Optimal Counter Strategy & Counter-Strategy for Blackjack Without Upcards

[DSchles]

Dealer would be dealt no cards at all, only drawing after players' hands have been dealt.

k_c

I understand. But you mentioned hole-card flashing. You eliminate that with just not taking a hole card. It has nothing to do with the upcard, as well, which would be overkill towards preventing flashing.

Don

[Cacarulo]

This thread has caught my attention, and I really couldn't resist. Although my CA allows me to analyze when the dealer shows only one card, or two (in the case of hole-carding),
it's not prepared for when the dealer shows none. Nevertheless, I made some modifications taking advantage of what already exists, as JohnGalt007 correctly suggested.
The interesting thing is that I arrived at the same optimal strategy but with a slightly higher player edge. For the case of 6D, S17, DOA, NDAS, SPA1, SPL1, NS,
I obtained -2.003457%. If the game is DAS/SPL3, the strategy adds an extra variation: always split 9,9. In this case, the player edge changes to -1.912557%.
Clearly, if BJ pays 2:1, I would love to play this game. However, I'm not 100% sure of the advantages obtained, so don't take it as gospel truth.

Sincerely,
Cac

[k_c]

This thread has caught my attention, and I really couldn't resist. Although my CA allows me to analyze when the dealer shows only one card, or two (in the case of hole-carding),
it's not prepared for when the dealer shows none. Nevertheless, I made some modifications taking advantage of what already exists, as JohnGalt007 correctly suggested.
The interesting thing is that I arrived at the same optimal strategy but with a slightly higher player edge. For the case of 6D, S17, DOA, NDAS, SPA1, SPL1, NS,
I obtained -2.003457%. If the game is DAS/SPL3, the strategy adds an extra variation: always split 9,9. In this case, the player edge changes to -1.912557%.
Clearly, if BJ pays 2:1, I would love to play this game. However, I'm not 100% sure of the advantages obtained, so don't take it as gospel truth.

Sincerely,
Cac

Don't agree with your results.

9-9 s17, NDAS, SPL1

stand      -0.0049307389531300094
hit        -0.63799907995510718
double     -1.2278929297191714
split      -0.030700995078118826

9-9 s17, DAS, SPL3

stand      -0.0049307389531300094
hit        -0.63799907995510718
double     -1.2278929297191714
split 1    -0.0054744808778548204
split 2    -0.0057449226985539989
split 3    -0.0058208716922732578

Overall EV
s17, NDAS, SPL1: -2.47821%
s17, DAS, SPL3: -2.40076

k_c

[Cacarulo]

Don't agree with your results.

9-9 s17, NDAS, SPL1

stand      -0.0049307389531300094
hit        -0.63799907995510718
double     -1.2278929297191714
split      -0.030700995078118826

9-9 s17, DAS, SPL3

stand      -0.0049307389531300094
hit        -0.63799907995510718
double     -1.2278929297191714
split 1    -0.0054744808778548204
split 2    -0.0057449226985539989
split 3    -0.0058208716922732578

Overall EV
s17, NDAS, SPL1: -2.47821%
s17, DAS, SPL3: -2.40076

k_c

Hmmm, I must have a bug somewhere. Like I said, don't take my EVs as gospel.
I checked your EVs through simulation, and they're correct.

Sincerely,
Cac

[k_c]

icount thanks and actually it was one of your posts that helped me get started ... 'the best thing is to generate all the possible sequences for the dealer and the player and store them because you will keep on using them. The best way to do it is by brute force enumeration using loops.'
https://www.blackjackinfo.com/commun...ramming.21048/



like instead of say ..
10, 8, 1, 2
10, 8, 2, 1..

..just use the prob of one of them * 2?

Been using Python. .. id love to start learning c++ and may do that. I figured it was just my method that's the bottleneck ..


Here is my dealer calc prob function that I call for every possible player hand and return the probability .. if you wouldn't mind having a look.

Don't know if this is your cup of tea but I translated my code for dealer probs to Excel/VBA. Translating code from c++ to VBA required a few work arounds. Translating to another language could similarly require work arounds but I think it would mostly translate pretty directly to language that supports object oriented programming.

http://www.bjstrat.net/software.html

There is no charge for downloads but I would appreciate any donations to my PayPal account identified on this page.

k_c

[Cacarulo]

Don't agree with your results.

