davek: double vs 6 deck

[Brick Waller]

> If there are 2 cards removed from 2 decks
> and there are 7 aces remaining, is the
> dealer's chance of getting an ace the same
> as if 2 cards were removed from 6 decks and
> only 23 aces remain?

Does this mean the dealer gets more blackjacks at double deck than players do,isn't that what we're talking about?

[onetoomany]

If it's any consolation, I learned it from John Patrick. [ok,,,just kidding]

[onetoomany]

> No, I'm saying that the dealer is more
> likely to match a player's blackjack in a
> game with fewer decks, and it doesn't mean
> anything.

Respectfully disagree,,,

In a game with fewer decks there are gonna be fewer blackjacks, so you wouldn't want the few (or only one) you get to be canceled by the dealer getting one also. Might be when you have a big bet out there and then you get a push. I'd say that does mean something. You didn't lose on the hand, but you are counting on those situations to put you over the top, and it didn't happen.

[Sun Runner]

> I "know" you have better odds the
> fewer the decks, even if you play straight
> basic strategy,

So, is this the answer to davek's original question .. that you get 0.34 more BJs per deck?

[Norm Wattenberger]

According to Griffin (chapter 8) half of the difference is in doubling. When you double, two of the cards are low and it is good to have them removed. But their removal is more important in SD. The remainder of the difference is the BJ bonus and standing on stiffs, again more important in SD because of card removal.

[Norm Wattenberger]

It occurs to me that SD games with no cut-card have no cut-card effect, further improving advantage. Although this does not mean a difference in 'Basic Strategy EV' since it is defined as being off-the-top advantage, it does affect BJ as played.

[Fuzzy Math]

We could take this illustration further -- if you played with half a deck (2 aces) and the player gets a blackjack, what would the probability be that the dealer gets one too? Or if you played with a quarter of a deck (just one suit from one deck), it would be impossible to have more than one blackjack per round (per shuffle).

You could also look at it this way -- the reason you get more BJs with fewer decks is because the effect of removing one ace is greater. With fewer decks you are less likely to be dealt a second ace, and therefore all other outcomes increase in probability (including, of course, getting a ten). This all hinges around the fact that the probability of an ace coming next is lower with fewer decks in play. Since the dealer faces those same odds of getting an ace as the player does, we must conclude that when the player gets a BJ, the odds of the dealer getting a BJ diminish as the number of decks decrease. Simply put: If the player's odds of getting an ace decrease, then the dealer's odds cannot stay the same.

[Parker]

> Respectfully disagree,,,

> In a game with fewer decks there are gonna
> be fewer blackjacks, so you wouldn't want
> the few (or only one) you get to be canceled
> by the dealer getting one also. Might be
> when you have a big bet out there and then
> you get a push. I'd say that does mean
> something. You didn't lose on the hand, but
> you are counting on those situations to put
> you over the top, and it didn't happen.

Okay. I've never claimed to be a math whiz (that's Don's department).

One of these days I'll learn never to post before I've had my coffee. :-)

Seriously, I must admit that I have learned a great deal about the game since I started hosting these pages.

[onetoomany]

No biggie, that's what this place is all about, sharing knowledge and all that. And you are probably a harder critic on yourself than others here would be - no one expects you or anyone else to have all the answers all the time.

My sister says a person needs to make an error now & then just to show they really are mortal.

[onetoomany]

> Does this mean the dealer gets more
> blackjacks at double deck than players
> do,isn't that what we're talking about?

No. In any given game the dealer has the same chance as a player of getting a blackjack. What we were talking about was how the number of decks in the game affects the chances of a dealer getting a blackjack on the same round as a player.

If you are playing a 6 deck game you are more likely to have your blackjack cancelled by the dealer getting a blackjack also, than if you were playing a single deck game.

[Brick Waller]

"I believe that with fewer decks there is much less chance that the dealer will get a blackjack at the SAME TIME a player gets one."

Yes,you're correct,I reread your post and noticed the word "SAME TIME".

Sorry

> No. In any given game the dealer has the
> same chance as a player of getting a
> blackjack. What we were talking about was
> how the number of decks in the game affects
> the chances of a dealer getting a blackjack
> on the same round as a player.

> If you are playing a 6 deck game you are
> more likely to have your blackjack cancelled
> by the dealer getting a blackjack also, than
> if you were playing a single deck game.

[Norm Wattenberger]

I ran some long sims. Blackjack has little to do with the difference. Only when the dealer has a ten up does it matter. 11v10 is the biggest difference in favor of SD. Dealer five up is very different. There is one huge difference. A8v6 is much better in shoes. I think I know why. I'll study this further and post it on Don's Doamain.

[Don Schlesinger]

The math is very straightforward to calculate tied naturals for any number of decks. It's easy to see that, starting with one deck, player and dealer push naturals 0.1773% of the time. By the time we get to 8 decks, they push 0.2185% of the time.

So, while the probability of an united natural decreases as number of decks increases, the probability of tied naturals increases as number of decks increases.

Don