 16. This counts for only 26.63% of all possible two-card hands. Blackjack is a game that is most often played with six-to-eight decks shuffled together and mixed in a shoe. Whether that shoe is favorable to the player or to the house largely revolves around one factor—how many ten-value cards remain in play.

Twenty-One is just about the friendliest game to a player you can find in a casino. Even if a novice knows little more than the easy-to-learn basic strategy of blackjack and only sometimes plays with his gut, the house will only have around a 2.5% advantage which is better than any other table game or slot out there. Now just imagine how successful someone could be at the tables armed with just a little bit more knowledge than “the basics”.

This is where blackjack calculators come into play. Standard 21 dealt from a single deck is a simple game, but casinos have added rule variations and side bets into different versions while also expanding the number of decks used to as many as eight. At this point even the experts can get tripped up and make a mistake.

However, now thanks to the wonder of the Internet, calculating how all of these changes affect the house odds is only just a few clicks away. Check the boxes of all the variables that apply to a game, hit “calculate”, and instantly you can make an informed decision on any number of intertwined factors.

Best Blackjack Calculators

Casino Advantage: This calculator is especially valuable to online blackjack players because there are tons of casinos to choose from, each with a slightly different set of rules for their games. Land-based operators usually abide by a single set of House rules and there are few or no other choices available.

Often the rule variations are a give and take proposition – some favor the House, while others favor the player. Casino, or House Advantage calculators sort all of these odds out and present the numbers clearly. The most sophisticated calculators will even take into account very minor advantages, for example, whether the house uses a cut card, which would favor the dealer’s odds of winning. Approximately 7,000 combinations are boiled down to a single, understandable number in these calculations.

Strategy Advisor: There are plenty of advanced blackjack theories rattling around out there that promise to take the House Edge and flip it on its head, and needless to say: most of these are straight garbage and should not to be listened to. Even though there may not be a single “best strategy” for people to rely on, there may be a plan that best suits their skill level and playing style.

That is the theory behind the strategy advisor that matches players with individualized game plans after a short self-rated skill evaluation. Players enter their decisions and the calculator analyzes the data and gives advice on how they can improve their game.

Game Calculators: Special blackjack variations such as Spanish 21, (a 48-card deck with the tens removed), are no longer a mystery with certain game calculators. Before trying these variants players can now learn how the game is stacked against them; after all, casinos are not introducing new blackjack variants because they want to be nice to the player. The numbers will always be in favor of the House.

The calculator for each unique version will give players the exact odds in every type of situation and will suggest the mathematically correct decision to take.

Bankroll Calculators

There are many online calculators to help blackjack players manage the financial side of their career. Depending on a player’s appetite for risk, the size of the beginning bankroll, available playing time, and the goals for the session, these calculators can determine a probable range of results for what will lie ahead.

One of the most popular of these calculators was in existence long before the Internet Age. It is the “Gambler’s Ruin” that calculates the probability of a gambler increasing his or her stake before going broke. The numbers that are entered are 1) the amount of the beginning bankroll, 2) the target win percentage, 3) the length of time of the session, and 4) the size of the bet.

By playing around with the initial numbers a player can know the potential Risk of Ruin and plan a blackjack session appropriately. Although, many would argue that trying to predict the future in this way is nothing more than a fool’s wager.

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

Version 21, June 2014; New Software.
BjBustOdds 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.

  • My blackjack software to calculate accurately the odds, including the source code, was available for a limited time. The offer was withdrawn for patenting reasons — the source code was outrageously cheap.
      You can view, however, free text files that show all possible blackjack hands based on Dealer's rules, plus 'card decks' of various sizes:
    • Blackjack Dealer Bust: New Software to Calculate Odds, House Edge.

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!

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.exe 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:

BjBustOdds

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):

@ECHO OFF
PATH C:;C:BAT;C:BAS;C:LOTTERY;%PATH%
doskey co=copy $1 $2
doskey d=dir /O:N /P

Advantage

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:

Blackjack House Advantage Calculator

@ECHO OFF
CLS
C:
CDBjBustOdds
BjBustOdds

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:

cdBjBustOdds

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

CD

    Please be mindful that generating all possible blackjack hands as ARRANGEMENTS might not be possible with write-to-disk enabled. Both BjDeck1.TXT (52 cards) and BjDeck2.TXT (48) will need output files in excess of 10 gigabytes!!! You have to comment out the source code: BjBustOddsOrder.bas. You do that by replacing all PRINT #3 statements by 'PRINT #3 (' is the comment symbol in PowerBasic).

    Of course, if you can convert the source code to a 64-bit compiler that creates TRUE 64-bit EXE files that run in a 64-bit operating system (e.g. Windows 7 or 8).

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.

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.

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):

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

Blackjack House Advantage Calculator Price

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!

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.

    BjDeck1.TXT
  • 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.
  • Axiomatic one, I decided to prove that my programmatic method of calculating the blackjack odds is FLAWLESS. I am not yet offering the source code for it is extremely valuable. But I offer TOTALLY FREE a program that generates the first 2-card blackjack hands: Blackjack2Cards. The software shows every 2-card hand perfectly, plus 100% accurate statistics, such as PAT hands, STIFF hands, PAIRS, DOUBLE DOWNS, BJ NATURALS. You can also download for free two text files that show all BJ 2-card hands, both as ARRANGEMENTS (order counts) and COMBINATIONS (order is not important).
  • Download Blackjack2Cards.
  • Download BJ2CardArranH16.1D – 2-card BJ hands as ARRANGEMENTS.
  • Download BJ2CardCombsH16.1D – 2-card BJ hands as COMBINATIONS.

Blackjack House Advantage Calculator Estimator

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