9-9 s17, NDAS, SPL1

stand      -0.0049307389531300094
hit        -0.63799907995510718
double     -1.2278929297191714
split      -0.030700995078118826

9-9 s17, DAS, SPL3

stand      -0.0049307389531300094
hit        -0.63799907995510718
double     -1.2278929297191714
split 1    -0.0054744808778548204
split 2    -0.0057449226985539989
split 3    -0.0058208716922732578

Overall EV
s17, NDAS, SPL1: -2.47821%
s17, DAS, SPL3: -2.40076

k_c

I've found one bug, but there's another one lurking around that's driving me crazy.
The following is a list with only the splits. We might be 100% in agreement regarding
Standing, Hitting, and Doubling, but not so much in Splitting, and I don't understand why.
And I know it has nothing to do with the splitting routine. I use:
6D,S17,DOA,NDAS,SPA1,SPL1,NS

 Hand     Standing            Hitting             Doubling            Splitting
 ========================================================================================
 A-A   -0.43060979624647    0.00744776368644   -0.26632182751754    0.32345757722700 => P
 2-2   -0.43653687111080   -0.19848037379651   -0.82496851203056   -0.26756733803531 => H
 3-3   -0.43630981351727   -0.23994435597042   -0.80213035117781   -0.30935774135543 => H
 4-4   -0.43611644886577   -0.12478675211270   -0.42657887496346   -0.35091934452573 => H
 5-5   -0.43592296988447    0.10090965028670    0.19998889536827   -0.39465798844387 => D
 6-6   -0.43741256140498   -0.32256918500666   -0.62914539795086   -0.42655201559236 => H
 7-7   -0.43467868632438   -0.42615416938779   -0.81383273090416   -0.37818712820015 => P
 8-8   -0.43560801408521   -0.50653068462492   -0.96495613905881   -0.20179842181804 => P
 9-9   -0.00493073895313   -0.63799907995511   -1.22789292971917   -0.00423297207660 => P
 T-T    0.58091388727359   -0.85790041631634   -1.66869779473729    0.24006930382789 => S

To reach the line where the player has a 9-9, I use the following table as a starting point.

   Hand      Standing    Hitting     Doubling    Splitting
================================================================
 9-9 vs A   -0.093071   -0.626095   -1.252191   -0.121888   => S
 9-9 vs T   -0.171080   -0.643985   -1.287970   -0.299057   => S
 9-9 vs 9   -0.185235   -0.613052   -1.226103   -0.105627   => P
 9-9 vs 8    0.099261   -0.587148   -1.174296    0.193427   => P
 9-9 vs 7    0.399576   -0.587176   -1.174353    0.343323   => S
 9-9 vs 6    0.280805   -0.604091   -1.208183    0.387321   => P
 9-9 vs 5    0.200047   -0.611359   -1.222718    0.319391   => P
 9-9 vs 4    0.174080   -0.614207   -1.228414    0.256731   => P
 9-9 vs 3    0.144792   -0.622799   -1.245598    0.198208   => P
 9-9 vs 2    0.124232   -0.623270   -1.246540    0.152445   => P

Why, if all the expected values are correct, am I not getting the correct result ONLY
in the splitting column?

Sincerely,
Cac

[k_c]

I've found one bug, but there's another one lurking around that's driving me crazy.
The following is a list with only the splits. We might be 100% in agreement regarding
Standing, Hitting, and Doubling, but not so much in Splitting, and I don't understand why.
And I know it has nothing to do with the splitting routine. I use:
6D,S17,DOA,NDAS,SPA1,SPL1,NS

 Hand     Standing            Hitting             Doubling            Splitting
 ========================================================================================
 A-A   -0.43060979624647    0.00744776368644   -0.26632182751754    0.32345757722700 => P
 2-2   -0.43653687111080   -0.19848037379651   -0.82496851203056   -0.26756733803531 => H
 3-3   -0.43630981351727   -0.23994435597042   -0.80213035117781   -0.30935774135543 => H
 4-4   -0.43611644886577   -0.12478675211270   -0.42657887496346   -0.35091934452573 => H
 5-5   -0.43592296988447    0.10090965028670    0.19998889536827   -0.39465798844387 => D
 6-6   -0.43741256140498   -0.32256918500666   -0.62914539795086   -0.42655201559236 => H
 7-7   -0.43467868632438   -0.42615416938779   -0.81383273090416   -0.37818712820015 => P
 8-8   -0.43560801408521   -0.50653068462492   -0.96495613905881   -0.20179842181804 => P
 9-9   -0.00493073895313   -0.63799907995511   -1.22789292971917   -0.00423297207660 => P
 T-T    0.58091388727359   -0.85790041631634   -1.66869779473729    0.24006930382789 => S

To reach the line where the player has a 9-9, I use the following table as a starting point.

