Influence of Penetration
In the article of House edge mentioned before, we focus on the impact the rules of the game offered by different casinos have on the player advantage. Likewise, in assessing the blackjack game, penetration is an unavoidable topic. In fact, a book named < The Blackjack Formula 
> published in 1980 has studied the relationship between the penetration and the expected value the card counters would gain.
> published in 1980 has studied the relationship between the penetration and the expected value the card counters would gain.Penetration means the total number of cards which can be played before the next shuffling. For example, when half of the playing cards are cut off, the penetration is 50%. And one deck of cards cut from four decks of cards, can have a penetration of 75% (you can play three decks of cards.) The higher penetration the casinos offer, the better for card counters. In fact, the impact of the penetration is obviously far greater than the difference between counting systems and different gambling rules and any other factors. It can be witnessed by many modern in the modern computer simulation results. In other words, a good penetration is much more significant than a good card counting system or and a good game rule.
It can be understood that in a deck of cards, the number of cards that can be issued is closely related with the profit the players make, because the relatively low penetration rate means that the card is thickly cut. Relatively speaking, the reshuffling will be occurred earlier, in which players can only play fewer cards, so that the chance to have good cards with high true count would be reduced markedly and to a large extent affect the profitability. The following statistics lists the penetration rate at various true counts. It is obvious that the lower penetration is, the less chance the high true count appears.
Penetration( Out of 100)
Index 50% 65% 75% 85%
+1 15 15 13 13
+2 8 7 8 8
+3 3 4 4 5
+4 1.5 2.5 3 4
+5 1 1 2 2
+6 1 1 2 2
+7 0 1 1 1.5
+8 0 0 0.5 1
+9 0 0 1 0.5
+10 0 0 0 0.5
Obviously, you can see from the table, if you play the game with 50% penetration cutting off half of the cards, there would averagely be 29 hand of cards with the true count higher than +1 for every 100 hands. Because you tie with the casino's advantage at true count of +1 (the default house edge for the casino is 0.5%), then you only have 14 hands of cards with more advantages than casinos if you play the hands without the true count of +1.
In contrast, in the case of penetration of 85%, you will have 31.5% of chance to tie with the casino, and almost 25% chance to win the casino, so the opportunity to profit is greatly improved. In theory, the game with less than 68% of penetration is not worthy of playing which is a waste of time and money. We need to spend time and capital in the places where we can make money much easier. While some casinos provide bad gambling rules, if they have a relatively good penetration, then we still can effectively defeat them.
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