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?

Dog Hand

and stand on soft 17 is worth about 0.2%Quote:DogHandThe 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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Quote:DogHandThe 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 BJ’s if the dealer has a BJ. Is my thinking correct?

Quote:ALOHOMORAHello 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?

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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

Quote:ALOHOMORAHow 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%.)

Quote:Ace2When 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:avianrandyMy 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

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Quote:ALOHOMORADealer 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%.)

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?

Quote:acesideIsn’t 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)