ALOHOMORA
ALOHOMORA
Joined: Sep 3, 2023
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September 3rd, 2023 at 6:43:43 AM permalink
Hello everybody,

I have recently played at a new casino in my country with the following blackjack rules:
No hole card
Stand at Soft 17
Double after split
Resplit to 4 hands
Can resplit Ace
Can double down on any two cards
Blackjack pays 3:2
If Ace King blackjack pays 2 to 1

Does this game have a positive expected value?
Hunterhill
Hunterhill
Joined: Aug 1, 2011
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September 3rd, 2023 at 7:42:59 AM permalink
Does the ace King blackjack have to be suited?
The mountain is tall but grass grows on top of the mountain.
ALOHOMORA
ALOHOMORA
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September 3rd, 2023 at 11:03:43 AM permalink
No they dont have to be
Ace2
Ace2
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September 3rd, 2023 at 11:19:29 AM permalink
I estimate that it has a positive EV of about 0.3%. What country?
Itís all about making that GTA
ALOHOMORA
ALOHOMORA
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September 3rd, 2023 at 11:23:12 AM permalink
Really? Eastern Europe
DogHand
DogHand
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September 3rd, 2023 at 12:31:08 PM permalink
The A-K bonus means that one-fourth of the BJ's pay 2:1, rather than 3:2. Since BJ's come on average every 21 rounds, this bonus adds +0.5 bets per 88 rounds, so it adds +0.57% to the base EV.

Dog Hand
Ace2
Ace2
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September 3rd, 2023 at 1:19:42 PM permalink
Quote: DogHand

The A-K bonus means that one-fourth of the BJ's pay 2:1, rather than 3:2. Since BJ's come on average every 21 rounds, this bonus adds +0.5 bets per 88 rounds, so it adds +0.57% to the base EV.

Dog Hand
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and stand on soft 17 is worth about 0.2%
Itís all about making that GTA
SOOPOO
SOOPOO
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September 3rd, 2023 at 7:24:09 PM permalink
Quote: DogHand

The A-K bonus means that one-fourth of the BJ's pay 2:1, rather than 3:2. Since BJ's come on average every 21 rounds, this bonus adds +0.5 bets per 88 rounds, so it adds +0.57% to the base EV.

Dog Hand
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Maybe a tad less +EV. You push some of the AK BJís if the dealer has a BJ. Is my thinking correct?
Ace2
Ace2
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September 4th, 2023 at 12:45:35 AM permalink
Infinite deck, the 2:1 rule is worth 161/13^4 =~ 0.564% to the player
Itís all about making that GTA
avianrandy
avianrandy 
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September 4th, 2023 at 5:30:30 AM permalink
My concern would be what happens to your split and double if dealer gets blackjack since their is no hole card? Otherwise sounds like a good game
ALOHOMORA
ALOHOMORA
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September 4th, 2023 at 7:19:37 AM permalink
Dealer gets all
avianrandy
avianrandy 
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September 4th, 2023 at 7:40:15 AM permalink
Game may not be +ev then. I will leave it to the math gurus. Good luck to you
ALOHOMORA
ALOHOMORA
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September 4th, 2023 at 7:42:10 AM permalink
You dont split Aces or double 11 when dealer has a 10.
ALOHOMORA
ALOHOMORA
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September 4th, 2023 at 7:42:38 AM permalink
You also dont split 8's
ChesterDog
ChesterDog 
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September 4th, 2023 at 1:51:51 PM permalink
Quote: ALOHOMORA

Hello everybody,

I have recently played at a new casino in my country with the following blackjack rules:
No hole card
Stand at Soft 17
Double after split
Resplit to 4 hands
Can resplit Ace
Can double down on any two cards
Blackjack pays 3:2
If Ace King blackjack pays 2 to 1

Does this game have a positive expected value?
link to original post



You can use the Wizard's blackjack house edge calculator to find if the player has a positive expected value for this game. See https://wizardofodds.com/games/blackjack/calculator/

For the no hole card rule, be sure to choose, "No" for, "Player loses only original bet against dealer BJ."

