Dealer upcards...
- Thread starter chasekwe
- Start date
The probability of dealer busting 4's: 40%, 5's 43%, 6's 42%.Here is a good link http://wizardofodds.com/askthewizard/blackjack.html
This link should help to answer your question:
http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)
Just sum the products of the EV and probabilities for each upcard.
-Sonny-
http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)
Just sum the products of the EV and probabilities for each upcard.
-Sonny-
Actually, let me change my question because I asked it incorrectly and didn't get the answers I was looking for as a result.
In double attack blackjack when is it beneficial to double attack? In the past I've done it only on 4, 5 and 6 but I'm curious if those are the only numbers I should be doing it on.
Also, does anybody know odds for the "Bust it"? I've always just avoided that side game altogether but I have seen it benefit some people a great deal while I feel others perhaps got screwed. The more likely outcome is what I'd be curious about.
In double attack blackjack when is it beneficial to double attack? In the past I've done it only on 4, 5 and 6 but I'm curious if those are the only numbers I should be doing it on.
Also, does anybody know odds for the "Bust it"? I've always just avoided that side game altogether but I have seen it benefit some people a great deal while I feel others perhaps got screwed. The more likely outcome is what I'd be curious about.
According to my detailed sims you would double attack on 3-8. It's close to an even money decision against the 2.
This game is probably not beatable by counting. But... it does have an interesting feature of the dealer's up-card being the first card out of the shoe on each round. So there is a way to "attack" it. You'd need a very skilled sequencer and a big spread to beat it that way though.
This game is probably not beatable by counting. But... it does have an interesting feature of the dealer's up-card being the first card out of the shoe on each round. So there is a way to "attack" it. You'd need a very skilled sequencer and a big spread to beat it that way though.
Hi,
The rules I found for double attack were:
8 deck Spanish Shoe
S17
DOA
DAN
LS
SAN (Surrender Any Number)
SAS (Surrender After Split)
BJ 1:1
Player BJ always wins
DDR (Double Down Rescue)
I can handle all except the Double down rescue for now. The calculation should be simply the doubling of any positive EV to get the overall EV and the strategy does not depend on the bet size.
Not including DDR I get an EV of -0.36% and that you agree with Automatic Monkey that you should attack 2-8. The EV for a 2 upcard is 0.29% with these rules so it's not huge as he pointed out, but every bit helps.
DDR will help but probably not a whole lot.
Here are the EVs:
The strategy is pretty much the same as the Wizard's for Spanish 21 except he has a few extra splits and doubles which I assume are due to DDR:
http://wizardofodds.com/spanish21
Good luck,
MGP
The rules I found for double attack were:
8 deck Spanish Shoe
S17
DOA
DAN
LS
SAN (Surrender Any Number)
SAS (Surrender After Split)
BJ 1:1
Player BJ always wins
DDR (Double Down Rescue)
I can handle all except the Double down rescue for now. The calculation should be simply the doubling of any positive EV to get the overall EV and the strategy does not depend on the bet size.
Not including DDR I get an EV of -0.36% and that you agree with Automatic Monkey that you should attack 2-8. The EV for a 2 upcard is 0.29% with these rules so it's not huge as he pointed out, but every bit helps.
DDR will help but probably not a whole lot.
Here are the EVs:
Code:
UC 2 3 4 5 6 7 8 9 10 1
Prob 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.25 0.083
EV (%) 0.29 2.88 5.95 9.43 13.47 9.6 1.85 -6.72 -17.76 -31.28
Attack EV 0.58 5.76 11.9 18.86 26.94 19.2 3.7 -6.72 -17.76 -31.28
Net 0.048 0.48 0.992 1.572 2.245 1.6 0.308 -0.56 -4.44 -2.61
Total EV -0.362%http://wizardofodds.com/spanish21
Good luck,
MGP
Spanish 21 has an additional beneficial rule that a 21 drawn by the player always wins. That makes drawing to any stiff more desirable. That game also has DDR. The surrender options are next to useless in both games because there are no basic strategy surrender plays.
When I examined this game I estimated a house edge of significantly higher than 0.36%. If you don't mind, perhaps you could share your methodology with me, either here or in a private message.
When I examined this game I estimated a house edge of significantly higher than 0.36%. If you don't mind, perhaps you could share your methodology with me, either here or in a private message.
Oh yeah - I wasn't paying attention to that rule. I reran my CA with all the same rules except that player 21 wins. From what I read Double Attack has DDR as well.
So the player 21 wins rule accounts for some of the extra doubling and splitting - specifically if player 21 wins then you should do the following instead of the strategy posted further down:
Double: 16 vs 5, 18 vs 4
Split 22 vs 2, 33 vs 2, 99 vs 3
That means the DDR rule is the reason to Double 11 vs 9,10,A in the Wizard's strategy. Spanish 21 also gives some n-card bonuses so there lead to a couple of extra hits instead of split/double on the Wizard's strategy. It also implies that the rest of the strategy is probably correct (e.g. not splitting 22 vs 2 and 99 vs 3).
Actually it's TD strategy to Surrender 17 vs A.
