Casino Promo Evaluation

wwcd

Well-Known Member
#1
There was a casino that I like to play BS blackjack due to their friendly minimums ($3). They just started a promo as follows:

Receive double times (2X) your wager for suited Blackjacks and receive triple times (3X) your wager for Royal Blackjack in posted suit.

Their normal rules are 6D H17 DAS DA2, NS: so I guess 0.66% house edge. What does the above promo do to the house edge? Any chance that it goes positive?

FYI, they run this promo on a certain weekday from morning till late evening.

Thanks!
 

shadroch

Well-Known Member
#2
One out of four BJs will be suited, so you get a nice bit of EV there, but what is a Royal Black Jack? Is that an Ace/King of a particular suit? That will come up much less frequently, perhaps one every few hours of play.
 

SleightOfHand

Well-Known Member
#3
shadroch said:
One out of four BJs will be suited, so you get a nice bit of EV there, but what is a Royal Black Jack? Is that an Ace/King of a particular suit? That will come up much less frequently, perhaps one every few hours of play.
Also its in the "posted suit" so thats another 1/4 you gotta multiply (for the royal)

WoO posts 2:1 suited blackjack as a .57% advantage

PS: remember you have to subtract a little bit from the .57% of the 2:1 suited BJ because (I assume) that the Royal Black Jack is a subset of the suited Black Jack

If it just means a Black Jack that includes a face card (J,Q,K) of a specified suit, the 3:1 bonus gives ~.335%
The 2:1 gives an additional ~.484% for a total of -.159% HE (roughly)
Hope I did that right
 
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wwcd

Well-Known Member
#4
OK I got pretty excited, so I couldn’t wait and did the calculation myself. If my calculations are correct, the house edge in this case moves from 0.66% to 0.22%. I initially thought of royal blackjack to include Ace/King, Ace/Queen, and Ace/Jack of the same suit, which yielded 0.08% player edge. However, as shadroch mentioned, royal blackjack is probably just Ace/King of the same suit. Here are the details of my logic, let me know if there are any flaws:

There are 64 possible ways of blackjack suit combinations (i.e. Ace of Hearts and King of Hearts, Ace of Diamonds and Queen of Spades and so on.), each with a 1.6% probability. Of these 64 possibilities, 4 of them will be paid 3X, 12 of them will be paid 2X, and 48 of them will be paid 1.5X. As a result, weighted average payout will be 1.688X, instead of the usual 1.5X.

In a game of 60 hands/hour, $5 wagered/hand; total of $300 will be played. The normal return on these hands would be $298.02, with 0.66% house edge. During these 60 hands, 1.42 blackjacks will occur (60 hands x 2.37% probability). Under normal conditions, these 1.42 blackjacks would have paid $10.65 (1.42 x $7.50); however in our case these 1.42 blackjacks will pay $11.99 (1.42 x $8.44). $8.44 is calculated by multiplying 1.688 with $5 wager. Since $11.99 is $1.33 higher than $10.65, total payout during the 60 hands will go from $298.02 to $299.35. This calculates into 0.22% house edge.

Now, this joint has better blackjack games with higher minimums. There is a double deck with surrender option with $10 minimum. This game might have a break-even house edge with the promo. However, I usually am cautious with double deck games, since there is a lot of preferential shuffling going on, so I might just stick to the regular 6D shoe game and enjoy some cheaper fun.

Also, if I want to count during such a game, what could be the best way? Counting aces might be a good idea I think, since blackjacks are pretty valuable. But what should I count them against? Ace-five?
 

Sucker

Well-Known Member
#5
Assuming six decks:
You'll get a blackjack about 4.7% of the time; so a suited blackjack will be about 1.175% of the time. Because the payout is double instead of time & a half; you gain .5 bet when this happens. This will add about .5875% to your EV.

A royal blackjack, which I'm assuming is AK suited, will occur at the rate 48/312 x 6/311, or .3% of the time. Because it pays TRIPLE, every .3% of the time you'll gain 1.5 extra bets. This will add .0675 to your EV. This means that the promotion will subtract a total of about .655 EV. from the house edge of .66. The house edge is going to be about .005%. So basically, a perfect BS player is playing almost exactly a break even game.

