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.