motizer
Joined: Oct 18, 2011
• Posts: 2
April 5th, 2015 at 12:51:45 PM permalink
I found a site some time ago that listed many of the rules of Blackjack and showed how each rule changed the percentage for the house. I do not remember the site or I'd reference it. I placed it in a spreadsheet and copied it below this post.

However, it only took the changes to 2 decimal places and I'm sure the rounding errors are compounded when adding multiple rules.

On WizardofOdds.com, there is a "rule change calculator":

This calculator takes the changes out to 5 decimal places however, it doesn't list the actual changes in a chart format, it only gives the final result.

A casino I used to gamble in recently changed their rules. According to the chart I mentioned first, the changes went from .52% to 2.32%.

According to the Wizard's chart, the change went from 0.52741% (which was close to the original) to 1.88710% which is significantly different.

Is it possible to get a list of all rule changes and their effect on hold percentage per dollar wagered to 5 decimal places?

Motizer

1 0.02
2 -0.31
3 -0.43
4 -0.48
5 -0.52
6 -0.54
7 -0.55
8 -0.57
Effects in Percent
Common Rules 1-Deck 2-Deck Multi-Deck
Double on 10-11 only: -0.26 -0.21 -0.18
Double on 9-10-11 only: -0.13 -0.11 -0.09
Hits Soft 17: -0.19 -0.2 -0.21
No Resplits: -0.02 -0.03 -0.04
Double After Splits: 0.14 0.14 0.14
Resplit Aces: 0.03 0.05 0.07
Draw to Split Aces: 0.14 0.14 0.14
Late Surrender: 0.02 0.05 0.08
Late Surrender (H soft17): 0.03 0.06 0.09

Less Common Rules
Double on 8-9-10-11 only: -0.13 -0.11 -0.09
Double on 11 only: -0.78 -0.69 -0.64
Double 3 or More Cards: 0.24 0.24 0.24
Double after Ace splits: 0.1 0.1 0.1
Double on 3+ cards: 0.24 0.23 0.23
No Ace Splits: -0.16 -0.17 -0.18
Early Surrender: 0.62 0.62 0.63
Early Surrender (H soft17): 0.7 0.71 0.72
Early Surrender v. 10 only: 0.19 0.21 0.24
BJ Pays 6-to-5: -1.74 -1.71 -1.71
BJ Pays 1-to-1: -2.32 -2.28 -2.26
BJ Pays 2-to-1: 2.32 2.28 2.26
Suited BJ Pays 2-to-1: 0.58 0.57 0.56
21 Pushes Dlr. 10-up BJ: 0.2 0.2 0.2
No Hole Card (European): -0.1 -0.11 -0.11
5-card 21 Pays 2-to-1: 0.2 0.2 0.2
6-card 21 Pays 2-to-1: 0.1 0.1 0.1
Suited 678 Pays 2-to-1: 0.01 0.01 0.01
7-7-7 Pays 3-to-2: 0.01 0.01 0.01
6 Cards Unbusted Wins: 0.1 0.1 0.1
No Insurance: 0 0 0
Multi-Action: 0 0 0
Over/Under: 0 0 0
Royal Match 0 0 0
Super 7s: 0 0 0
I'm just another water molecule in a sea of ignorance.
beachbumbabs
Joined: May 21, 2013
• Posts: 14246
April 5th, 2015 at 1:02:37 PM permalink
I think this table is what you're looking for. However, a table that listed all the variations the Wizard and JB have in their strategy calculator would be a matrix of almost 7,000 rule combinations, which seems impractical to print out. So if the link doesn't do it for you, I don't have a better answer.

Edit: just as a note, since the table is listed in percentages, these numbers would be correct to 4 decimal places. Not quite 5 as you wanted, but to the nearest 10,000th, so pretty close.
If the House lost every hand, they wouldn't deal the game.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2930
April 5th, 2015 at 1:37:48 PM permalink
Quote: beachbumbabs

I think this table is what you're looking for.

As you say it's the best that's easily available (unless someone knows different) and is good enough for practical purposes and comparing good and bad games. I've never run fully (non-infinite) correct Blackjack calculations but have heard they aren't easy (have to take each card gone into consideration and is best done in a program).

One of the easiest methods to get a rough approximation is to run a simulation - sadly Blackjack is quite volatile so you have to run many billions of hands before you get near the correct answer. As it happens I'm trying to create a simulator and finding it difficult to get near the wizard's calculator figure for UK Blackjack. However you'll find the technical figure (i.e. shuffling after every hand) which is the one usually quoted doesn't apply in practice - either a shoe dealt game which has 50%+ penetration or a CSM which has at least 10% penetration (as some cards that have just been used cannot appear in the next round) affects the House Edge.