House Advantage

How can the two deck game have a lower house advantage than the six deck game when the six deck allows rsa and ls? I thought house advantage assumed no counting.

State the exact rules, including DAS, for the two games you want to compare, and we'll tell you what the house edge is for each.

The answers will assume no counting and just off-the-top BS edge for the player.

Don

A smart guy - I even think it was our host Stanford Wong - has found a way to calculate the value of various number of decks. It has been established that with identical rules the house edge for infinite decks is 0.64% higher than for single deck. In order to find the improvement for a given number of decks over infinite, the rule says that you just have to divide by that number. So for 6 decks this gives 0.64%/6 = 0.11% improvement.For double deck, we get 0.64%/2 = 0.32% improvement.
Now you can see that with identical rules the house edge for 6 decks is by 0.21% higher than for double deck. This cannot be totally compensated by RSA (0.07%) and LS (0.08%). The DD-game will still be by 0.06% better
for the player.
I hope this wasn't too complicated.

Francis Salmon

Actually, the interpolation by reciprocals is from Griffin, p. 115.

Don

2deck, s17, ds. .19 adv.
6 deck, s17, ds, ls, rsa. .26 adv

I don't understand how " better" rules are worse for player.

"2deck, s17, ds. .19 adv.
"6 deck, s17, ds, ls, rsa. .26 adv

"I don't understand how 'better' rules are worse for player."

You're not making a proper comparison. If you have better rules and the SAME number of decks shuffled, then better rules are, indeed, better. But, if you have those better rules on a 6-deck game, compared to poorer rules on a 2-deck game, you have to determine which is more important to the basic strategy player: the rules, or the number of decks shuffled.

In this instance, with identical rules, going from 6 decks to 2 decks is worth 0.22% off the top. LS and RSA together are worth only 0.14%, so that isn't enough to compensate for the fewer decks in the DD game.

Clear?

Don

Thanks. I understand that rsa and ls are good for the player, but won't overcome the loss from additional decks.
Now, I believe you, and certainly Stanford, that more decks are in the house favor. But, intuitively, I don't understand why more decks is bad for the player. I could see the difference if you are counting, in that the count info doesn't have much meaning at the beginning of several decks. But I thought the adv % assumed no counting.
So why is it that more decks result in more adv for the house?

Your question has been the subject of much discussion over the years. The "knee-jerk" reaction is always to state that you get a slightly greater frequency of naturals with fewer decks, which is true.

But, there are other reasons. Effects of removal of any single rank of card are much more important with SD or DD than they are with multi. As a result, your doubles and splits are more successful with fewer decks, as, often, especially for doubles, the cards that comprise your hand are cards that you wouldn't want to receive for the hit card.

Also, when the dealer shows a bust card (2-6), he breaks more frequently with fewer decks than with multi, again, because a card that might be helpful for the dealer to receive as a hit card is actually the upcard, and it's no longer available.

Anyway, you get the idea. Several different principles all conspire to make off-the-top edge better for the player the fewer the number of decks.

Don