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 Shoe Penetration


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Shoe (Deck) Penetration In

Card Counting Blackjack


Shoe (Deck) Penetration as a Game Condition

Effect of Penetration on True Counts Frequencies

Effect of Penetration on a Card Counter’s Advantage

Penetration as a Casino Countermeasure



Shoe (Deck) Penetration as a Game Condition

Before dealing the cards to the players, a dealer offers one of the players to make a cut. A plastic card used for that purpose will indicate a point for a new shuffle. The number of the cards left behind the shuffle point determines how far a dealer goes into a pack before reshuffling or, in other words, how big or small the shoe penetration is. Thus, the depth of the penetration is one of the conditions of the game along with the rules and tolerated bet spread. The importance of that condition is hard to overestimate. It is so important it can make or break a card counter’s attempt to beat a particular game.

Effect of Penetration on True Counts Frequencies

The importance of the shoe penetration comes from its effect on the True Counts frequencies. A card counter enjoys the best advantages during the game at the positive True Counts. Every increase by one in a True Count increases a card counter’s advantage by about +0.5%. Obviously, the more frequent positive True Counts will be, the more often a card counter will be playing with advantage against the house and that will lead to a better positive outcome of the game.

The depth of the penetration leaves a specific number of the cards out of play. Shallow penetration means a big number of the cards will not be dealt. How that number affects the frequencies of the True Counts? By definition, a True Count equals a Running Count divided by the number of decks (or half or quarter decks for a single deck) still remaining in the shoe. That number includes the cards behind the shuffle point. The bigger that number is, the bigger that divider will be. The same Running Counts will be converted into smaller True Counts. In result, the decrease in depth of penetration should lead to the increase in the frequency of small True counts and diminished frequencies of the higher True Counts. Since high True Counts deliver to a card counter the biggest advantages, the detrimental effect of a shallow penetration and how it happens and works becomes clear.

A Table below shows the comparison of the frequencies of the positive True Counts for 75% and 67% penetrations. The assumptions are a 6-deck game, a full table, an average of 21 cards played per round, a player playing High-Low (Hi-Lo) strategy and standard Las Vegas rules.


True Count









Frequencies in %

75 % 









67 % 



















For ex, +1 in this table means all True counts from +0.5 to +1.5. The count of “0” includes an exact 0 plus all True counts that fall into (-0.5, +0.5) interval.

This table shows a drastic effect of smaller penetration on the frequencies of high True Counts. The decrease of only 10.6% from 75% to 67% in penetration leads to the astonishing decreases (35% and 70%) in the frequencies of the high True Counts equal +6 and equal +7 and higher. These are the counts when a card counter enjoys the highest advantages of +2.44% and +2.94% respectively in our example. 

Effect of Penetration on a Card Counter’s Advantage

Smaller penetration means less frequent high True Counts. The diminished frequency of the high True Counts shrinks the overall advantage that a card counter might have provided that all other conditions of the game stay the same.

For ex, if we’ll use Stanford Wong’s theoretical spread of 1-10 (“Professional Blackjack”), a card counter playing perfect High-Low Strategy can get +0.2% theoretical advantage against the house if the penetration is 75%. If the penetration is 67% his advantage will be +0.08%. Thus, the decrease in penetration by only 10.6% explodes into a 60% drop in a player’s advantage.

If a more realistic spread of 1-6 is employed, then a card counter’s advantage at best is +0.096% with 75% penetration. If a pit boss will tell the dealer to shuffle earlier at 67%, then a card counter’s advantage disappears altogether. A player will face a theoretical disadvantage of -0.03%. In this case a drop of 10.6% in penetration turned an advantageous game with positive expectation into a guaranteed theoretical loser with negative advantage. And no card counting “expert” in the world can do a thing about it provided that he plays through the shoes dealing with all negative and positive counts which most of the players do. The disadvantage in the real game, obviously, will be a lot bigger due to inevitable occasional mistakes.

Penetration as a Casino Countermeasure

The devastating effect on a player’s advantage produced by the change in penetration means that manipulating penetration size is the best anti – card counting legal countermeasure the casinos were able to come up with. The mathematicians that worked for casinos were just as brilliant as those who were writing card counting books and devising countless counting systems. Since Thorp’s “Beat the Dealer” was published, the casinos used dozens of legal, semi-legal and down right illegal methods to counter overestimated card counting threat. All they really needed to kill all card counting attempts was decreasing penetration when it was necessary. Shallow penetration can kill any game and make it unbeatable for any card counting expertise. The ultimate use of the penetration factor comes in the form of continuous shuffling machines, which appeared in the early 1990s. These machines put a card counter in front of the freshly shuffled shoes every round making it impossible in principle to use a card counting approach. In result, the Basic Strategy with its guaranteed loss of -0.56% is the only strategy left for the players to use. Casinos, however, do not need to go that far. It’s better for them to keep counters on the hook but make a penetration shallow enough to guarantee a win for casinos and loss for the counters.

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