Hit Soft 17 odds

I 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.

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: gospeedgo11

I 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%

AAAAAAA 6.486 E-07 %



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

Quote: billryan

AAAAAAA 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: gordonm888

It 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)

Thank 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)?

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: gordonm888

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%

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

Quote: gospeedgo11

Thank 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: Jufo81

Some 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.

I did not. I took the easy math classes in school. After Geometry, I took business math, surveying and statistics, sets and logic.
Never got around to calculus or some of the higher math. honestly, I've never needed it.

Quote: gospeedgo11

Thank 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)?

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!

So it’s a blackjack and a baccarat game?

How is the player playing his hand?

Can’t I just put $100 on the dealer to win and $10 on my blackjack bet and then keep hitting my hand until I bust and win $90

I'll come back to this in a few hours and explain my rules. The short answer is you won't be able to do that.

Here are the rules for my homemade game. 6 deck shoe, 3:2 BJ, DA2, split once, DAS, split ace one card, late surrender.

1. Players can choose to bet on the player hand or dealer hand. There will be one player hand played against one dealer hand (similar to online live blackjack how many people can play one hand differently).

2. Players cannot bet on both the dealer and player hand.

3. If the player bets on the dealer hand, the player has no control how the dealer plays the hand; it is simply hit on 16 or lower and soft 17.

4. If the player bets on the dealer hand, the player has control on how he wants to play his hand. However, the dealer only plays against the perfect basic strategy hand.

5. The house assumes the financial risk for player doubles. Players betting on dealer hand can choose to double as the dealer as well when the basic strategy calls for doubling (although this is a bad idea from the dealer's point of view).

6. When strategy says to surrender, betting the dealer automatically win 1 to 2. I'm thinking of getting rid of surrender altogether to even out the house edge.

7. After all player's decisions are made, the appropriate cards will be dealt or not.

All of these decisions will use different colored chips or lammers with names to indicate player decisions. Players can use a special chip to indicate they with to play solely by the book.

Example hand:

Players 1, 2, and 3 bet on player. Player 4 bets on dealer. All bet $10. Player hand is dealt a 10-4 and dealer is showing a 10. Player 1 wants to hit. Player 2 wants to surrender. Player 3 wants to stand. After all decisions are made, a card is dealt for player 1's decision (if nobody decided to hit, a card would still be dealt because the dealer must play against a basic strategy hand).

A 10 is revealed as the player's hit card. The dealer now plays. He has a 10-5 and busts with an 8 (Note that the card that the player may or may not have taken is not the same card to be used, i.e. players can steal the "bust card" sometimes). Player 1 busted, losing $10. Player 2 surrendered, losing $5. Player 3 wins $10. Player 4 wins $10 because he was against the basic strategy hand, and would not have busted against the basic strategy hand because the player would have busted first.

Example hand 2:

Players 1 and 2 bet on the player hand. Player 3 bets on the dealer hand. All bet $10. Player hand is 8-3 and dealer is showing a 10. Player 1 decides to double. Player 2 decides to just take a hit. The player card is a 5. Player 1 is stuck with a 16, but player 2 decides to hit again. Next card is a 4, and player 2 decides to stand. The dealer reveals 10-9 for a 19. Player 1 loses $20, player 2 wins $10, and player 3 wins $10 because he is playing only against the basic strategy hand which had a 16 ($20 if he decided to back the double bet).

Let me know if you have any feedback for this game.

Quote: Jufo81

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?

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.

Not quite, I wanted to make this game like baccarat, where each bet has a small house edge less than 1%. Read the rules I posted and see if my game can achieve this or not.

So all players must bet exactly the same amount ???

No, I just used the same amount for clarity and simplicity. The game can probably have a wide range like $5-$500 or $10-1000.