Reason number of decks matter in blackjack

Quote: USpapergames

I like this strategy. Might just have to borrow it for my 1st published book, whenever I get to complete it ;) So I'm assuming the target IQ level is 110-120 since you say "aim at the person about one standard deviation" so I'm assuming "about" means that they are almost or slightly above the 2nd standard deviation.

Quote:

I like your solution but I find it hard for me to implement it, any suggestions on how to help? I know communication isn't my strong point but dumbing down my communication to its simplest form just doesn't seem to work either :/

Quote: Wizard

Yes, I recall that, but not the details. Was it a player positional disadvantage as well?

Quote: Mental

I am not clear about the point that you are making here.

Consider a heads up game with a five-card deck composed of four tens and a single ace. Dealer and player will always stand because they will always have a 20 or BJ in the first two cards. Whenever dealer or player gets a BJ, they will get it first. There is only one BJ possible on each hand.

One fifth of the time, they will push with each having 20. 40% of the time, dealer will have BJ and 40% of the time, the player will have BJ. The player will win a full unit every five hands, on average.

Now take out a ten, and the player wins a full bet every 4 hands, on average.

Quote: TinMan

Before my last Vegas trip, I printed out in color BS charts for 1,2,4-8 decks from WOO BS generator. Had versions with surrender and no surr. H17 and S17 for all but the single deck game. Laminated them double sided so each card has the surr and no surr charts. Total of 10 charts. Really handy. Obviously none of this captures true count adjustments just BS. I’d been meaning to do it for awhile.

Quote: Wizard

One question I get from time to time is why does the number of decks matter in blackjack if one is not counting cards?

This post shall address my initial analysis, which I open up for peer review.

First, let's establish some baseline rules:

• Dealer hits soft 17
  
• Blackjack pays 3 to 2
  
• Dealer peeks for blackjack
  
• Player may double after a split
  
• Player may NOT surrender
  
• Player may re-split up to four hands, including aces
  
• Continuous shuffler used
  
• Total-dependent basic strategy followed
  

My house edge calculator shows the house edge as follows:

• One deck = 0.014%
  
• Eight decks = 0.577%
  

This makes the effect of the difference in number of decks 0.563%.

Before I go on, all figures in this analysis are the result of billions of hands played by random simulation.

Let's work on this like an onion, starting with a simplistic balanced version of blackjack and then add the effects of the rules that are not equal both ways.

Imagine a blackjack game where the player follows a "mimic the dealer" strategy of hitting to 17 and also hitting a soft 17. Also let a winning blackjack pays 1-1. Finally, add a rule that if both the player and dealer bust, that the result is a push. This game is perfectly balanced for a zero house edge.

Next, let's remove the rule about a push if both player and dealer bust. Instead, we use the real blackjack rule that if both the player and dealer bust, then the dealer wins. Here is the player expected value adding that rule for one and eight decks:

• One deck = -8.237%
  
• Eight decks = -8.157%
  
• Difference = -0.079%.
  

Why does the player lose more with a single deck? It's because there is more busting on both sides in a single-deck game, resulting in more double busts. The absolute value of the percentages above, to be exact. Why is there more busting with a single deck? I figure it's because both sides are hitting hands with more small cards than large, resulting in hitting into a deck/shoe that is high-card rich. This effect of removal is simply stronger with a single deck.


Next, let's consider the value of a blackjack paying 3-2. It is easy to calculate the effect of this mathematically, as follows:

Decks	Prob player BJ	Prob dealer BJ	Prob winning BJ	Value
1	4.827%	3.673%	4.649%	2.325%
8	4.745%	4.605%	4.527%	2.263%
Diff	0.081%	-0.932%	0.123%	0.061%

Here is the effect of the two rule changes thus far. So, the eight-deck game is still a little better.

• Player loses if both bust = -0.079%
  
• Blackjack pays 3-2 = 0.061%
  
• Total = -0.018%
  

Next, let's improve the player's strategy by using basic strategy with a hard total of 12 to 16, which is:

Player has 13 to 16 vs. dealer 2-6 = Stand
Player has 12 vs. dealer 4-6 = Stand
Otherwise, hit with hard 12 to 16.

Here is the effect of that strategy improvement.

• One deck = 3.703%
  
• Eight decks = 3.270%
  
• Difference = 0.433%
  

So this change in strategy is more helpful with a single deck. I assume this is because hitting with 12 to 16 is more dangerous in a single-deck game, because the 12 to 16 are likely composed of more small cards than large, resulting in hitting into a deck/shoe rich in high cards, thus more busting. In other words, the effect of removal again.

Here is where we are at now of the reason a single-deck game is better for the player.

• Player loses if both bust = -0.079%
  
• Blackjack pays 3-2 = 0.061%
  
• Strategic standing on 12 to 16 = 0.433%
  
• Total = 0.415%
  

Next, let's add proper doubling strategy. We will use the appropriate basic strategy for the given number of decks. Here is the value of adding doubling the player's game.

• One deck = 1.653%
  
• Eight decks = 1.380%
  
• Difference = 0.273%
  

Doubling is thus much more valuable in a single-deck game than a shoe. I figure it's because the player likely has two small cards when doubling, like a 6 and 5, resulting on doubling into a shoe/deck that is ten-card rich. Again, this effect of removal is stronger with one deck than eight.

