Mathematics in gambling: counting cards, card counting at blackjack, black jack, basic strategy.

Mathematics In Casino Blackjack & Gambling: Card Counting

By Ion Saliu, Counter At-Large

Mathematics of gambling: counting cards, card counting at blackjack, black jack.

Posted by Terry Morgan on November 15, 2000.

In Reply to: Gambling Mathematics Applied to Blackjack: The Myth Of Card Counting posted by Ion Saliu on August 19, 2000.

: I'm fascinated by this. I had never been in a casino until about seven years ago I bought a second-hand copy of "Blackjack Your Way to Riches". I started to get interested in card counting, tried it out, and found that in general I made money; not great amounts, but enough to pay for my trip and leave a few hundred over. I did lose from time to time, and still do, but overall I am well up. Then I started playing over the 'net, but the card counting becomes less useful when the deck is shuffled only a third in, so I decided to just try using basic strategy -- I found that my winnings went up, contrary to what I had been led to expect. Counting obviously has its place, but I don't think it's on the net, and I think the maths is more subtle than the books suggest.

Now I'm started to get interested in roulette. Playing over the net, I started with $350 and, betting on birthdays, made tens of thousands of doillars in a few hours. I have tried to analyse why it worked (and of course replicate it!) but although I have had some winnings the sequences mostly lead to losses. Was it just beginner's luck? Can you recommend a good book on roulette strategy?

: • My emphasis has been MATHEMATICS IN GAMBLING. If there is a gambling system, I analyze it mathematically, first and foremost. It includes COUNTING CARDS, the most talked about gambling system. Many gamblers fall in love with one or more systems. Sometimes they go beyond that and worship their system. Card counting has become a religion for at least two decades.

: Mathematically, the card counting system has a minor influence today, if any. I showed in a previous post the only impact counting can have in a single deck game, Player against Dealer. A +2 count, generously translated into a 2% Player’s advantage results in a 0.01% better chance to get a blackjack (a “natural”). Such a chance increases, at best, from 4.77% to 4.78%.

: The main mathematical aspect is the SEQUENCE of the remaining cards. Card counting does not even attempt to “predict” the card sequence. In reality it is impossible to “detect” the sequence of the remaining cards. The number of sequences is staggering. They are calculated by the FACTORIAL operator (N!). Let’s exemplify briefly in an ideal situation. Before Edward E. Thorp’s “Beat the Dealer” book (an important work, indeed) the Dealer dealt all the cards in a single deck. Therefore, the penetration was 100%. A card counter would wait up until the last quarter of the deck or so.

: Why this aura of legend surrounding card counting at blackjack? Even more mystique is added when considering that Las Vegas is still barring card counters from playing blackjack. Says Carl Sifakis: “And what of the casinos today? Blackjack is a much bigger game today than it was before ‘Beat the Dealer’ appeared. More people than ever patronize the tables and casinos today make more money from the game than ever before. That’s a significant bottom line.” Roger Gros, senior editor of “Casino Player” magazine writes in his 1996 “Casino Gambling the Ultimate Play-To-Win Guide”: “After all, casinos make most of the money they make at the table games via blackjack. It’s great advertising when someone reports a big win at the blackjack tables. Players have been encouraged for many years to believe that blackjack can be beaten, and the casinos don’t want to do anything to disrupt that message.” (pg.30).

: I think the legend of card counting plays as the most successful means of advertising for the casinos. It certainly attracts a large number of players who believe counting at blackjack is a road to riches. There are also other ways that the card counting legend favors the casinos. Read any book on card counting and virtually all of them contain the same cliché. “If you are a card counter, make some bonehead plays so that the pitboss won’t ban you!” I think many card counters take the advice seriously. They do make bonehead, stupid plays from time to time just to hide their card-counting skills. What a stupid strategy for the player! What a profitable play for the casino! It is admitted that counting cards offers no more than a 2% advantage for the player. That’s a slim margin by all standards. Making bonehead plays can easily wipe out the slim, potential 2% advantage. The casinos owe big time to all authors of card-counting books. Then, in places where it is legal to ban skilled players from the blackjack action, the casinos commit downright robbery.

Mathematics in gambling: counting cards, card counting at blackjack, Ken Uston, Thorp Beat the dealer.

Blackjack: Software, Content, Resources, Systems, Basic Strategy, Card Counting

See a comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.

Of major interest: Blackjack, Black Jack: Basic Strategy, Card Counting; Charts & Tables, Probability, Odds, Software.

  • Blackjack Split Pairs Strategy Table.
    Color-coded chart to learn the best Split Pairs strategy. When you get your first two cards, look at this table first. The pairs occur the least in a blackjack game. If your hand is not a pair, move to the next chart: Double Down.

  • Blackjack Double Down Strategy Table.
    Color-coded chart to learn the best Double Down strategy. After consulting the Split Pairs table, look next at this table. The Double Down situations occur more often than pairs at blackjack. If your hand is not a Double Down situation, move to the next chart: Hit or Stand.

  • Blackjack Hit Stand Strategy Table.
    Color-coded chart to learn the best Hit or Stand strategy. After consulting the Double Down table, finally look at this table. The Hit or Stand decisions are by far the most frequent and important situations in blackjack.

  • Blackjack Basic Strategy Tables Split Double Down Hit.
    All three color-coded charts in one file, in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.

  • Basic Strategy Chart for Multiple Deck Blackjack.
    The traditional method of learning the Basic Strategy: all decisions in a table. The dealer up card is listed across (horizontally), while the player's first two cards are listed vertically in the leftmost column. For example, dealer's up card is 5. Player's first two cards: A+4; the right move: D (Double Down). It makes it somehow more difficult to learn the best decisions.

    This is real mathematics of gambling: counting cards, card counting at blackjack.


    Web site by Ion Saliu, founder of lottery software science, gambling mathematics.

    | Home | Search | New Writings | Odds, Generator | Contents | Forums | Sitemap |

    Web site by Ion Saliu, founder of lottery software science, gambling mathematics.