Given identical sets of rules, the house advantage increases with each deck added (I think it tops out at something like 28 decks).
So a 6 deck game compared to an 8 deck game has a lower house edge, if the rules are the same. Also, the 6 deck shoe will be shuffled slightly more frequently than the 8 decks, so you will play less hands overall per hour and therefore lose slightly less.
First hand in a single deck game, you get an ace as your first card.
What are the chances that you get a 10 as your second card and get a blackjack? (16 tens / 51 remaining cards) = .3137 or about 1/3 the time.
Now in an eight deck game, first hand, you get an ace. What are your chances of getting a blackjack?
(128 tens / 415 remaining cars) = .3084 (slightly less than above.)
Notice that it is equally likely to get an ace as your first card in each game, but what happens after is slightly worse as each deck is added. This happens in a lot of different situations, suppose you have two small cards that add up to 11 and double down. The probabilty (with two small cards removed from play by being in your hand) of getting a 10 card for 21 on your double is slightly greater playing against a smaller number of decks.
If the dealer has four small cards and has to hit again, what are the chances of getting a big card and busting, as opposed to getting another small card for 21? Well, if he is using eight decks instead of 6, he has 2 more decks worth of small cards that he could possibly draw and make his hand.
I ran two 200 mil hand sims - one with 8 decks and one with 6 decks - same rules.
Shufflepoint 312 cards, (75.00% penetration)
Shufflepoint 234 cards, (75.00% penetration)
Face up game
Head on game
System used is basic strategy with basic strategy play
American rules - hole card game
Surrender is not allowed
Dealer stands on all 17
Doubling is allowed on any two cards
Doubling is allowed after splitting
Hand can be split 3 times, up to 4 hands
No resplit of aces
Only one card to split aces
Different tens can be split
6-deck Initial bet advantage:-0.43768%, St. Err. 0.008161%
8-deck Initial bet advantage:-0.45269%, St. Err. 0.008165%
6-deck Estim. payoff per 100,000 rounds played is -437.68,
8-deck Estim. payoff per 100,000 rounds played is -452.69
Frequency of blackjack: 4.743%
Frequency of pushing: 9.058%
Frequency of hard doubling: 8.404%
Frequency of soft doubling: 1.708%
Frequency of splitting: 2.787%
Frequency of blackjack: 4.741%
Frequency of pushing: 9.067%
Frequency of hard doubling: 8.413%
Frequency of soft doubling: 1.707%
Frequency of splitting: 2.823%
Look at it from a strictly mechanical point of view.
Each deck of cards adds 4 more small cards to the total
pushing the point at which there are 2 small cards
for each Ten count card further away. Six decks-24 extra small cards
8 decks 32 extra small cards-than do not make Black Jacks.
Do you have the numbers for simultaneous blackjacks.?..
I was also under the impression that the dealer matching your blackjacks occurred more frequntly the more decks used.(simultaneous blackjacks are bad for the player because as a player you want to exchange blackjacks so you get the 50 percent bonus)
Imagine a game of blackjack where only a quarter deck was used(13 cards- one of each rank).Think of your edge when you have a (5,6) to double against a 4 for example. The dealer couldnt push your blackjack ever. Compositon dependent strategy would be huge. This fantasy i think helps illustate to people that the more decks in use the worse for the player(assuming same game rules).
I was thinking of basic strategy changes. A,4 vs 4 is a double with 26 or less decks, don't double A,4 vs 4 with 27 or more decks.
The infamous Mugwump team cleaned up on this bit of information in some private casinos in Eastern Nepal. The team was disbanded because the casino chips being used were made of black nepalese hash, and one day they unable to bet a sizable portion of their bankroll, when they knew they were getting an ace on their first card, because it was discovered several team members had smoked all the team's funds.
Later, some ex-mugwump members made a fortune in ostrich feathers beating CSMs in an Angolian casino. When discovered, the pit boss there simply had the players taken out back and shot by members of the local diamond cartel. This shows the importance of always using cover.
I'm sure your formulas are correct but is this really what we want to know: the probability of two Blackjacks ocurring simultaneously? I think we want to know the probability of a Dealer's Blackjack IN CASE we already have one. The difference between single deck and 8 decks will then appear to be much more significant.
In single deck, on 1000 Blackjacks about 37 will be pushed whereas with 8 decks, it would be 46.
I noticed you had posted those figures already in your post. I was just showing a different way of looking at the same thing. How often do blackjacks push VS how often do I push once I have a blackjack.
Also, after splitting pairs, the removal of unfavorable cards (that is the cards you split), is the other factor that makes playing with a lessor amount of decks lower in house edge.