   Hand      Standing    Hitting     Doubling    Splitting
================================================================
 9-9 vs A   -0.093071   -0.626095   -1.252191   -0.121888   => S
 9-9 vs T   -0.171080   -0.643985   -1.287970   -0.299057   => S
 9-9 vs 9   -0.185235   -0.613052   -1.226103   -0.105627   => P
 9-9 vs 8    0.099261   -0.587148   -1.174296    0.193427   => P
 9-9 vs 7    0.399576   -0.587176   -1.174353    0.343323   => S
 9-9 vs 6    0.280805   -0.604091   -1.208183    0.387321   => P
 9-9 vs 5    0.200047   -0.611359   -1.222718    0.319391   => P
 9-9 vs 4    0.174080   -0.614207   -1.228414    0.256731   => P
 9-9 vs 3    0.144792   -0.622799   -1.245598    0.198208   => P
 9-9 vs 2    0.124232   -0.623270   -1.246540    0.152445   => P

Why, if all the expected values are correct, am I not getting the correct result ONLY
in the splitting column?

Sincerely,
Cac

What I do is the following:

one split allowed

1. OverallEVx = value of drawing to first pair card
   For 9-9 (loss to dealer BJ) 6 decks, SPL1, NDAS, OverallEVx = -0.039403112634580864
2. If lose all to dealer BJ
   overallSplitEV = 2 * OverallEVx = -0.078806225269161728
3. If OBO, one split hand is not at risk so "rebate" is given if dealer has BJ
   prob dealer BJ = 0.048105230191042903
   overallSplitEV = -0.078806225269161728 + 0.048105230191042903
   overallSplitEV = -0.030700995078118825

multiple splits

1. compute values for overallEVx[numsplits] and overallEVPair[numSplits]
2. from above compute SPL1, SPL2, SPL3 for lose all to dealer BJ
3. for OBO compute number of expected hands
   for SPL1 number of expected hands = 2
   for > SPL1 number of expected hands depends upon number of pair cards and non-pair cards present and splits allowed
4. "rebate" = (number of expected hands - 1) * (prob dealer BJ)
   adjust SPL1, SPL2, SPL3 by relevant "rebate"

This is same way I compute for 1 known dealer card (up card)

k_c

[Cacarulo]

What I do is the following:

one split allowed

1. OverallEVx = value of drawing to first pair card
   For 9-9 (loss to dealer BJ) 6 decks, SPL1, NDAS, OverallEVx = -0.039403112634580864
2. If lose all to dealer BJ
   overallSplitEV = 2 * OverallEVx = -0.078806225269161728
3. If OBO, one split hand is not at risk so "rebate" is given if dealer has BJ
   prob dealer BJ = 0.048105230191042903
   overallSplitEV = -0.078806225269161728 + 0.048105230191042903
   overallSplitEV = -0.030700995078118825

multiple splits

1. compute values for overallEVx[numsplits] and overallEVPair[numSplits]
2. from above compute SPL1, SPL2, SPL3 for lose all to dealer BJ
3. for OBO compute number of expected hands
   for SPL1 number of expected hands = 2
   for > SPL1 number of expected hands depends upon number of pair cards and non-pair cards present and splits allowed
4. "rebate" = (number of expected hands - 1) * (prob dealer BJ)
   adjust SPL1, SPL2, SPL3 by relevant "rebate"

This is same way I compute for 1 known dealer card (up card)

k_c

Thanks k_c for your feedback! What I want to do, without having to reprogram my CA's code, is to be able to use the data obtained
in the traditional way to calculate the case where the dealer doesn't show any cards, or has both cards face down.
Somehow, I managed to calculate the cases of standing, hitting, and doubling, but not splitting.
I also don't want to drive myself crazy. Something that should be simple is getting too complicated.

