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View Full Version : BlackJack: Why Do More Decks Increase the House Advantage?

TomBrooks
09-19-2005, 04:33 AM
In Blackjack, why does playing with more decks provide the house with a better advantage? I don't see why it should make any difference. (Ignoring any card counting factors.)

The Wizard of Odds provides a different strategy charts for One, Two, and Four-or-More Deck games. But why would the strategy be different? While there are more cards, the relative number of any particular card to the total number of cards remains the same.

For one deck, Woo provides a Correction page for changing the action on certain specific holdings. I can see where that provides an advantage.

BruceZ
09-19-2005, 05:40 AM
[ QUOTE ]
In Blackjack, why does playing with more decks provide the house with a better advantage? I don't see why it should make any difference. (Ignoring any card counting factors.)

The Wizard of Odds provides a different strategy charts for One, Two, and Four-or-More Deck games. But why would the strategy be different? While there are more cards, the relative number of any particular card to the total number of cards remains the same.

For one deck, Woo provides a Correction page for changing the action on certain specific holdings. I can see where that provides an advantage.

[/ QUOTE ]

This is discussed in Peter Griffin's The Theory of Blackjack, which is the primary reference for this kind of question. It says that over half of the difference comes from an increased advantage of doubling in single deck, and that the rest comes from an increased advantage of standing on stiff hands. In both cases, the idea is that the 2 cards that the player holds make a larger difference in the composition of the remaining cards in single deck than they do when they are removed from multiple decks.

In the case of doubling, the cards that are removed are more likely to be cards which would be disadvantageous for the player to draw, so removing them increases the value of the double. Also, the probability that the player draws a 10 is higher, and the probability that the dealer has a hole card of 10 with an up card of 2-6, which would give him a stiff hand, is higher.

When the player holds a stiff hand, he is likely to hold 1 or more cards that would help the dealer when his up card is 2-6, so standing against these values becomes more favorable when these cards are removed, but the difference is greater in single deck than multi-deck.

Note that the probability of being dealt a blackjack in a single deck game is 4/52 * 16/51 (times 2 since the A and 10 can come in either order), while in an N deck game it is 4N/52N * 16N/(52N-1) times 2, which is lower. Griffin says that this effect is canceled out by an increase in the advantage of pair splitting in multi-deck games. I just mention it to show how the probability of being dealt a particular 2-card hand changes.