Number of decks question.

Well, I've finally got here from Wizard of Odds.com which is just wonderful. Thanks for all your splendid advice and statistics.

Just to put it out there, this is a newbie question. I understand so far, that in Blackjack we are destined to win fewer hands than we lose, but we make up for it by getting 3:2 for BJ and hopefully winning more double-downs, and splits than we lose etc... I think I get how all the "game rule" factors affect the house edge (standing soft 17, etc...). One thing I know, but don't know why:

Why does playing with fewer decks decrease the house edge?

Thanks!

If I can add-on to the original question... for those of us who just look at the probability charts, we can clearly see the numbers are in our favor with fewer decks. And most of us, myself included, will do just that and be perfectly happy explaining to ourselves "it's because the expected value is slightly higher."

But explaining the question about the number of decks *to a friend who hates math* by putting it into layman's terms is where I have an issue. They 'want' an answer like "the house hitting on a soft 17 is bad for the player because it gives the house a chance to raise his total, and it's more likely to get better be getting a low number or else another 10 (and be in an equal or better position than he was before) than it is that he would bust."

If I give my friend an answer like that, he's satisfied. So to tack-on to DJGenius's question, any "layman's terms" way to explain this would also be appreciated.

The simplest answer is that you get better chances to make better hands with fewer decks. Let's say you are given an Ace as the first card. In a single deck game, there are 51 cards left, and 16 will give you a blackjack (31.4%). In a 6 deck game, there are 311 cards left, and 96 will give you a blackjack (30.9%). When you do the percentages, you'll see your chance at a blackjack increases about a half percent. So there are more blackjacks in a single deck game. Though the dealer will get more too, you win 3:2 when you get them, but only lose even money when you lose them. "Card removal" also helps in situations like double downs. If you get a 5 and a 6, you have a higher percentage of NOT getting a 5 or a 6 again as your double down card, and more likely to get the Ten that you want.

Another good thing to think about is bust possibilities. Lets say the dealer is dealt a couple smaller cards like 6,7 to make a hand of 13. In single deck, there are now 2 cards removed (one 6 and one 7) that would give the dealer a strong hand. Thus he is more likely to bust. The same occurs for the player, however dealers hit stiff hands more often. In 6 decks, this effect of card removal is obviously far smaller.

Of course two small cards like 6,5 will mean it is more likely to make 21. However as a player we would usually get paid 2:1 on this situation because we doubled down, whereas the dealer would not. As the poster above said, fewer decks make double downs more powerful.

Single-deck also causes basic strategy to be more precise. Because compositions and card-removal become important, basic strategy is more powerful.

All these situations plus the increase in blackjacks mean that if the liberal rules of good multi-deck blackjack are applied to single deck the game has a player advantage. This shows the power that using one deck has on the game.

I address this issue in my Ask the Wizard questions about blackjack. This one is about half way down.

Thanks to everyone for all those great answers.

I think I'm starting to get it. The fewer decks you play with, the greater the effect of card removal. I guess this helps us more than the dealer, because we can change the way we play and the dealer cannot. Also, the situations that occur that seem to help us both, favor the player more due to double-downs, and 3:2 BJ.

It seems that there are many small advantages that happen in different situations, and they all add up to help the player more than the dealer, which is maybe why it's difficult to explain it with one simple rule or phrase.

I find the bit about basic strategy being more powerful the most interesting.

Here's what the Wizard directed me to, I hope it's OK to quote it:

"Every legitimate blackjack expert agrees the house edge decreases as the number of decks goes down, all other rules being equal. However it is hard to explain why. First, it is true that you are more likely to get one small card and one big card in single-deck than multiple-deck. For example if we define a small card as 2 through 6, and a large card as any 10-point card or ace then the probability of getting one of each in single deck is 2*(20/52)*(20/51) = 30.17%. The probability in 8-decks is 2*(160/416)*(160/415) = 29.66%. Although stiffs can cut both ways the player has the free will to stand, the dealer must always hit them."
-- wizardofodds.com (Nov. 19, 2003)

Sorry I missed that one, as I haven't had time to comb the whole site yet, and thanks again - such interesting stuff!

The Wizard's quoted answer makes a lot of sense. It really comes down to the fact that the player's 'free will' is more useful in single-deck blackjack. If you were forced to mimic the dealer you would not be able to gain much from the reduction in decks.

Here's a no-math answer:

Ever notice that the fewer the decks, the more likely it's a 6:5 game?

That's to counter the player's advantage with fewer decks. (OK, not a player 'advantage', but a decrease in the casino's edge.)