My second question is what is the odds of the dealer busting after reaching/revealing a soft 17?

Any help would be appreciated, I am asking this because I am making a homemade game of a mixture of Blackjack and Baccarat, where players can choose to put money on the player hand or dealer hand. My idea for the dealer's house edge is that if a player bets on the dealer hand and the dealer wins after reaching/revealing a soft 17, it pushes instead of wins. Player's hand house edge is around 0.60% with my rules, and I'm trying to get around the same with the dealer.

Quote:gospeedgo11

My second question is what is the odds of the dealer busting after reaching/revealing a soft 17?

I can only answer this. The odds (with infinite decks) are 21.21%

Quote:gospeedgo11I was unable to find it on the internet or this forum. The first question I have is what is the odds of the dealer having a soft 17 in any given hand? Assume six decks. For example, it could be a 6-A but also 3-3 then draw to an ace.

I get about 1.8% probability of dealer having a soft 17.

6A 1.1872%

5AA 0.1321%

42A 0.2757%

33A 0.1321%

AAA4 0.0125%

AA23 0.041%

A222 0.0125%

AAAA3 0.001069%

AAA22 0.002342%

AAAAA2 0.000835%

AAAAAAA 6.486 E-07 %

Total : 1.7968687%

Explain this, please? I am not familiar with the notation. What is this 486 E-07%

Quote:billryanAAAAAAA 6.486 E-07 %

Explain this, please? I am not familiar with the notation. What is this 486 E-07%

It is called scientific notation.

6.486E-07 = 6.486 x 10

^{-7}= 0.0000006486

Quote:gordonm888It is called scientific notation.

6.486E-07 = 6.486 x 10^{-7}= 0.0000006486

He knew that. He just wanted to see you type out allllllll those zeroes. (Kidding)

My rules are currently 6 deck shoe, 3:2 BJ, DA2, split once, DAS, split ace one card, late surrender. The wizard's calculator puts this at 0.60374%. If no surrender it becomes 0.69205%. That would make the dealer's house edge bet 0.73%. It balances it out more. Now I'm just talking to myself haha.

Anybody please correct if I'm wrong here. Thanks again!

Quote:gordonm888I get about 1.8% probability of dealer having a soft 17.

6A 1.1872%

5AA 0.1321%

42A 0.2757%

33A 0.1321%

AAA4 0.0125%

AA23 0.041%

A222 0.0125%

AAAA3 0.001069%

AAA22 0.002342%

AAAAA2 0.000835%

AAAAAAA 6.486 E-07 %

Total : 1.7968687%

Some combinations are missing there or did you include different orderings in the above, that is 33A includes 3A3 and A33 etc?

Quote:gospeedgo11Thank you Jufo and Gordon. To recap, in my game players can bet that the dealer will win. But if the dealer wins after having a soft 17, the players betting on the dealer will push instead of win. If I combine the 1.7968687% of getting a soft 17 and multiplying it by 78.79% chance of not busting it comes out to 1.42%. Does this mean that the house edge for this game when betting on the dealer would be 0.82% (1.42%-0.60%), 0.60% coming from the approximate house edge)?

1.42% would be the probability of dealer having Soft 17 and not busting, but it doesn't mean that the dealer will win that hand, so it's more complex than that.

And no, you can't calculate the house edge of betting on the dealer like that as it is not directly opposite to the player bet.

So, your target is to have the bet "dealer wins" as close to zero house edge as possible? And this is assuming that the player side plays optimally because if they don't then bet "dealer wins" will have an edge. If dealer pushes is the "dealer wins" bet a push or a loss?

From dealer's side the probabilites are this (Source: https://wizardofodds.com/games/blackjack/appendix/4 ):

Loss 42.42%

Push 8.48%

Win 49.09%

If you want to make this zero house edge by making some wins become pushes the win probability has to be equal to lose probability so you will need to increase the frequency of pushes by 6.67%. The hit soft 17 push rule change will not achieve that.

Quote:

My rules are currently 6 deck shoe, 3:2 BJ, DA2, split once, DAS, split ace one card, late surrender. The wizard's calculator puts this at 0.60374%. If no surrender it becomes 0.69205%. That would make the dealer's house edge bet 0.73%. It balances it out more. Now I'm just talking to myself haha.

If you also want to make the player bet as close to zero house edge as possible, you could allow early surrender with puts it very close to 0% HE.

Quote:Jufo81Some combinations are missing there or did you include different orderings in the above, that is 33A includes 3A3 and A33 etc?

Yes, 33A included 3A3 and A33 and so on for the other combinations. The sequence doesn't matter in the way I calculated it.