For a 6-deck shoe, the calculator gives these two house edges:
0.47406% for Basic strategy with cut card
0.45406% for Basic strategy with continuous shuffler

We subtract each of the above house edges from 0.56654%, which is the advantage from the extra 0.5 paid for player's AK vs dealer's non-blackjack in a 6-deck shoe, to find the player's advantage:
0.56654% - 0.47406% = 0.09248% player advantage for Basic strategy with cut card
0.56654% - 0.45406% = 0.11248% player advantage for Basic strategy with continuous shuffler
ALOHOMORA
ALOHOMORA
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September 4th, 2023 at 2:33:09 PM permalink
How do you calculate the 0.56654% advantage?
ChesterDog
ChesterDog 
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HunterhillALOHOMORA
September 4th, 2023 at 2:59:29 PM permalink
Quote: ALOHOMORA

How do you calculate the 0.56654% advantage?
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In a 6-deck shoe, there are 312 cards, which includes 24 aces, 96 ten-valued cards, and 24 kings.

The probability of the player's getting dealt an ace-king blackjack is: 2 * (24/312) * (24/311). And the probability that the dealer does not then get blackjack is: 1 - 2 * (23/310) * (95/309).

The player's ace-king blackjack pays 2 to 1, which is 0.5 more than the normal 1.5 to 1. So, for a 6-deck shoe, the additional contribution to the player's EV is: 0.5 * [2 * (24/312) * (24/311)] * [1 - 2 * (23/310) * (95/309)] = 0.56654% approximately. (By the way, this is close to Ace2's infinite-deck calculation of 161/13^4 = ~ 0.564%.)
Ace2
Ace2
Joined: Oct 2, 2017
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ALOHOMORA
September 4th, 2023 at 3:01:08 PM permalink
When I input the stated rules into the calculator for 6-deck I get 0.33% house advantage. Less 0.56% for the 2:1 payout is player advantage of 0.23%
Itís all about making that GTA
ChesterDog
ChesterDog 
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September 4th, 2023 at 3:53:43 PM permalink
Quote: Ace2

When I input the stated rules into the calculator for 6-deck I get 0.33% house advantage. Less 0.56% for the 2:1 payout is player advantage of 0.23%
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Quote: avianrandy

My concern would be what happens to your split and double if dealer gets blackjack since their is no hole card? Otherwise sounds like a good game
link to original post



Quote: ALOHOMORA

Dealer gets all
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In using the Wizard's blackjack house edge calculator, I chose "No" to "Player loses only original bet against dealer BJ" and got 0.47406% for the house edge. (But choosing "Yes," gives about 0.33%.)
aceside
aceside
Joined: May 14, 2021
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ChesterDog
September 4th, 2023 at 4:07:06 PM permalink
The most likely rule for this game is player loses all bet that was put out on the table upon a dealer blackjack.
Ace2
Ace2
Joined: Oct 2, 2017
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ChesterDog
September 4th, 2023 at 4:30:45 PM permalink
Regardless, the 2:1 bonus does give the player a small advantage, but nothing to write home about. You probably wonít even realize you have a slight advantage until youíve played a million hands
Itís all about making that GTA
aceside
aceside
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September 4th, 2023 at 4:34:04 PM permalink
But this is huge compared to other minors people have been striving for.
Dobrij
Dobrij
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September 4th, 2023 at 11:29:02 PM permalink
Hi to all!

What if try to calculate easier? Blackjack with a king is 25% of all blackjack's, we can imagine that in this case the payout for blackjack increased by 25%. Is it possible to enter a payout ratio to the EV calculator of 1.87 instead of 1.5?
aceside
aceside
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Dobrij
September 5th, 2023 at 1:11:16 AM permalink
Isnít it 1.625? The extra payout for each blackjack is 0.5/4=0.125, and then the total becomes 1.5+0.125=1.625.
Dobrij
Dobrij
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September 5th, 2023 at 3:42:43 AM permalink
Quote: aceside

Isnít it 1.625? The extra payout for each blackjack is 0.5/4=0.125, and then the total becomes 1.5+0.125=1.625.
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Yes, 1.625 is correct, I was wrong)

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