Excluding blackjacks who has the overall edge with an Ace, dealer or player?

**Secretariat** · 12-21-2020, 07:55 PM

OK, we all want aces. It's the most valuable card for the player.
However, excluding players and dealers blackjacks,
who's got the overall edge with an ace at 6D, S17, DAS, no RSA and no LS?
With two cards soft hands, I believe the players advantage to be around 16,7%. Right?
However, I can't figure out what's the overall dealer's advantage with upcard Ace against any two card combination, including 17-18-19-20.
Page 443 of BJA gives the answer for each player's hand, but it's tough to figure out the overall dealer advantage since it must be adjusted with the frequency of each hand.

**Dog Hand** · 12-21-2020, 09:58 PM

Originally Posted by Secretariat

OK, we all want aces. It's the most valuable card for the player.
However, excluding players and dealers blackjacks,
who's got the overall edge with an ace at 6D, S17, DAS, no RSA and no LS?
With two cards soft hands, I believe the players advantage to be around 16,7%. Right?
However, I can't figure out what's the overall dealer's advantage with upcard Ace against any two card combination, including 17-18-19-20.
Page 443 of BJA gives the answer for each player's hand, but it's tough to figure out the overall dealer advantage since it must be adjusted with the frequency of each hand.

Secretariat,

I used the WoO's table for 6D S17: see

https://wizardofodds.com/games/black...dix/9/6ds17r4/

I found that, if neither the player nor the dealer has a BJ, then when the dealer has an A upcard, the player's EV is about -9.5%. The only +EV hands are 10, 11, 19, and 20: everything else is -EV.

Hope this helps!

Dog Hand

**Secretariat** · 12-22-2020, 07:33 AM

Originally Posted by Dog Hand

Secretariat,

I used the WoO's table for 6D S17: see

https://wizardofodds.com/games/black...dix/9/6ds17r4/

I found that, if neither the player nor the dealer has a BJ, then when the dealer has an A upcard, the player's EV is about -9.5%. The only +EV hands are 10, 11, 19, and 20: everything else is -EV.

Hope this helps!

Dog Hand

So if we're right, players advantage with an ace (16,7%) minus dealer advantage (9,5%) with and ace, would lead to a nearly 7% player advantage on the first two cards with an Ace. I presume that some of that advantage would be taken away with multiple draws since the dealer draws more often than the player and that the player can no longer soft double down. At the end of the day, who has the net advantage and by how much? Would be nice to have Don's comments on this?

**Dog Hand** · 12-22-2020, 08:00 AM

Originally Posted by Secretariat

<snip> and that the player can no longer soft double down.<snip>

Secretariat,

Why is the player not allowed to double on a soft hand?

Dog Hand

P.S. In my previous post I forgot to add that, with no dealer BJ, AA vs. A is also +EV.

**DSchles** · 12-22-2020, 08:48 AM

Originally Posted by Dog Hand

I used the WoO's table for 6D S17

Insulted that you didn't use the BJA3 p. 443 appendix, but you're forgiven.

Don

**DSchles** · 12-22-2020, 08:55 AM

Originally Posted by Secretariat

Would be nice to have Don's comments on this?

You have to do the grunt work, hand by hand, as I know of no other way to do it, since you're specifying just a single card for each and no naturals allowed. Traditional charts and combinatorial analyzers don't work that way.

Nonetheless, when a player starts with an Ace, we know his edge is almost 51%, globally, vs. all dealer upcards. That edge is only 12% vs. dealer's Ace, assuming that he doesn't have a natural (has a playable Ace). It's easy to realize that the huge majority of that 51% edge comes from the potential to get a natural. You would achieve that about 4/13 of the time, or 30.8% of the time, and since you get paid 150%, that edge swells to 46.2%. Clearly, since the original edge against the dealer's ace was only 12% of the 51%, you now are not going to have any edge at all if you eliminate the chance of the player's natural.

Don

**DSchles** · 12-22-2020, 08:57 AM

Originally Posted by Dog Hand

Why is the player not allowed to double on a soft hand?

He was talking about soft hands with multiple draws. But why are we talking about soft doubles, when the dealer shows an Ace?

Don

**Dog Hand** · 12-22-2020, 09:23 AM

Secretariat,

Perhaps I misunderstood the original post. Are you asking for the EV for hands where both the dealer and the player have an Ace, and neither has a BJ? If so, then my previous replies in this thread are invalid.

Dog Hand

**Secretariat** · 12-22-2020, 10:00 AM

Hi Dog Hand. Yes, the player is allowed to soft double. So you can hit or soft double but after the first draw (3rd card in hand), you can't soft double anymore. That's when I presume aces, overall play more against the player and therefore reduces the player's advantage. Since the dealer also hits more often than the player the ace plays more in his favor, especially when he gets an ace on 16 against our stand stiff.

**Secretariat** · 12-22-2020, 10:22 AM

Hello Don! Obviously, we don't soft double against the ace. Maybe my OP is not clear. Most models are based on the player's first two cards vs dealer's upcard. On one side, we have all our soft hands including AA, vs dealer's upcard 23456789TA. My understanding is that the player has an overall 16.7% edge with an ace in hand, excluding blackjacks.
It's more difficult to evaluate the dealer's advantage when he has a playable Ace against all our possible 2-card hands (excluding blackjacks). What would be the dealer's overall advantage when he has an ace? Dog Hand says it's around 9,5%. That's almost a 7% difference, leaving the player with a 7% advantage when either the player or the dealer has an ace. The frequency of each hands is also a factor to consider.
Now, once we go beyond the 3rd card, am I right to presume that drawing aces favors the dealer more than the player since the player can't double down anymore and since the dealer draws more often. I have no idea how to quantify that advantage since there are so many possible card combinations. So Back to the original questions. How has the edge with an ace excluding blackjacks?

**Secretariat** · 12-22-2020, 10:23 AM

Correction to the question" So Back to the original questions. WHO has the edge with an ace excluding blackjacks?

**DSchles** · 12-22-2020, 10:56 AM

Originally Posted by Secretariat

Correction to the question" So Back to the original questions. WHO has the edge with an ace excluding blackjacks?

Again, don't be lazy! Do the grunt work from page 443. Take the best expectations of each of the nine starting hands (positive for A,A, A,8, and A,9, and negative for all the rest), weight by frequency -- all the same except for A,A, which is slightly less than half of all the others -- and see which wins.

My money is on a slight edge to the player, but I wouldn't bet on it.

Don

**DSchles** · 12-22-2020, 11:08 AM

Rereading, you seem to be asking different, yet very strange, questions. 1) Player starts with an Ace that can't turn into a blackjack. What is his edge vs. all possible playable dealer upcards? 2) Dealer starts with an Ace that can't be a blackjack. What is his edge vs. all player two-card starting hands?

I think I already answered the first question. Almost all of the 51% edge that the player Ace enjoys vs. all upcards is due to the potential for a natural. What's left is about 5% or so.

Conversely, I think a dealer's playable Ace vs. all player two-card starting, non-blackjack, hands is enormous.

Don