Actually I did in my previous message. I took the EV's for each upcard given the rules I listed without DDR, and doubled those in which the EV was positive and took the weighted average of the EV's to come up with the overall EV. The values are all there.
Anyways, so here's what I'm getting as the TD strategy. I'm assuming that DDR is the reason for the doube 11's mentioned above so I've changed my CA's strategy only for those hands:
So the player 21 wins rule accounts for some of the extra doubling and splitting - specifically if player 21 wins then you should do the following instead of the strategy posted further down:
Double: 16 vs 5, 18 vs 4
Split 22 vs 2, 33 vs 2, 99 vs 3
That means the DDR rule is the reason to Double 11 vs 9,10,A in the Wizard's strategy. Spanish 21 also gives some n-card bonuses so there lead to a couple of extra hits instead of split/double on the Wizard's strategy. It also implies that the rest of the strategy is probably correct (e.g. not splitting 22 vs 2 and 99 vs 3).
Actually it's TD strategy to Surrender 17 vs A.
Actually I did in my previous message. I took the EV's for each upcard given the rules I listed without DDR, and doubled those in which the EV was positive and took the weighted average of the EV's to come up with the overall EV. The values are all there.
Anyways, so here's what I'm getting as the TD strategy. I'm assuming that DDR is the reason for the doube 11's mentioned above so I've changed my CA's strategy only for those hands:
Code:
Hard 2 3 4 5 6 7 8 9 10 1
4 H H H H H H H H H H
5 H H H H H H H H H H
6 H H H H H H H H H H
7 H H H H H H H H H H
8 H H H H H H H H H H
9 H H H H D H H H H H
10 D D D D D D D H H H
11 D D D D D D D H H H
12 H H H H H H H H H H
13 H H H H H H H H H H
14 H H S S S H H H H H
15 S S S S S H H H H H
16 S S S S S H H H H H
17 S S S S S S S S S R
18 S S S S S S S S S S
19 S S S S S S S S S S
20 S S S S S S S S S S
21 S S S S S S S S S S
Soft 2 3 4 5 6 7 8 9 10 1
12 -- -- -- -- -- -- -- -- -- H
13 H H H H H H H H H H
14 H H H H H H H H H H
15 H H H H H H H H H H
16 H H H H D H H H H H
17 H H D D D H H H H H
18 S S S D, S D, S S S H H H
19 S S S S S S S S S S
20 S S S S S S S S S S
21 S S S S S S S S S S
Pairs 2 3 4 5 6 7 8 9 10 1
A, A P P P P P P P P P --
2, 2 -- P P P P P -- -- -- --
3, 3 -- P P P P P P -- -- --
4, 4 -- -- -- -- -- -- -- -- -- --
5, 5 -- -- -- -- -- -- -- -- -- --
6, 6 -- -- P P P -- -- -- -- --
7, 7 P P P P P P -- -- -- --
8, 8 P P P P P P P P P P
9, 9 -- -- P P P -- P P -- --
10, 10 -- -- -- -- -- -- -- -- -- --All right, I get net EV's of:
Dealer 2- 0.045
Dealer 3- 0.407
Dealer 4- 0.815
Dealer 5- 1.27
Dealer 6- 1.72
Dealer 7- 1.36
Dealer 8- 0.27
Dealer 9- -0.549
Dealer X- -4.46
Dealer A- -2.70
Total= -1.82%
Against 9-A we seem to be on the same page but not against the low cards. This is after adjusting my strategy to be the same as what you are using. (My original one didn't take into account that DAN makes doubles less frequent and splits more frequent, ever so slightly.) My first thought is that maybe one of our sims isn't handling the multi-card DAS well.
The DDR rule can't add that much to the strategies as we are using them because it will only ever be used against dealer 8. DDR will make other doubles more likely, but we would have to deconvolve it from the automatic-win-on-21 rule in Spanish 21.
Dealer 2- 0.045
Dealer 3- 0.407
Dealer 4- 0.815
Dealer 5- 1.27
Dealer 6- 1.72
Dealer 7- 1.36
Dealer 8- 0.27
Dealer 9- -0.549
Dealer X- -4.46
Dealer A- -2.70
Total= -1.82%
Against 9-A we seem to be on the same page but not against the low cards. This is after adjusting my strategy to be the same as what you are using. (My original one didn't take into account that DAN makes doubles less frequent and splits more frequent, ever so slightly.) My first thought is that maybe one of our sims isn't handling the multi-card DAS well.
The DDR rule can't add that much to the strategies as we are using them because it will only ever be used against dealer 8. DDR will make other doubles more likely, but we would have to deconvolve it from the automatic-win-on-21 rule in Spanish 21.
Actually, mine's not a sim - it's a CA. How many hands did you run? You'd probably need several billion to make sure it's accurate. Is your player BJ always winning? My CA should be accurate for all the rules I listed.
Actually the Wizard uses DDR against 8-A. I tried to separate out the DDR part in my previous post and any differences beyond that shouldn't be more than about 0.3%.
Actually the Wizard uses DDR against 8-A. I tried to separate out the DDR part in my previous post and any differences beyond that shouldn't be more than about 0.3%.
