Although there are legends about old time blackjack players getting an edge by «casing» the single deck, the modern history of blackjack advantage system development starts in 1958 with the publication of the basic strategy for playing the hands by Cantey, McDermott, Maisel and Baldwin. Initially published in the American Journal of the American Statistical Association, it caused much excitement among both gamblers and statisticians. I remember someone showing me a dog-eared copy of the article, which I immediately copied and committed to memory.
Then the four originators published their basic strategy, all their work done on hand calculators, in a book called, I believe, Winning Blackjack, which has now become an extremely hard-to-find collectors item. I wish I had saved my copy. The original basic strategy published in this book is very close to that which is in use today.
I was working in the Aerospace industry in 1958 when Winning Blackjack was published. The book became the reason for frequent trips to Las Vegas. Myself and two or three friends would meet at a rendezvous point in the San Fernando Valley, get on the Hollywood Freeway, connect to the San Bernardino Freeway, stop in Barstow for coffee, making the 296-mile drive in about six hours. Our first stop was the Dunes where we would look for Ralph, our favorite dealer, and play single-deck blackjack dealt to the bottom well into the night (remember this was before Thorp's book). Our $100 bankroll was converted $20 at a time into real silver dollars, which were the dollar chips of choice in those days, and we would grind away with our $1-unit bets well into the night.
Playing almost even against the house as we were, we never lost much and actually ended many trips money ahead. Our betting strategy was to increase our bet $1 on successive wins and hope for a winning streak.
Getting back to the publication of the basic strategy, it was the dawn of the developmental work, which continues right up until this day. It started by sparking an interest in Ed Thorp with his realization that blackjack is different from roulette and craps because, unlike craps and roulette, the outcome of each hand depends on prior events, i.e. which cards had been dealt and which cards remain in the deck to be played. Statisticians use the words «independent trials» and «dependent trials» to describe this phenomenon.
Development of a Blackjack Computer Model with Will Cantey & Herb Maisel
I accepted a position with a start-up company in 1961 and moved east to the Washington D.C. suburban area. I was disappointed that my monthly trips to Vegas would cease, but this was more than compensated by three individuals who became friends and co-workers.
In the early days of the Cold War, lots of dollars were flowing from the Defense Department into the private sector for military studies. The start-up firm secured a lucrative contract with a joint Army/Air Force Task Force for the development of a War Game Simulation Model.
Imagine my surprise on my second or third day of work when I learned that Will Cantey and Herb Maisel were on the civilian staff of this agency (two of the four developers of the original basic strategy). As we got to know each other, another friend, Tony C., suggested an off-time project, using our collective expertise on simulation models and computer programming, to develop a blackjack simulation model.
Tony was the designer, I was the programmer and Will and Herb were the consultants. Many long hours were spent after working hours on this project and we had a lot of fun in deciding how to shape it and in formulating the studies we would conduct with the working model.
My job was to write the program, initially just to play blackjack hands between one player and a dealer using basic strategy. Once this was completed, the studies we performed were concerned mainly with number of players in the game, rules of play (we were fascinated by the liberal rules in the Pioneer Club such as doubling down on any number of hands) and betting tactics and strategies.
The 709 Computer at this agency had open time on many night shifts, so we had opportunities to «play» many 100,000-hand samples. About six hours were required and the lights on the computer console would quit flashing to make it appear that the computer was in an endless loop with nothing happening. The first time we had to convince the operator to let it run and he was amazed when end-of-job occurred at precisely the time we had predicted.
It is interesting to note that Cantey, Maisel and Tony were aware that blackjack was a dependent trials game and that the odds of winning were affected by the cards left in the deck. We came to this realization perhaps about the same time Thorp did, but did not possess sufficient knowledge or motivation to see it through to the development of a card counting system. Our computerized simulation of blackjack would, however, be used in the future to provide independent verification of Thorp's 10-count system.
The Thorp «Ten-count System»
Thorp was the first to exploit this idea of dependency. He devised a counting system for beating the game and published it in his book Beat the Dealer in 1962. He called it the Ten-count System, and it was aimed at the single-deck game, then standard in all Nevada casinos. It was extremely difficult to learn and thus impractical for all but the most skilled players.
I have vivid memories of learning Thorp's Ten-count System. You had to keep a running count of tens (10, J, Q, K) and «others» yet to be played - an exact count, not an estimate. You started with two numbers for the single-deck game - 36 and 16 - and you counted backwards from these two numbers as the cards were played. This, then, gave you a running count of Tens and Others remaining to be played. After each round you divided your count of remaining others by the count of remaining tens to compute what we came to call the «Thorp Ratio.» This number gave the player an indication of his advantage; i.e. if the Thorp Ratio was 2.0, e.g. 30 others and 15 tens remaining in the deck, the player's advantage on the next hand was 1%.
Thorp presented a betting table for plugging the ratio into which yielded a betting spread of from one to five units. After dividing others by tens and rounding to two decimal places, e.g. getting a number like 1.57, you mentally compared the resulting ratio with this table to find the proper range and thus the correct bet size for the player advantage on the next hand.
This process was extremely difficult to apply in real world casino conditions and Thorp, recognizing this in the second edition of his book, recommended that a rough estimate, to within 0.1 or 0.2, would be satisfactory.
Nonetheless, Thorp and some early single-deck players he personally taught cleaned up after the book was published in 1962 and forced the Nevada casinos to change the rules of blackjack; e.g. restricting double downs to 11 only. The media publicized this story in dramatic fashion and the book became a best seller. Tens of thousands of new blackjack players bought Thorp's book to get in on what they thought would be a «gravy train».
The casinos, realizing that the negative publicity was hurting their profit margins, quickly restored the rule changes, but introduced more subtle changes to thwart the legions of card counters who were invading Nevada to make their fortunes.
Most gave up because of the demanding mental strain of keeping the two counts, dividing or estimating the Thorp Ratio, and then making the mental comparison to find the appropriate bet size. But the damage had been done and casinos introduced two procedures which changed the game forever: (1) Shuffling the deck on suspected card counters and (2) Introducing multi-decks and dealing blackjack from a shoe instead of from the dealer's hands.
Jerry Patterson, a gambling instructor, author and player for 25 years, is author of Casino Gambling: A Winner's Guide to Blackjack