atg
atg
Joined: Sep 14, 2010
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September 14th, 2010 at 1:40:43 PM permalink
Assuming the player is not counting cards, why does fewer decks benefit the player?
NightStalker
NightStalker
Joined: Jul 25, 2010
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September 14th, 2010 at 3:34:31 PM permalink
Effect of removal of cards involved in the hand is more in lower decks.
If your first card is ace. Your probability of getting a blackjack is higher in Single deck than in double.
Same holds true for dealer showing a '5' and hitting it with another '5' in hole..

Thus, house edge increases with decks. Playing perfect composition strategy will help to lower the difference..
pacomartin
pacomartin
Joined: Jan 14, 2010
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September 14th, 2010 at 4:53:55 PM permalink
The Wizard of Odds Blackjack appendix 9 gives you the expected value for each combination of cards.
For instance a player pair of tens against a dealer 10. If you choose to "stand" the EV are:
0.583154 for single deck
0.568553 for two decks
0.561473 for four decks
0.557987 for 8 decks

You can actually program a spreadsheet to calculate the EV for this relatively simple case. There are a lot of cases, but since the player chooses to stand, you only need to work them out for the dealer. Make one of your variables, the number of decks.

Almost all the plays have a better EV for a fewer number of decks.

In general the previous answer gives the best "overall explanation".
mkl654321
mkl654321
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September 14th, 2010 at 5:12:10 PM permalink
The player benefits from certain combinations, such as a natural, and two-card combinations that can be doubled down profitably, like 6-5 or 9-2. The more decks are used, the less prevalent any one combination will be relative to all others.

For example, you get a blackjack approximately 5% less often in a multi-deck game than in a single-deck game. Of course, the dealer will get them less often, too, but the dealer only gets paid even money when she gets one; you get paid 3:2 (unless you're a moron, in which case you only get paid 6:5).

This can be seen in this way: give yourself an Ace. What are the chances of getting a blackjack? In the case of a single deck, there are 16 cards out of the remaining 51 that will do the trick. In a six-deck shoe, there are 96 cards out of 311. 16/51 > 96/311. (Or, in comparing to a two-deck game, 16/51 > 32/103, which is perhaps easier to see.)
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
pacomartin
pacomartin
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September 14th, 2010 at 5:18:33 PM permalink
The following table is fairly easy to construct. If you have a pair of tens against a dealer 10, and the dealer has peeked and does not have blackjack then what is the probability that the dealer will tie you with one card.


You can see that the dealer has a better chance of a push with only one card if the number of decks increases. Working out the expected value for the complete case is tedious, but if the dealer has better chance of a push with one card, it ends up he has a better chance of a tie or a win with multiple cards.


decks tens remaining tens remaining cards Dealer tie drawing one card
1 16 13 49 26.53%
2 32 29 101 28.71%
4 64 61 205 29.76%
8 128 125 413 30.27%
Wizard
Administrator
Wizard
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September 14th, 2010 at 6:30:53 PM permalink
I attempt to answer that question in my blackjack FAQ.
It's not whether you win or lose; it's whether or not you had a good bet.
blackorange
blackorange
Joined: Sep 17, 2010
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September 17th, 2010 at 3:16:03 AM permalink
I believe that while removing an ace from a deck gives better odds of getting a 10, with more decks, the more the margin is thinned out, thus more cards equals less impact with each card removed...

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