Why Penetration Matters
by Nicholas Colon
[Nicholas Colon is a former MIT team player/manager, now a writer, lecturer, gaming consultant and Las Vegas poker player.]
As even the most novice players know, the fundamental premise of card counting is that it calls for the player to make small bets when the casino has an edge over the player and in turn calls for you to make big bets when the player has an edge over the casino. Whatever counting system is used it provides a method of calculating how big the edge is, and in turn determines the best betting strategy given your bankroll constraints.
The casino companies have mostly done away with "traditional" single-deck blackjack games (the 6:5 games out there arenít "real"), because the count in a single-deck game is very volatile; just seeing two more small cards (+1) than big cards (-1) on the first hand creates a true count (TC) of over 2 for the next hand. Casinos avoid games where the player can easily gain an advantage over the house.
To avoid several opportunities where the player can get an advantage, casinos decided to offer multi-deck games where their starting edge is bigger and the count is less volatile. However in a multi-deck game the count can continue to increase hand after hand. This does mitigate the lower volatility, but what holds true for plus counts holds true for minus counts. In a single-deck game, a minus count is soon shuffled away because the dealerís running out of cards, but in a multi-deck game the minus count can continue until itís time to shuffle.
Another way the casino industry seeks to reduce potential player advantages is by dealing out only a percentage of the cards in the shoe. On average, this percentage dealt is approximately 75%. Card counters refer to this percentage dealt as "penetration". This factor alone can make a difference in whether or not the blackjack game is beatable. The reason penetration matters is because if the penetration is not deep when the count starts going your way out comes the shuffle card. By limiting the penetration, casinos also limit the volatility of the shoe.
It is possible to measure the effect penetration has on a card counterís long-term advantage. In general, the deeper the penetration, the better it is.† This assertion begs the question what is deep penetration?† Most of the information that answers this question has come from simulations run on the software called "Statistical Blackjack Analyzer."†
The analysis only applies to live blackjack games found in real brick and mortar casinos.† A different analysis applies to online blackjack. For those games the programming code must be taken into account.
The game I chose for the simulations has the following rules: six decks, the dealer hits soft 17, double on any first two cards, including after splits; pairs can be split to form up to four hands, the dealer "peeks" when they have an Ace up, and late surrender is available. These rules give the casino an approximate edge of 0.54%. Call it 0.50%. This is a decent game by 2021 standards, and it is a typical game that can be found in most Las Vegas casinos. If your local game has better rules, then the simulations will be on the conservative side.
Now let's consider an example where the penetration is very shallow, say 66%, and the betting schedule is very conservative, at just one times the TC in chips. At a TC of 1 or lower, one chip is bet; at TC 2, two chips is the bet; at TC 3, three chips are bet and so on, all the way up to a maximum bet of twelve chips. With such shallow penetration, youíll rarely make a twelve-chip bet because the shuffle card is going to come out before that count is reached.
The simulations at this penetration show that a TC of more than 6 will occur only at a rate of once every 300 hands.†This includes all TCs of 7 or more. Essentially youíre using a 1-6 bet spread in a six-deck game. This bet spread is not large enough to make any significant amount of money.† A 1-6 spread is the bare minimum that a counter needs to make any money using a straight counting game, with comps being added as part of your expected win. A long-term edge in dollar amount is -0.10%.†
In other words, using this basic betting system youíve cut the house edge down by 80%, but are still playing a losing game when comps are not accounted for. If all else remains the same — rules, bet schedule, etc. — and the penetration is deepened to 5 of 6 decks (83%), the long-term edge moves up to +0.32%.† Even with these two scenarios it is easy to see the effect of penetration on professional blackjack play.
The bigger the bet spread doesnít always mean a better game. Consider a new situation with the same rules as before with a full 1-12 bet spread being used, where the penetration is 75%. If you bet one unit at TC 1 or lower, two units at TC 2; four units at TC 3; eight units at TC 4; ten units at TC 5 and 12 units at TC 6 or higher, the long-term edge is 0.45%. This is a worse edge then before.† Situation one is not only better but it wonít get you banned from the casino. The most compelling aspect about simulation one is there are no big jumps in your bet that might attract unwanted attention from casino game protection personnel.
In the end, penetration impacts the overall advantage of the game substantially.
And there is some additional information to consider:
Where is the "killer" edge? Well, it canít be found at a game where the dealer hits soft 17, but if thatís all youíve got, then you need to seek out a table where 5 of the 6 decks are used (83% penetration), you need to get your twelve-unit bet out at TC 4 AND you need to abandon the shoe at TC -2. Using this methodology will yield a long-term edge of 1.22%.† This is pretty good for the circumstances. If you can find a game where the dealer stands on soft 17 and late surrender is still available, a long-term edge of 1.40% is attainable.. ♠
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