Combinatorial Analysis of BJ Press

#1
BJ Press is a new game from Shufflemaster. The rules, as I understand them, are as follows:

Shoe BJ, H17, DAS

Player BJ always wins, but pays 1:1

Players place three equal bets, one for each of two hands of BJ plus a Press bet.

If all four of the player's cards are of the same color, he loses the Press bet. If not, he moves that bet to the hand of his choice.

The hand is played out as a normal BJ hand.


Now I'm not sure what happens if the dealer has a natural. As I see it, the dealer checks for natural after the Press decision is made. Also, I am assuming the original bet plus the Press bet can be doubled or split together as if it was one bet. Shufflemaster's documentation isn't any better than that.

Results: I get a player edge of a whopping 0.00218% using a lazy man's CA. I took CVData data for the probabilities and advantages of all the possible BJ hands in a H17 DAS game, but neglected the fact that when two hands are dealt being dealt one changes the probabilities of receiving all others, plus it affects the dealer's card. I used 0.123 as the probability of 4 cards being the same suit in an 8D game. This rule also does have a minimal effect on the play of the hands but I neglected that.

Code: Here is my Liberty BASIC code. Liberty BASIC is a useful interpreted BASIC and a free, fully-functional trial version is available for download. Please let me know if I screwed anything up, this is important.

Code:
'program press

dim a(35)
dim p(35)


p(1)=.01189 'prob of hard 5
p(2)=.01188 'prob of hard 6
p(3)=.02377 'prob of hard 7
p(4)=.02377 'prob of hard 8
p(5)=.03564 'prob of hard 9
p(6)=.03565 'prob of hard 10
p(7)=.04749 'prob of hard 11
p(8)=.08309 'prob of hard 12
p(9)=.08306 'prob of hard 13
p(10)=.07117 'prob of hard 14
p(11)=.07115 'prob of hard 15
p(12)=.05928 'prob of hard 16
p(13)=.05927 'prob of hard 17
p(14)=.04739 'prob of hard 18
p(15)=.04737 'prob of hard 19
p(16)=.01188 'prob of A2
p(17)=.01188 'prob of A3
p(18)=.01188 'prob of A4
p(19)=.01187 'prob of A5
p(20)=.01186 'prob of A6
p(21)=.01186 'prob of A7
p(22)=.01186 'prob of A8
p(23)=.01185 'prob of A9
p(24)=.04741 'prob of Natural
p(25)=.00575 'prob of AA
p(26)=.00577 'prob of 22
p(27)=.00576 'prob of 33
p(28)=.00575 'prob of 44
p(29)=.00575 'prob of 55
p(30)=.00575 'prob of 66
p(31)=.00574 'prob of 77
p(32)=.00574 'prob of 88
p(33)=.00574 'prob of 99
p(34)=.09400 'prob of XX

a(1)=-0.2190 'advantages of hands as above
a(2)=-0.2393 'I'm not retyping, don't bust my balls OK?
a(3)=-0.2166
a(4)=-0.1191
a(5)=-0.0055
a(6)=0.1271
a(7)=0.1580
a(8)=-0.3144
a(9)=-0.3448
a(10)=-0.3693
a(11)=-0.3926
a(12)=-0.4124
a(13)=-0.2959
a(14)=-0.0205
a(15)=0.2568
a(16)=-0.0233
a(17)=-0.0459
a(18)=-0.0649
a(19)=-0.0855
a(20)=-0.0605
a(21)=0.0188
a(22)=0.2398
a(23)=0.5755
a(24)=1
a(25)=0.1622
a(26)=-0.0803
a(27)=-0.1018
a(28)=-0.0936
a(29)=0.1296
a(30)=-0.1422
a(31)=-0.1359
a(32)=-0.0556
a(33)=0.0340
a(34)=0.5747

'this block checks for typoes in
'variable defs
for l = 1 to 34
psum=psum+p(l)
asum=asum+a(l)
next l

print psum
print asum

for h1= 1 to 34
for h2= 1 to 34

handprob=p(h1)*p(h2)
bigbet=1.877*max(a(h1),a(h2))
'0.123 of a bet is lost due to the rule
'where you lose the press bet if colors
'of your 4 cards match

smbet=min(a(h1),a(h2))

r=(bigbet+smbet)*handprob

rtotal=rtotal+r
next h2
next h1

print rtotal*100/(3*34*34);"%"

end
 

weavin42

Well-Known Member
#2
I can tell you this, if you have a blackjack on one of your two hands and the dealer also has blackjack (with a 10 showing, I don't know how it works with an Ace showing), ALL of your bets push. I'll ask next time I go to the casino with Blackjack Press what they do if the player has a blackjack and the dealer has and ace showing.

I'm curious as to how you assigned each hand an advantage, is this just an average advantage generated by CVdata with correct BS for all up cards? I think the press decision (and therefore also the house edge) is a little more complex than an average advantage.

An optimal BS for this game (ignoring the fact the double downs are really pseudo-quad downs) would be to look at an EV chart of hand totals and 'press' the bet with the highest EV. Such a table can be found at BJmath found here. (Archive copy)

The advantage for each hand total changes based on the dealers up card and whether you hit, double, stand or split. Double down hands are a little bit different as well because instead of double the original bet it is 3.74 times the original bet, which would change the advantage. In choosing the correct press, the advantage would be the difference in the EV. Multiply that difference by the probability and sum for all hands would give the HE with correct play ignoring the 1.87:1 average payout for blackjack and the push ALL rule on dealer BJ and player BJ.

I want to add press BS to a regular BS chart so I can use it at a table without memorizing it. However, before I do all that I would like to know the exact house edge to see if the game is really worth my time.

Another thing I really don't know is how the EV's change at a given count (for a given system). However, you could get away with spreading 1-20 pretty easily since you are playing two hands.

After all that is said, I'm pretty tired right now so I might be off in my thinking. PM me if you want to work on this further or let me know where I'm wrong.

Josh
 

Geoff Hall

Well-Known Member
#3
Hand e.v's

AM,
Have you averaged out the value of each total against all dealer upcards in order to arrive at the single decimal figure ?

To clarify, if a player is dealt a 'Blackjack', (against dealer A or 10), he can 'Press' the bet and get paid before the dealer checks for 'Blackjack'. In other words, if both the player and dealer have a 'Blackjack' then the player will make a nett gain of 1 unit providing his cards are not all of the same color. However, there are a couple of versions approved and the casino is entitled to 'push' all of the players' bets instead i.e. if dealer and player have a 'Blackjack' then the player will win 0 units - this rule adds around 0.14% to the house edge.
 
Top