If they add comps to this, it sounds like it might be a great way to spend an evening!
 

SleightOfHand

Well-Known Member
#6
wwcd said:
OK I got pretty excited, so I couldn’t wait and did the calculation myself. If my calculations are correct, the house edge in this case moves from 0.66% to 0.22%. I initially thought of royal blackjack to include Ace/King, Ace/Queen, and Ace/Jack of the same suit, which yielded 0.08% player edge. However, as shadroch mentioned, royal blackjack is probably just Ace/King of the same suit. Here are the details of my logic, let me know if there are any flaws:

There are 64 possible ways of blackjack suit combinations (i.e. Ace of Hearts and King of Hearts, Ace of Diamonds and Queen of Spades and so on.), each with a 1.6% probability. Of these 64 possibilities, 4 of them will be paid 3X, 12 of them will be paid 2X, and 48 of them will be paid 1.5X. As a result, weighted average payout will be 1.688X, instead of the usual 1.5X.

In a game of 60 hands/hour, $5 wagered/hand; total of $300 will be played. The normal return on these hands would be $298.02, with 0.66% house edge. During these 60 hands, 1.42 blackjacks will occur (60 hands x 2.37% probability). Under normal conditions, these 1.42 blackjacks would have paid $10.65 (1.42 x $7.50); however in our case these 1.42 blackjacks will pay $11.99 (1.42 x $8.44). $8.44 is calculated by multiplying 1.688 with $5 wager. Since $11.99 is $1.33 higher than $10.65, total payout during the 60 hands will go from $298.02 to $299.35. This calculates into 0.22% house edge.

Now, this joint has better blackjack games with higher minimums. There is a double deck with surrender option with $10 minimum. This game might have a break-even house edge with the promo. However, I usually am cautious with double deck games, since there is a lot of preferential shuffling going on, so I might just stick to the regular 6D shoe game and enjoy some cheaper fun.

Also, if I want to count during such a game, what could be the best way? Counting aces might be a good idea I think, since blackjacks are pretty valuable. But what should I count them against? Ace-five?
From my calculations, if royal blackjack is only AK, I get a HE of .0096%. This is using the rough estimation that blackjacks occur 1/21 times

Royal BJ = 1/21*1/4*1/4*1/4*1.5
Suited BJ = (1/21*1/4*1/4*3/4+1/21*1/4*3/4)*.5
 
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Sonny

Well-Known Member
#7
Sucker said:
A royal blackjack, which I'm assuming is AK suited, will occur at the rate 48/312 x 6/311, or .3% of the time.
Don't forget to subtract the royal BJs from the suited BJs since they overlap.

-Sonny-
 

wwcd

Well-Known Member
#8
Sorry folks, I screwed up the probability of blackjack. I calculated it as 2.37%, which only counts A-10 sequence but neglects the other. The probability of a blackjack is 4.7%.

In this case my calculation yields a -0.23% house edge, meaning a positive EV game.
 

wwcd

Well-Known Member
#9
wwcd said:
In a game of 60 hands/hour, $5 wagered/hand; total of $300 will be played. The normal return on these hands would be $298.02, with 0.66% house edge. During these 60 hands, 1.42 blackjacks will occur (60 hands x 2.37% probability). Under normal conditions, these 1.42 blackjacks would have paid $10.65 (1.42 x $7.50); however in our case these 1.42 blackjacks will pay $11.99 (1.42 x $8.44). $8.44 is calculated by multiplying 1.688 with $5 wager. Since $11.99 is $1.33 higher than $10.65, total payout during the 60 hands will go from $298.02 to $299.35. This calculates into 0.22% house edge.
Correcting my original message in the light of the correct blackjack probability:

In a game of 60 hands/hour, $5 wagered/hand; total of $300 will be played. The normal return on these hands would be $298.02, with 0.66% house edge. During these 60 hands, 2.84 blackjacks will occur (60 hands x 4.73% probability). Under normal conditions, these 2.84 blackjacks would have paid $21.30 (2.84 x $7.50); however in our case these 2.84 blackjacks will pay $23.97 (2.84 x $8.44). $8.44 is calculated by multiplying 1.688 with $5 wager. Since $23.97 is $2.67 higher than $21.30, total payout during the 60 hands will go from $298.02 to $300.69. This calculates into -0.23% house edge, hence a positive EV game.
 

