Posted by Ion Saliu on August 19, 2000; and later (the later, the better!)

In Reply to: Ken Uston and card counting in blackjack: CBS's 60 Minutes posted by Mr. T on August 15, 2000.

• My emphasis has been on MATHEMATICS IN GAMBLING. If there is a gambling system, I analyze it mathematically, first and foremost. It includes BLACKJACK 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 Blackjack 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 blackjack 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. Let’s say the counter estimated that around 13 cards were remaining in the 52-card deck. The legend has it that many struck it big at the blackjack tables simply by betting huge amounts towards the end of the deck. Mathematics, however, does not confirm such claim. To calculate the number of possible sequences of 13 cards in blackjack, we use 13! = 1x2x3x…x12x13. The result is: 6,227,020,800 (over 6 trillion sequences). Let’s be fair. There would be only 10 unique cards among 13, since 10=J=Q=K. In this case, 10! = 3,628,800 (over 6 million possible sequences)! Imagine an even better situation for Player, that the count is +3 and that there are no “neutral” cards remaining (e.g. 7 , 8).

We can use software to generate 13-card sequences. The composition would be 8 high cards (H) and 5 low cards (L). I used my software for the task (SHUF-5.EXE or SHUF-6.EXE). The program generated thousands of sequences, from card 1 to card 13. I considered 1-5 as L and 6-13 as H. Here are the three final sequences of the run:

L, H, L, H, H, H, L, H, L, H, H, L, L
H, L, H, H, H, L, L, H, H, H, H, L, L
H, H, L, L, L, H, H, H, L, H, L, H, H

Let’s play the first sequence now, between one Player and the Dealer.
Player gets L, Dealer gets H. Player gets H, Dealer gets H. Player stands, Dealer stands. Dealer wins one hand. Player gets H, Dealer gets H. Player gets L and stands, Dealer gets H and wins the 2nd hand. Player gets L, Dealer gets H, Player gets H, Dealer gets L and draws L; more probably, Dealer wins the hand.
In the 2nd sequence, Player gets H, Dealer gets L, Player gets H and stands, Dealer draws L, and must draw to LH, gets an H and busts. Player wins the 1st hand. Player gets L, Dealer gets L, Player gets H and stands, Dealer gets H and draws another H (bust). Player wins the 2nd hand.

It is very, very complicated. We are dealing with over three and a half million sequences. The matters are a lot more complicated when we consider the neutral cards and multiple players. The impact of card counting appears to be near negligible. I count cards sometimes up to the latest card. I call it the “real running count”. At the end of a round the count is positive, for example. When it is my turn to make a decision after my first two cards, the count turns out to be very negative. A blackjack card counter would have bet bigger at the beginning of the round. When it was his/her turn to make a decision, the count would be clearly negative. The player might expect a low card. Quite often, Player gets the opposite, a busting high card. I noticed frequently such sequences. They seem to be totally random. If you are a faithful card counter, you should expect to lose serious money for a significant number of rounds (hands).

Sometimes, but rarely, card counting might help in hitting or double-down decisions. Once, I shocked the audience when I doubled-down on 12 against dealer’s 6. The dealer announced his pitboss my play. Curiously, I won! The count was very negative. I did it more for showmanship…

• • The personal side of my previous posts on Thorp and Uston relied on blackjack and gambling books I have read. I have never claimed I experienced first hand Thorp’s or Uston’s casino playing. First of all, I praise the two computer programmers who took on a very difficult challenge. Trying to discover rules in random events such as gambling represents an enormous task. Yes, the casinos did change the rules after Thorp published his book. The simple fact that the casinos added “penetration” to the deck diminished the effect of counting to fractions of a percentage point.

One problem I have with the two blackjack authors and researchers is the fact that they reached a point of worshipping card counting. I am sure they did a large number of computer simulations. I am sure they noticed the negligible effect of the system. Yet they continued to influence a large number of potential casino players that card counting was the road to the riches. I would like to present a few more excerpts on Thorp and Uston. Carl Sifakis writes in his 1990 “Encyclopedia of Gambling” (pg. 36-37).

Dr. Thorp is still in computerized mathematical research, but he is now concerned with looking for values in stocks… The late Ken Uston, author of numerous books on counting, was at the end of his life involved in computer work in the Middle East, helping Kuwait track billions of dollars in investments. He was not playing blackjack in Atlantic City, although he had won a court case that barred casinos in New Jersey from refusing to let counters play. In fact, Uston, upon winning that case, didn’t hit the blackjack tables in Atlantic City but signed up to do TV commercials for Resorts International, the very target of his suit… One long time gambler, Murray Friedkin, says of Thorp in ‘Big Julie of Vegas’ by Edward Linn: ‘Thorp is the smartest man in the world; if you don’t believe me, ask him…Whatever Thorp may say, I can tell you that if he has made any money on blackjack he made it by writing a book.

The late gambling expert John Scarne derided the counters and challenged Thorp to a $100,000 match at blackjack. He later extended the challenge to other leading counting advocates. There were some nos, then yeses, then considerably more backing and filling; the blackjack contest never came off.”
Edward O. Thorp is associated with another gambling “system”: the “Big Toe Method” of beating the “Wheel of Fortune” (“Big Six”). Says Carl Sifakis in the same book I quoted above: “Is the Thorp Big Toe Method still in use? The bottom line is that the money wheels of all kinds are still in place in the casinos, something that would not be the case if there was a way they were being beaten considerably.” (pg. 31).

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 blackjack 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 blackjack 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 blackjack player! What a profitable play for the casino!

It is admitted that counting cards offers no more than a 2% advantage for the blackjack 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.

From what I have read, the casinos show a strong bias towards barring a blackjack player when he/she is at a serious LOSS! I read once that a known card counter was losing some $14,000. Exactly at that point, the pitboss approached the counter and asked him to leave the blackjack game! Get it? The $14,000 went immediately to the casino bottom line. Meanwhile, the player was deprived of a reasonable chance to recuperate his loss. After all, blackjack is almost an even-odds game for a player using the basic strategy. It is fair to expect swings in the winning and losing columns of the player. Of course, the banned player is allowed to play blackjack again. The pitbosses pretend to have forgotten him/her, until another significant loss for the player. The player is thrown out again! If the known counter is winning, the rationale is that a swing in the fortune will follow. Sooner or later, the player will encounter a severe loss. That’s when you ask a counter to get out! What casino would be happy if a winner does do take the money and run? BRRRRRRRRAHAHAHAHA!!!!!

In conclusion, mathematics must offer the main perspective when gambling is concerned.

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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.
  • The myths of blackjack: card counting; best links.
  • Blackjack card counting by Edward E. Thorp, Ken Uston and real math.
  • Blackjack card counting by Edward E. Thorp, Ken Uston and real math II.
  • Ken Uston on CBS 60 Minutes.
  • Mathematics in casino blackjack & gambling: card counting.
  • Roulette, Blackjack Systems Challenge Test in Casinos.
  • Roulette, Blackjack Systems Challenge Test in Casinos 2.
  • Blackjack, Roulette, Systems Test in Casinos.

  • • Of interest:
    The Philosophical Science Of Winning And The Law.
  • Blackjack, Basic Strategy, Card Counting; Double Down, Hit, Stand, Split Pairs; Charts & Tables; Probability, Odds, Rules.
  • Baccarat, Super Baccarat: Theory & Software.

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