Card Counting

This will probably be a real spam magnet but anyhow….

Some time ago, while I was still at uni, with a few friend I tried card counting blackjack. Like all casino games blackjack is in the house’s favour. However over the course of a deck (or several decks) this is not always the case for every hand. By keeping track of the cards that have come out of the deck, you can determine when the game is in your favour and increase your bet accordingly. Contrary to popular opinion you don’t need to track the actual cards that have been removed but rather keep a running tally on their effect on the game.

Certain cards are good for the player. A deck rich in aces gives more chance of blackjack with its higher pay out and a deck rich in tens gives the dealer who must hit automatically until he gets 17 or more, a much higher chance of going bust. Conversely a deck rich in 4, 5 and 6’s is bad for the player. The dealer will more rarely go bust as these cards will save him from going bust when he gets to totals of 14-16. The basics of such a system of counting and betting were first shown by Edward O. Thorpe and rely on both inferring a proportional measure of the expectation for a single bet and the use of the Kelly Criteria, in essence betting amounts proportional to your expected chance of winning.

In a small deck this is particularly effective as you get towards the end of the cards, but it’s also effective in large decks as well. Particularly if they place the cut card, which determines the point when the decks are reshuffled, near the end. Casinos of course take a dim view of the idea that someone else other than the house could be playing a positive expectation game and so try to stop it typically by banning the players in question. Counting is not illegal, but the casino is free to exclude anyone they don’t like.

The reality of the situation though is that unless you have a large bank roll you are better off working at McDonald’s, and if you are playing alone its pretty easy to detect someone with wild swings in their betting patterns, particularly if they are winning money. Still it was possible for us on many trips to the casino to sit off a table not playing until the deck was “hot” and then jump in and lay some bets. This makes you pretty obvious but if you are serious low rollers like we were when we were uni students then I doubt they are worried particularly.

Successful counters these days work in teams. A reasonably interesting book on the subject is Bringing Down the House, which although it concentrates too much on the glamour of the high-roller lifestyle and not enough on the actual scheme.

As for our little project, it slowly disappeared into nothing more than an occasional drunken trip to the casino where we would attempt to count through the haze. I note though now that the Star City Casino has put in continuous shuffle machines and the whole hope of counting is gone. I wonder whether it is actually a positive revenue deal for them. After all people like me will only play if they have the knowledge that they might just be able to have an edge even though in practice they rarely will. For the casino I guess giving this money away is worth it if it means avoiding serious counters.

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19 Responses to Card Counting

  1. Sacha says:

    Interesting, Steve. So would you keep a cumulative total of the cards that had come out?

  2. yobbo says:

    Jon Finkel made millions as part of a blackjack team. The book “Johnny Magic And The Card Shark Kids” tells all about it, along with a lot of mtg-related stuff you probably already know.

  3. Steve says:

    Sacha,

    Yes you keep a running tally generally. You can make a rough proportional estimate of your expectation return, by dividing the current count by the amount of decks left to play. You then bet roughly increasing in proportion to this.

    Kelly criterion comes out of information theory as the best betting strategy if you can make this estimate correctly.

  4. Steve says:

    Yobbo,

    Yeah I have been meaning to get it and read it some time.

  5. […] Card counting – Steve Edney discourses learnedly on card counting to beat the house at blackjack, before observing that continuous automatic shuffling has made it impossible anyway nowadays, at least at Melbourne’s Crown Casino. […]

  6. […] Card counting – Steve Edney discourses learnedly on card counting to beat the house at blackjack, before observing that continuous automatic shuffling has made it impossible anyway nowadays, at least at Melbourne’s Crown Casino. […]

  7. yobbo says:

    BTW Steve, Card Counting may be legal in America, but it’s not in Australia. Casinos in Australia are an arm of the state, and the state protects their interests.

    A card counter was arrested in Star City in the 90’s. Can’t remember his name.

  8. Steve says:

    Can’t speak for other states, but from when I read the rules back then and when I skimmed them just then in sydney it would have to be for either using devices or communicating strategy to another player. both of these are not allowed. Just sitting there keeping track of what has happenned though yourself is not banned.

  9. Sacha says:

    Yobbo and Steve – could you just count cards in your head – how would anyone know what you were doing?

  10. Steve says:

    they would know by the fact that to make money you have to vary your bet fairly widely. You need to be big when the game is in your favour and back right off when it isn’t. This is why individual counters get caught easily their play is easy to detect, even if you can’t prove what they are doing.

  11. yobbo says:

    Yes, you can count in your head quite easily, that’s what most people do.

    Like Steve said, they will detect you by your betting patterns. The casino staff in the camera room (if not the dealers themselves) will be counting too, and if you bet the minimum when the count is bad and the maximum when the count is good, they will know.

    The way the MIT and other blackjack teams attempted to get around this was by using multiple players.

    One player would be dressed as a tourist and sit at a table betting the minimum every hand and counting. When the count became favourable, he would signal to the “Gorilla” by ruffling his hair or something.

    The “Gorilla” would be another member of the team, dressed as some kind of high-stakes player (in one case, a russian MIT student who pretended to be an arms dealer) who would saunter up to the table, pretending to be drunk, accompanied by his entourage, and start betting the maximum.

    Sometimes they would have up to 4 or 5 different players working the same table.

    Bringing Down The House” tells the full story.

  12. Sacha says:

    How interesting!

  13. Zach says:

    How do you derive your chances of winning from the true count so you can plug them into the Kelly criterion?

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