I understand what you're doing, but for example, one of your numbers, -0.039403112634580864, I haven't been able to reproduce it.


Specifically, how can I arrive at this number (-0.030700995078118825) based on my EVs from the table where I have calculated 99vA, 99vT, 99v9, ..., 99v2?

Notice that I have been able to arrive at the EVs for standing, hitting, and doubling from that table.

Thanks in advance.

Sincerely,
Cac

[k_c]

Thanks k_c for your feedback! What I want to do, without having to reprogram my CA's code, is to be able to use the data obtained
in the traditional way to calculate the case where the dealer doesn't show any cards, or has both cards face down.
Somehow, I managed to calculate the cases of standing, hitting, and doubling, but not splitting.
I also don't want to drive myself crazy. Something that should be simple is getting too complicated.

I understand what you're doing, but for example, one of your numbers, -0.039403112634580864, I haven't been able to reproduce it.


Specifically, how can I arrive at this number (-0.030700995078118825) based on my EVs from the table where I have calculated 99vA, 99vT, 99v9, ..., 99v2?

Notice that I have been able to arrive at the EVs for standing, hitting, and doubling from that table.

Thanks in advance.

Sincerely,
Cac

The values in your table are given up card is known. For a hand of 9-9 standing is the same whether 1 or 0 dealer cards are known. Also hitting and doubling are the same because you would never hit or double 9-9 regardless of 1 or 0 cards known. However, there's a difference between 1 or 0 dealer cards known for splitting. Knowing 1 card is more optimal than knowing 0 cards. I don't think you can get the less optimal values by starting with the more optimal.

k_c

[Cacarulo]

The values in your table are given up card is known. For a hand of 9-9 standing is the same whether 1 or 0 dealer cards are known. Also hitting and doubling are the same because you would never hit or double 9-9 regardless of 1 or 0 cards known. However, there's a difference between 1 or 0 dealer cards known for splitting. Knowing 1 card is more optimal than knowing 0 cards. I don't think you can get the less optimal values by starting with the more optimal.

k_c

I understand, that means I didn't choose the best example (9-9). So the next question is: are there other player hands where standing, hitting, or doubling are different for both dealer card scenarios?
Thanks.

Sincerely,
Cac

[k_c]

I understand, that means I didn't choose the best example (9-9). So the next question is: are there other player hands where standing, hitting, or doubling are different for both dealer card scenarios?
Thanks.

Sincerely,
Cac

I'm sure there are. For 0 dealer cards known you are starting with the premise that nothing is known. For 1 card known premise is up card is known. For a given player hand potential is always there that strategies may be different.

k_c

[Cacarulo]

I don't think you can get the less optimal values by starting with the more optimal.

It is very likely, so I conclude that it will not be possible to do it as I thought. Anyway, the topic remains very interesting.

Sincerely,
Cac

[JohnGalt007]

I suppose I could get eors for 0 dealer cards if I wanted. Not that interested though.

k_c

I ran a few sims with the aforementioned basic strategy, assuming flat betting and using 400 million rounds per sim, to approximate the effects of removal for each rank in both the 1-deck and 6-deck games. Here were my results:

EOR of Ace (1 deck): -0.639%
EOR of 2 (1 deck): +0.248%
EOR of 3 (1 deck): +0.363%
EOR of 4 (1 deck): +0.503%
EOR of 5 (1 deck): +0.666%
EOR of 6 (1 deck): +0.293%
EOR of 7 (1 deck): -0.078%
EOR of 8 (1 deck): -0.195%
EOR of 9 (1 deck): -0.181%
EOR of 10 (1 deck): -0.411%

EOR of Ace (6 decks): -0.082%
EOR of 2 (6 decks): +0.058%
EOR of 3 (6 decks): +0.084%
EOR of 4 (6 decks): +0.106%
EOR of 5 (6 decks): +0.131%
EOR of 6 (6 decks): +0.069%
EOR of 7 (6 decks): -0.002%
EOR of 8 (6 decks): -0.027%
EOR of 9 (6 decks): -0.020%
EOR of 10 (6 decks): -0.051%

I also obtained figures comparable to yours for the overall EV for the 1-deck and 6-deck games via sims: -2.115% and -2.396% respectively.