Optimal Counter Strategy & Counter-Strategy for Blackjack Without Upcards

[JohnGalt007]

I was wondering whether and to what extent an upcard-less blackjack variant would be analyzable and/or exploitable. Insurance is not available in this case, so any player naturals would have to be paid out immediately after inspection of the dealer's two downcards to see if the player wins or pushes. Furthermore, the player's decisions would be based solely on the value of his own hand rather than the probable strength of his hand relative to that of the dealer's. He would inevitably be hitting, standing, doubling down, and splitting in sub-optimal EV situations due to lack of information of one of the dealer's cards, so that his overall edge would be lower. Thus, if such a game was offered and the EV with basic strategy turned out to be much lower than that of ordinary blackjack, the house may consider offering slightly +EV rules to compensate and make the game more attractive to the ploppies (e.g. early surrender). I also suspect that combinatorial analysis of basic strategy would be substantially easier, since one wouldn't have to condition on nearly as many sub-cases and specific situations with a given hand (e.g. hard 12 vs. 3, hard 12 vs 4., etc.) because one doesn't have knowledge of that upcard. Thoughts?

[k_c]

I was wondering whether and to what extent an upcard-less blackjack variant would be analyzable and/or exploitable. Insurance is not available in this case, so any player naturals would have to be paid out immediately after inspection of the dealer's two downcards to see if the player wins or pushes. Furthermore, the player's decisions would be based solely on the value of his own hand rather than the probable strength of his hand relative to that of the dealer's. He would inevitably be hitting, standing, doubling down, and splitting in sub-optimal EV situations due to lack of information of one of the dealer's cards, so that his overall edge would be lower. Thus, if such a game was offered and the EV with basic strategy turned out to be much lower than that of ordinary blackjack, the house may consider offering slightly +EV rules to compensate and make the game more attractive to the ploppies (e.g. early surrender). I also suspect that combinatorial analysis of basic strategy would be substantially easier, since one wouldn't have to condition on nearly as many sub-cases and specific situations with a given hand (e.g. hard 12 vs. 3, hard 12 vs 4., etc.) because one doesn't have knowledge of that upcard. Thoughts?

My CA computes for case where only player hand is known, just doesn't output

Strategy no dealer cards known (S17, SPL1, SPLA1, NDAS, 1 card to split aces, double any 2 cards):

Nothing surrendered
Split A-A, 7-7, 8-8
Double Hard 10,11
Stand >= Soft 18, hit < 18
Stand >= Hard 15, hit < 15

Overall EV
1 deck -2.13%
6 decks -2.48%

k_c

[JohnGalt007]

My CA computes for case where only player hand is known, just doesn't output

Strategy no dealer cards known (S17, SPL1, SPLA1, NDAS, 1 card to split aces, double any 2 cards):

Nothing surrendered
Split A-A, 7-7, 8-8
Double Hard 10,11
Stand >= Soft 18, hit < 18
Stand >= Hard 15, hit < 15

Overall EV
1 deck -2.13%
6 decks -2.48%

k_c

Thanks for checking! Not at all surprised by the strategy recommendations. My CA doesn't compute for an unknown dealer card, but the law of total expectation should handle it in a pinch; e.g., E(stand on 17) = E(stand on 17|dealer's 1st card is A) + E(stand on 17|dealer's 1st card is 2) + ... + E(stand on 17|dealer's 1st card is T). Which CA are you using that allows you to turn off the dealer upcard setting?

[k_c]

Thanks for checking! Not at all surprised by the strategy recommendations. My CA doesn't compute for an unknown dealer card, but the law of total expectation should handle it in a pinch; e.g., E(stand on 17) = E(stand on 17|dealer's 1st card is A) + E(stand on 17|dealer's 1st card is 2) + ... + E(stand on 17|dealer's 1st card is T). Which CA are you using that allows you to turn off the dealer upcard setting?

It's my own CA.

It maintains a list of possible player hand compositions, 1 entry per hand comp. Hand comp parameters include EVs and strategies for each hand comp versus each up card as well as overall EVs and strategies for each comp.

