Arnold Snyder’s Blackjack Theories

Last Updated on January 11, 2017 by Trevor Hallsey

In Arnold Snyder’s 1980 book “The Blackjack Formula,” he put forth a theory that would send ripple effects throughout the world of professional blackjack players. He explained a concept called “deck penetration” and how it relates to a player’s win ratio. He then presented a simple formula that players could use to determine their anticipated win rate based on table conditions. The strategy is just as applicable today as it was some 35 years ago. It is worth players’ while to add this insight to their toolkits.

The Theory Explained

The table conditions primarily responsible for determining the House Edge are the number of decks in play and the House Rules applied to the game. As all players know, the more decks used, the greater the House Edge. Where a single-deck game with favorable rules may give a card counter an advantage of +0.02%, the same game played with a double deck will swing the advantage to the House at -0.31%. With four decks in play under the same rules, the House Edge increases to -0.48%, with six decks it is -0.54% and at eight decks the House claims an advantage of -0.57%.

Snyder recognized that the removal of cards during play was effectively shifting the edge to the player. He referred to this as “depth of deal” or “deck penetration”. It is a measure of how far into the shoe a dealer is before the cards are reshuffled. Anywhere from 2% to 90% of the total cards may be dealt out.

According to Snyder’s theory, the deeper into the shoe the game goes, the better. More cards dealt out means more cards seen by the card counter. And more cards seen means a more accurate count. He also noted how penetration affects the betting spread required for profitability. In general, the shallower the penetration, the larger the betting spread must be to beat the game. And with a bad set of rules and poor penetration, it might not be possible to beat the game with any spread.

Putting Penetration to the Test

Today, most advanced card counters accept these principles without question, but in the 1980s, the concept was nothing short of revolutionary. Was there really any great difference between a single-deck game with 55% penetration and one with 65% penetration? After all, 10% is just five cards. Yet Snyder’s calculations showed conclusively that the player’s advantage nearly doubled—a huge breakthrough.

In his book, the future Hall of Famer advised players to avoid single deck games unless more than 50% of the cards are dealt out between shuffles. For double-deck games, the penetration should be at least 65%. With four or more decks, 70% of the cards should be dealt out as a bare minimum. What’s more, regardless of how many decks are in play, a 10% difference in penetration can make a huge difference in profit potential, meaning a six-deck game with about 5 decks dealt for 85% penetration is greatly preferable to a six-deck game with just 75% or about four and a half decks dealt out.

Fortunately, where multi-deck games are concerned, it’s quite easy to identify tables with high deck penetration. Simply look for where the dealer inserts the cut card before placing the decks in the shoe. It should be an easy matter to estimate the percentage of cards that will be put into play.

Trevor Hallsey