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
Luck is what happens when preparation meets opportunity.
Don't agree with your results.
9-9 s17, NDAS, SPL1
9-9 s17, DAS, SPL3Code:stand -0.0049307389531300094 hit -0.63799907995510718 double -1.2278929297191714 split -0.030700995078118826
Overall EVCode:stand -0.0049307389531300094 hit -0.63799907995510718 double -1.2278929297191714 split 1 -0.0054744808778548204 split 2 -0.0057449226985539989 split 3 -0.0058208716922732578
s17, NDAS, SPL1: -2.47821%
s17, DAS, SPL3: -2.40076
k_c
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
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
To reach the line where the player has a 9-9, I use the following table as a starting point.Code: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
Why, if all the expected values are correct, am I not getting the correct result ONLYCode: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
in the splitting column?
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
What I do is the following:
one split allowed
multiple splitsCode: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
This is same way I compute for 1 known dealer card (up card)Code: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"
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
Luck is what happens when preparation meets opportunity.
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
Luck is what happens when preparation meets opportunity.
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.
Last edited by JohnGalt007; 03-03-2024 at 03:51 PM.
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