Let's update our effect list:

• Player loses if both bust = -0.079%
  
• Blackjack pays 3-2 = 0.061%
  
• Strategic standing on 12 to 16 = 0.433%
  
• Strategic doubling = 0.273%
  
• Total = 0.689%
  

The only thing left to change (remember, we are not allowing surrender) is the splitting rule. Here is the effect of adding the appropriate splitting strategy:

• One deck = 0.544%
  
• Eight decks = 0.669%
  
• Difference = -0.125%
  

Interesting! Splitting is more effective in an 8-deck shoe. This should no be surprising as it is harder to form a pair in a single deck game than a shoe. Be be specific, the probabilitiy of getting any pair in two cards is 1/17 = 5.882%. In an eight deck shoe it is 7.470%. Not to get off topic, but it interesting how little splitting actually helps the player. So, there is more splitting and re-splitting going on in the shoe game.

Let's update our table again.

• Player loses if both bust = -0.079%
  
• Blackjack pays 3-2 = 0.061%
  
• Strategic standing on 12 to 16 = 0.433%
  
• Strategic doubling = 0.273%
  
• Strategic splitting = -0.125%
  
• Total = 0.563%
  

As a reminder, the difference from my blackjack house edge calculator matches the 0.563%. Yay!

I love graphs, so here is one of the various effects I looked at.

g]

Again, I plan to write this all up in a more formal way and will indclude more details. For now, I open it up to comments and questions. I've been working on this for about a week, so hope to get some feedback.

I would like to thank Don Schlesinger for his help and advice.

Quote: moses

The math? Single Deck straight up. You have 12. Only 16 out of 52 cards will break that hand.
You have 16. 32 out of 48 (excluding Ace) cards will break that hand before the dealer ever has to make a move.

Don S. Would you rather hit 16 and get an Ace for 17? Or start your next hand with an Ace?

Quote: kewlj

Am I missing something? Are you hole-carding? How do you know the next card is an ace?

If you aren't hole-carding and don't know, the same question could be asked of a 4 or 5. Would you rather hit your 16 with a 4 or 5 or stand and start your next round with a 4 or 5? Not so appealing now. Lol.

Quote: lilredrooster

..............................

Moses:

in another thread you mentioned you play in Reno

I googled and it said there are 20 casinos in Reno

how many of them have good BJ games?

and how long of a walk is it between the 2 casinos that are farthest away from each other?


thanks


*

Quote: moses

Reno has changed considerably. Id suggest renting a car.

Quote: moses

KJ. Read the post as a whole. The 4 and 5 are two of the only 16 cards that will improve the 16. 32 will break your hand before the dealer makes a move. Thus hitting means you will break twice as often as opposed to standing. The Ace will get you to 17. But if the dealer has 17 thru 20, that same Ace would be the first card of your next hand. So would you rather have 17? Or an Ace to start your next hand?

The same could be said with KJ scenario. There are 16 2 thru 5. The 4 and 5 will likely put you in the winners circle. But that is ONLY 8 out of 52 cards. Not so appealing now is it? lol
There are also 16 cards with a value of 10. So the 10 that breaks your hand is often the first card of your next hand.

Quote: Wizard

I disagree.

The way this issue is often expressed is in the following question:

If a casino offered a game with exactly 0% house edge, who would come out ahead in the long run?

A. The casino
B. The players
C. Neither. The net casino profit (on a percentage basis) will always hover close to zero.

The answer is C.

Since this is getting a bit off topic, I'll split this off there seems to be further discussion about it.

Quote: moses

Yoy mentioned you also prefer straight up play. Why? Not being a smart alec.

Quote: moses

Back to the oringinal question. Suppose you knew your next card was going to be a Ace. You are playing straight up. You have 16 and are facing dealers 7,8,9,10,A. Lets say your count is close to even. Are you going to hit knowing there is a good chance this will be the first card of your next hand?

Quote: moses

Not that KJ ask, but my primary purpose for straight up play is the option having the next card drawn could the last of your current hand. But is could also frequently be the first card of your next hand.

It has nothing to do hole carding etc. etc. But rather the same purpose a counter decides to hit or stand.
True count comes downs to percentages. However, there are different ways of arriving at the solution.

Quote: moses

Lets use the first hand of the deck as an example. You have 9.7. Dealer has 10 up. If you hit? There are still 4 Aces that will get you to 17. There are 16 cards that will land you between 18 and 21. There are 29 cards that will break you AND the dealer doesnt have to do a thing.

Of those 29 cards. 15 have a value of 10. 4 Aces still remain. If an Ace was in the hole the dealer would have flipped over a blackjack and we wave good-bye to that chip in the circle.

What is the good buy? Stand. There are still 20 cards in the hole that will make the dealer hit. There are only 25 now that forces a stand.

Now you have 19 prime cards 10,A that could start your next hand 15 of which would've broke your hand or 4 would get you to 17. From a money management standpoint? Im standing.

Quote: moses

67% of the time you will hit and lose and the dealer does nothing.

Quote: moses

(snip)
It seems there are 3 different philosophies regarding 16.

1.) Always Hit

2.) Always Stand

3.) play it stictly by the index.
(snip)