house edge vs #decks

for a s17,DAS,lsr game the house edge for various deck games are as follows:

single deck -0.18
double deck 0.16
four decks 0.31
six decks 0.36
eight decks 0.39

well we pretty much all know that is how it goes.
it just struck me today that i don't know why.
well i guess the question more properly is what are the reasons that the house edge
increases as the number of decks increase?

as an aside, why does basic strategy change according to the number of decks?

Ok I'll take a stab lol.

One reason is one gets fewer BJ's every X hands in 8D vs SD.

Basically it's all because the percentage of tens to non-tens changes as the number of decks change.

Like, with 1 ten gone, it's 15/51. With 2 decks it's 31/103.

Ours is not to wonder why, ours is but to do or die.

What the heck is that from anyway?

It's the ratios...

You would think the ratios of the cards would stay the same no matter how many decks, but they don't. With more decks it's slightly harder to get a blackjack, for example. I'm sure this is what's responsible for the changes in BS, as well.

A brief example...

Freshly shuffled deck/shoe, chance of first two cards being T, then A:

1 deck: 16/52 * 4/51 = .02413

6 decks: 96/312 * 24/311 = .02374

Actually, that's the chance first card is T, then A.

Not the chance of first 2 cards being T, then A.

But, I know ur saying the same thing, i.e. chances of BJ in 1D is first number *2.

Likewise for 6D

No big deal.

Effect Of Removal

The reason that the probabilities for getting a 'Blackjack' differ is that after getting the 1st card needed for 'Blackjack' then the 2nd card needed is slightly easier with less decks.

For example, in 1 deck, if you receive an 'Ace' then the chance of receiving a face card is slightly higher, than with multiple decks, as the removal of the Ace has a bigger impact with a single deck. In other words, it's not the probability of the first card that changes (as the proportion remains the same) it's the conditional probability of the 2nd card now that the deck has been depleted (albeit by just 1 card).

Conversely, the probability of being dealt a pair increases as the number of decks increase because the removal of the 1st card has less impact with more decks.

I like the way bryce carlson put it. I liked it so much i even memorized it.

Multiple decks, run flatter with respect to relative deviations from normal deck composition. Thus, reducing your advantage to be gained from counting cards.

Another reason for the increased casino edge is your chances of catching a facecard are reduced by 2.91% when you go from 1 to 4 decks.

My thoughts:
On borderline counts in a 6deck game ill find myself being more conservative on double down plays. I will also find myself being slightly more aggressive in hitting vs standing.(hitting more)

You will also have more pair splits, the more number of decks in play.
Note: Though we may recieve a pair of A's more often. You will win less than if you were to get a pair of A's in single deck.

from the charge of the light brigade...

https://answers.yahoo.com/question/index?qid=1006021002270

The quote should read: Their's not to make reply, their's not to reason why, their's but to do and die: into the valley of Death of death rode the 600".
=Alfred Lord Tennyson

And (if you REALLY care) it happened to the 13th Hussars (Light Calvary) during the Crimean War).

Senor Frog you are weird.

The way I learned it is that there is a larger pool of small cards for the dealer to make his hands. Things get more "clumpy" in that regard with fewer decks. When the big card is due, it is more likely to come. Too much random variation in 6D and 8D. I know that is unscientific, but it is about all I care to worry about it and supported by real life experience.

The card removal effect!

Lets look at two identical stuations with a different amount of decks first you are dealt 5-5 with one deck than you are dealt 5-5 with 6 decks both times the dealer has an upcard of a 7 which hand are you more likely to win your double down on? Well lets look what you have to draw from on the 1 deck there is 49 available drawing cards that you can theoratically get two of the
5's and one 7 is gone leaving you 31\49 cards you can catch to make a pat hand giving you a 63.26% chance to make a pat hand of 17 or better. On six decks you have 309 cards left in the deck to choose from so you have a 191 out of 309 cards that will give you a 61.81% chance to make a pat hand. That is why given the same rules having less decks is better. However you rarely get the same rules with fewer decks.

yeah this is what i was thinking. the ratios do start out exactly the same but for some reason that i can't make logical sense of you guys are all correct in that the ratios don't stay the same as cards are removed.
i just wish i could understand this in a way other than the purely mathematical. maybe an analogy to something similar that i do understand.

Thanks to both u and Wise Frog for refreshing my memory

It's kinda like when ur 17 and fall in love with the 34 yr old teacher.

But then u realize when u r 50, she will be 100 :grin:

and if you REALLY REALLY care...

Technically, it was the 13th Light Dragoons that held the right flank of the first line with the 17th Lancers on the left. The 11th Hussars, formed the second line. The 8th Hussars and the 4th Light Dragoons the third line.
For Canadians: After the battle Alexander Dunn was awarded the Victoria Cross by Queen Victoria herself, and became the first Canadian to receive the honour. His citation actually reads "...one of the handsomest men of his day..." in this day in age he'd be pure Hollywood.
BW

You're a better man than I, Gunga Din!

Saving Private Ryan.