The console version outputs overall EVs versus 1 or 0 up cards if computation of overall EV is the selected option. It doesn't output any of the individual component EVs/strategies for 0 up cards, only for 1 up card. The gui version computes values for 0 up cards but doesn't output them at all, only for 1 up card.

k_c

[JohnGalt007]

It's my own CA.

It maintains a list of possible player hand compositions, 1 entry per hand comp. Hand comp parameters include EVs and strategies for each hand comp versus each up card as well as overall EVs and strategies for each comp.

The console version outputs overall EVs versus 1 or 0 up cards if computation of overall EV is the selected option. It doesn't output any of the individual component EVs/strategies for 0 up cards, only for 1 up card. The gui version computes values for 0 up cards but doesn't output them at all, only for 1 up card.

k_c

Interesting! Did you program it yourself? In what language?

I also have to wonder how the EOR for each rank is affected without knowledge of the dealer upcard. I suspect it's slightly lessened, given that the lack of upcard information results in a sample space that's not narrowed down quite as much as it would be with that information.

[k_c]

Interesting! Did you program it yourself? In what language?

I also have to wonder how the EOR for each rank is affected without knowledge of the dealer upcard. I suspect it's slightly lessened, given that the lack of upcard information results in a sample space that's not narrowed down quite as much as it would be with that information.

Language is c++. I took some programming courses a while back and applied what I learned to developing a blackjack combinatorial analyzer and it kind of evolved.
My website program is basically the same program with output channeled to a web page rather than somewhere else.

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

k_c

[DSchles]

Now, for the 6-deck game, make the blackjack payout 2:1, and we have ourselves a game!

Don

[k_c]

Now, for the 6-deck game, make the blackjack payout 2:1, and we have ourselves a game!

Don

Thought of that a long time ago. Could tweak rules to offer a reasonable game and eliminate problem with hole card flashing for casinos.

Having no in with casino game offerings, I just kept it to myself.

k_c

[DSchles]

Thought of that a long time ago. Could tweak rules to offer a reasonable game and eliminate problem with hole card flashing for casinos.

Having no in with casino game offerings, I just kept it to myself.

k_c

Well, realize that, for hole card flashing, you just need to eliminate that card, not the upcard as well.

Don

[k_c]

Well, realize that, for hole card flashing, you just need to eliminate that card, not the upcard as well.

Don

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

k_c

[Super Natural]

It's my own CA.

It maintains a list of possible player hand compositions, 1 entry per hand comp.

k_c

hi kc thanks for the site it's been a great resource ..

I am trying to write a CA and can match all of your ev numbers for single deck but am stuck on speed. (and haven't tackled splitting yet, welp)

I stored all possible player hands like you mentioned. But to calc the hit ev I first need the stand ev of every one of these hands .. think my dealer prob calc takes 7ms .. this adds up. My approach must be flawed?

I read in the MGP CA help file his is done without brute force. I can't understand how your guys CA are so fast with any number of decks ..

[iCountNTrack]

hi kc thanks for the site it's been a great resource ..

I am trying to write a CA and can match all of your ev numbers for single deck but am stuck on speed. (and haven't tackled splitting yet, welp)

I stored all possible player hands like you mentioned. But to calc the hit ev I first need the stand ev of every one of these hands .. think my dealer prob calc takes 7ms .. this adds up. My approach must be flawed?

I read in the MGP CA help file his is done without brute force. I can't understand how your guys CA are so fast with any number of decks ..

Couple of thoughts. If you are looking for speed, you need to avoid scripting languages or interpreted languages and pick a language that's compiled to binary C++ or FORTRAN. You also need to use hand compositions( combinations) and figure out the multiplier and not permutations. You could also parallelize any big external loops. Also avoid recursion.

But the tough nut to crack are Splits it will heavily depend on the methodology you take. In my case, I use post-split optimal strategy which is really slow!

[Super Natural]

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/

You also need to use hand compositions( combinations) and figure out the multiplier and not permutations.

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.