Ah that's what I did!
I was using TBA numbers instead of IBA numbers, so when I convert to IBA by multiplying by the average total bet for each dealer upcard, I get a house advantage of 0.55%.
Then I add an estimate of 1.0435% to the player advantage when the dealer has an ace showing and 0.3478% for when the dealer has a 10 showing to represent the player-BJ-always-wins rule and that gets my house edge down to 0.376%. Looks like our models have converged. Next step: getting EOR's for the cards in this game.
Oh and the reason I say the DDR rule isn't that useful in this game is that in the BS we are using, you never DD on 9-A so a DDR will only happen against dealer 8. That is unless you modify the doubling BS to account for the benefit of DDR.
I was using TBA numbers instead of IBA numbers, so when I convert to IBA by multiplying by the average total bet for each dealer upcard, I get a house advantage of 0.55%.
Then I add an estimate of 1.0435% to the player advantage when the dealer has an ace showing and 0.3478% for when the dealer has a 10 showing to represent the player-BJ-always-wins rule and that gets my house edge down to 0.376%. Looks like our models have converged. Next step: getting EOR's for the cards in this game.
Oh and the reason I say the DDR rule isn't that useful in this game is that in the BS we are using, you never DD on 9-A so a DDR will only happen against dealer 8. That is unless you modify the doubling BS to account for the benefit of DDR.
Been done. The trick of this game is that you have to separate out the EV's for dealer upcards 2-8, double them, and add them to the sum of the EV's for all dealer upcards. Otherwise the house edge is up around 4%.
When calculating the EOR's you have to not only consider the advantage of removing the low cards making the dealer more likely to bust, but the disadvantage, because there are fewer low dealer upcards to "double attack" against. The advantage still outweighs the disadvantage, but not as much as it does in regular BJ.
I've assigned card weights of {-1,1,2,2,2,2,0,-1,-1,-2} to the Spanish pack and my preliminary results show a nice strong betting correlation. Now I'm trying to force CVIndex to generate a basic set of playing indices so I can get a better idea of what kinds of advantages we can get.
When calculating the EOR's you have to not only consider the advantage of removing the low cards making the dealer more likely to bust, but the disadvantage, because there are fewer low dealer upcards to "double attack" against. The advantage still outweighs the disadvantage, but not as much as it does in regular BJ.
I've assigned card weights of {-1,1,2,2,2,2,0,-1,-1,-2} to the Spanish pack and my preliminary results show a nice strong betting correlation. Now I'm trying to force CVIndex to generate a basic set of playing indices so I can get a better idea of what kinds of advantages we can get.
I found an error in how I was doing the EORs- I was just doubling EOR's for each card separately without taking the double attacks into account and then doubling them afterwards and it was mixing everything up.
Anyways, I did the EOR for 10 by hand though and it still disagrees with yours unfortunately.
With a 10 removed and fixing the strategy, the new TD EV should be -0.503% compared to -0.362%. I.e. the EOR for 10 should be -0.14%, which is much less than the 1% you list. I'm not sure where the discrepency is coming in though...
I also realized in the strategy I posted - I forgot to change the H's to D's for 11 vs 9-A, but I don't use those doubles for the calculations anyways so I'm actually using the strategy listed. I just think it's incorrect if DDR is allowed - in which case I think you probably should be doubling those.
Here are my new values for each upcard with a 10 removed:
I'll have to check the other EORs later...
Anyways, I did the EOR for 10 by hand though and it still disagrees with yours unfortunately.
With a 10 removed and fixing the strategy, the new TD EV should be -0.503% compared to -0.362%. I.e. the EOR for 10 should be -0.14%, which is much less than the 1% you list. I'm not sure where the discrepency is coming in though...
I also realized in the strategy I posted - I forgot to change the H's to D's for 11 vs 9-A, but I don't use those doubles for the calculations anyways so I'm actually using the strategy listed. I just think it's incorrect if DDR is allowed - in which case I think you probably should be doubling those.
Here are my new values for each upcard with a 10 removed:
Code:
UC 2 3 4 5 6 7 8 9 10 A
Prob 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.084 0.248 0.084
EV (%) 0.09 2.68 5.7 9.18 13.22 9.51 1.8 -6.69 -17.69 -31.17
Attack EV 0.180 5.36 11.40 18.36 26.44 19.02 3.60 -6.69 -17.69 -31.17
Net 0.015 0.448 0.952 1.534 2.209 1.589 0.301 -0.559 -4.388 -2.604
Total EV -0.503%
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Great we are converging again! The EOR of 1 for the 10 was not a percent, it was just a relative number generated with a Monkey Carlo simulation. All the other cards were rated relative to the 10.
I get very similar EOR's but I don't want to attempt an unbalanced count in an 8D game so I padded the low cards to balance it, giving me the {-1,1,2,2,2,2,0,-1,-1,-2} aforementioned.
I get very similar EOR's but I don't want to attempt an unbalanced count in an 8D game so I padded the low cards to balance it, giving me the {-1,1,2,2,2,2,0,-1,-1,-2} aforementioned.