Math Question about House Edge in BJ

Well I was hoping the Wizard would answer this question since he seems to be a math wiz. If anyone wants to crunch numbers and come out with a correct answer then I guess that could be acceptable.

I notice that when I play in Vegas and someone purchases a BS (basic strategy) card and uses it, they will use that one card no matter if they're sitting at a table where:

• It's a Shoe Game where the Dealer Hits S17,
• It's a Shoe Game where the Dealer Stands on S17,
• It's a Double Deck Game where the Dealer Hits S17, or
• It's a Double Deck Game where the Dealer Stands on S17 (etc., etc.)

The BS card that I see sold usually indicates BS for a Shoe Game where the dealer Stands on S17. However, the Wizard has several BS charts. Most people seem to just follow the BS on that little plastic card.

So, my question is, since I'm curious and love numbers, what would the house edge change to if a player were to use that BS card (BS for Shoe Games where the dealer Stands on S17) but on all the other different tables?

Since there seems to be a lot of different tables with different rules, I'll list a few of the more common ones I'm curious about:

Decks	Soft 17	DAS	Surrender	RSA	House Edge if Player Plays according to correct BS for this set of rules	House Edge if Player Plays according to BS card instead
2	Stand	Yes	No	Yes	0.20%	?
2	Stand	Yes	No	No	0.27%	?
6	Hit	Yes	Yes	Yes	0.28%	?
2	Hit	Yes	No	Yes	0.40%	?
2	Hit	Yes	No	No	0.45%	?
6	Hit	Yes	Yes	Yes	0.48%	?
6	Hit	Yes	Yes	No	0.55%	?
8	Hit	Yes	Yes	Yes	0.57%	?
2	Hit	No	No	No	0.60%	?
6	Hit	Yes	No	No	0.64%	?
8	Hit	Yes	No	No	0.66%	?
6	Hit	No	No	No	0.78%	?

I ask this question cuz I'm always thinking that a player is using that plastic BS card to obviously keep the house edge as low as possible but that he may unknowingly be giving the house a huge edge by using it at the wrong tables.

If you play the basic 6-deck S17 strategy for all games, you will give up very little, about 0.05-0.07%

If it helps, that's nothing compared to what you give up if you use BJ strategy when playing BJ Switch or Spanish 21 - which people do all the time.

Quote: HotBlonde

I ask this question cuz I'm always thinking that a player is using that plastic BS card to obviously keep the house edge as low as possible but that he may unknowingly be giving the house a huge edge by using it at the wrong tables.

The "correct decision" in basic strategy is the one that gives you the lowest house edge. But their are widely different advantages over the "2nd best play".
For instance if you have a pair of 8's against a dealer 6 up card, the decision to split gives you a very significant improvement over the "2nd best play" which is to hit.
If you have a pair of 8's against a dealer 10 up card, the decision to split gives a very minor improvement in edge over the the "2nd best play" which is to hit.

Rule changes in blackjack like DAS or Soft 17, or number of decks usually change the decisions that only resulted in marginal improvements anyway. The player will not give the house a "huge" advantage.

The cards are "abbreviated for memory" anyway. If you have a 12 against a dealer 4 the card will always tell you to stand. The "correct decision" is to hit sometimes, depending on the composition of your 12.

The casinos are not terribly bothered by the "cheat sheet" as long as you don't slow the game down. They know that many people will follow the "cheat sheet"and lose a hand that they would have won if they had made another decision. Most amateurs will revert to playing their gut after a few of those losses.

I'm sad that The Wizard did not want to tackle my question. :(

To be fair, it's quite a bit of work. Not difficult, but tedious.

I agree, but those of us who love math could look at it as a fun opportunity.

Hmm, I'm not sure. When I say tedious, I mean it's an easily solvable problem, with no inherent "I wonder what's going to happen" moments. It's just a question of slogging through the code to generate the answers. To me, slogging != fun. Slogging is what I get paid for. (Granted, I get paid for fun too, but that's because I love my job.)

This question was answered in Ask The Wizard #105

Quote:

You have the greatest gambling site in the world!! If I follow the basic strategy chart intended for "shoe" games in a double deck game what percentage am I sacrificing? Or if I use the double deck strategy in a shoe game what am I losing?
Thank you for the compliment. Assuming the dealer hits a soft 17 you are adding 0.012% to the house edge by playing 4-8 deck strategy in a two deck game. Playing double deck strategy in a 6 deck game costs 0.008%. To take this question further I wondered about a more extreme case of playing 4-8 deck strategy for the dealer standing on soft 17 in a single deck game where the dealer hits a soft 17. In this situation the incorrect basic strategy adds 0.038% to the house edge.

Quote: HotBlonde

I'm sad that The Wizard did not want to tackle my question. :(

Take it easy. I don't have time to read every thread. You asked the question in February, which was a very busy month for me.

As Miplet pointed out, I answered essentially the same question on my site years ago. Forgive me if I don't fill out the whole chart. For most people I think the strategy to memorize is 4-8 decks, dealer hits on a soft 17.

Quote: pacomartin

The "correct decision" in basic strategy is the one that gives you the lowest house edge. But their are widely different advantages over the "2nd best play".
For instance if you have a pair of 8's against a dealer 6 up card, the decision to split gives you a very significant improvement over the "2nd best play" which is to hit.

That is not the second best play. Standing is far better than hitting.