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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.

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