SleightOfHand

Well-Known Member
#10
wwcd said:
Sorry folks, I screwed up the probability of blackjack. I calculated it as 2.37%, which only counts A-10 sequence but neglects the other. The probability of a blackjack is 4.7%.

In this case my calculation yields a -0.23% house edge, meaning a positive EV game.
There is only 1 combination of a suited AK since its in the posted suit. Giving the result that I came up with.
 

Sucker

Well-Known Member
#11
Sonny said:
Don't forget to subtract the royal BJs from the suited BJs since they overlap.

-Sonny-
:eyepatch: You caught me on that one. I ADDED rather than subtracted. Thanks for the correction.

1/5 of the suited BJs will be royals and 1/4 of them will be in the specified suit. So I guess my figure of .5875 should be only 19/20 of that, or .5581. The house edge is somewhere around .03%, for all intents & purposes still pretty much a break even game.
 

SleightOfHand

Well-Known Member
#12
Sucker said:
:eyepatch: You caught me on that one. I ADDED rather than subtracted. Thanks for the correction.

1/5 of the suited BJs will be royals and 1/4 of them will be in the specified suit. So I guess my figure of .5875 should be only 19/20 of that, or .5581. The house edge is somewhere around .03%, for all intents & purposes still pretty much a break even game.
1/4 :p
 

Sucker

Well-Known Member
#13
Busted again.:laugh:

Anyway; I think we all can agree that the promotion won't exactly put the odds for a BS player in the players' favor, at least not to any significant extent.
 

miplet

Active Member
#14
wwcd said:
OK I got pretty excited, so I couldn’t wait and did the calculation myself. If my calculations are correct, the house edge in this case moves from 0.66% to 0.22%. I initially thought of royal blackjack to include Ace/King, Ace/Queen, and Ace/Jack of the same suit, which yielded 0.08% player edge. However, as shadroch mentioned, royal blackjack is probably just Ace/King of the same suit. Here are the details of my logic, let me know if there are any flaws:
...
If it's the place I'm thinking of (and they didn't change the rules since the last time I was there) it's winning suited bjs are paid 2:1, and winning suited bjs in the suit of the day are paid 3:1. For 6 decks the house edge is lowered by ((864/97032)*.5+(288/97032)*1.5)*(93376/95790)=0.8679882617948 %
For double deck by 0.8761830363065 %
For Spanish21 6 decks by 0.7839721254355 %

The promo was much better when any blackjack paid 2:1 and suited of the day 3:1.
 

Nynefingers

Well-Known Member
#15
SleightOfHand said:
There is only 1 combination of a suited AK since its in the posted suit. Giving the result that I came up with.
I get the same 0.0096%, but player edge, not house edge. But really, at that point it just means break even. Your edge is less than one bet in 10000 hands.
 

wwcd

Well-Known Member
#17
Nynefingers said:
I get the same 0.0096%, but player edge, not house edge. But really, at that point it just means break even. Your edge is less than one bet in 10000 hands.
After adjusting for one suited Ace and King only (so one in 64 blackjacks get 3X payout), I get the same number as well. So, it looks like it's a breakeven promo for 6D, and a potentially slightly positive promo for a DD with good rules. I might go ahead and play their DD game with $10 minimum, which also has surrender.

Any help with how to best count for this game? Ace - five?
 

SleightOfHand

Well-Known Member
#19
wwcd said:
After adjusting for one suited Ace and King only (so one in 64 blackjacks get 3X payout), I get the same number as well. So, it looks like it's a breakeven promo for 6D, and a potentially slightly positive promo for a DD with good rules. I might go ahead and play their DD game with $10 minimum, which also has surrender.

Any help with how to best count for this game? Ace - five?
Just use any standard card counting system. The A-5 count is extremely weak overall. Systems with higher BCs will be more effective. HiLo will do a great job.
 

moo321

Well-Known Member
#20
It should cut about .5% off the house edge.

However, before you go changing your betting ramp, remember that this promo increases variance. Essentially, that +1 count still has a slight HA until you hit a very rare suited blackjack.

So, I wouldn't adjust my betting ramp very much, although I would definitely play this promo.
 
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