Hi John,Originally Posted by JohnGalt007
There's an important point about EORs: they must sum to zero.
If you calculated them through simulations (CVData), you have to set the number of rounds to a specific value.
In 6D, for example, 40 rounds per shoe or fewer. In 1D, 3 rounds or fewer. This is very important to avoid the CCE (Cut Card Effect).
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
I found I could get EORs for the case of 0 known dealer cards from the console version of my program without any additional programming by inputting removal of 1 of each rank followed by computing the overall EV for each input.
S17, SPL1, SPLA1, NDAS, 1 card to split aces, double any 2 cards, no dealer cards known
1 deck full shoe EV: -2.12742%
6 decks full shoe EV: -2.47821%Code:Rem Overall EV EOR A -2.76959% -0.64217% 2 -1.80373% 0.32369% 3 -1.67418% 0.45324% 4 -1.50989% 0.61753% 5 -1.30989% 0.81753% 6 -1.70053% 0.42689% 7 -1.88761% 0.23981% 8 -2.23505% -0.10763% 9 -2.28742% -0.16000% T -2.53659% -0.40917%
k_cCode:Rem Overall EV EOR A -2.58454% -0.10633% 2 -2.42162% 0.05659% 3 -2.40166% 0.07655% 4 -2.37697% 0.10124% 5 -2.34727% 0.13094% 6 -2.42395% 0.05426% 7 -2.47876% -0.00055% 8 -2.50512% -0.02691% 9 -2.50451% -0.02630% T -2.54286% -0.06465%
I just finished re-calculating my own EORs from the sims, setting 2 rounds per shoe for 1-deck games and 30 rounds per shoe for 6-deck games. All of my EORs sum to zero, and I obtained similar numbers to yours, so I'm confident in both of our findings.
Overall EV of 1 deck: -2.113%
EOR of Ace (1 deck): -0.669%
EOR of 2 (1 deck): +0.331%
EOR of 3 (1 deck): +0.437%
EOR of 4 (1 deck): +0.598%
EOR of 5 (1 deck): +0.775%
EOR of 6 (1 deck): +0.372%
EOR of 7 (1 deck): -0.008%
EOR of 8 (1 deck): -0.151%
EOR of 9 (1 deck): -0.137%
EOR of 10 (1 deck): -0.387%
Overall EV of 6 decks: -2.403%
EOR of Ace (6 decks): -0.097%
EOR of 2 (6 decks): +0.051%
EOR of 3 (6 decks): +0.077%
EOR of 4 (6 decks): +0.100%
EOR of 5 (6 decks): +0.135%
EOR of 6 (6 decks): +0.056%
EOR of 7 (6 decks): -0.003%
EOR of 8 (6 decks): -0.025%
EOR of 9 (6 decks): -0.032%
EOR of 10 (6 decks): -0.067%
Hi k_c,
These EoRs are not adding up to zero and I think I know why. Clearly, you are using an 'optimal strategy' for each of the
removed cards and even for the mean. For the calculation of EoRs, it is necessary to use a 'fixed strategy' that can be
either CD or TD and apply that strategy to each of the calculated EoRs including the mean. In that way, they will add up to zero.
Therefore, if we apply the same strategy you calculated previously to each of the removals including the mean,
the following EoRs can be derived:
As you can see, the sum is zero. It is important to note that a simulator (such as CVDATA, for example) should obtain the same results.Code:1) 6D,S17,DOA,NDAS,SPA1,SPL1,NS EoR [A] = -0.1064591156 EoR [2] = 0.0565686956 EoR [3] = 0.0764859973 EoR [4] = 0.1010893701 EoR [5] = 0.1306842940 EoR [6] = 0.0539411353 EoR [7] = -0.0011815396 EoR [8] = -0.0268070877 EoR [9] = -0.0261811532 EoR [T] = -0.0645351491 Mean = -2.4783263122 SS = 0.0686553706 CHS = 0.0000000000 2) 1D,S17,DOA,NDAS,SPA1,SPL1,NS EoR [A] = -0.6657028874 EoR [2] = 0.3252436383 EoR [3] = 0.4442687610 EoR [4] = 0.5904081218 EoR [5] = 0.7709422304 EoR [6] = 0.3594745906 EoR [7] = -0.0034053944 EoR [8] = -0.1327485370 EoR [9] = -0.1432482903 EoR [T] = -0.3863080582 Mean = -2.1777174105 SS = 2.4535636517 CHS = 0.0000000000
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
I was just about to post that EORs sum to 0 as long as they are relative to a fixed strategy when I saw your post. I have to admit I learned that at some point but had forgotten and have just remembered. You are right that the EORs I posted were for compute mode of 'optimal'. If I change program compute mode to 'basic strategy' EORs should sum to 0.
k_c
Hi,
These EoRs are based on composition dependent basic strategy. The do sum to zero.
S17, SPL1, SPLA1, NDAS, 1 card to split aces, double any 2 cards, no dealer cards known
1 deck full shoe EV: -2.12895%
6 decks full shoe EV: -2.47833%Code:Rem Overall EV EOR A -2.78115% -0.65220% 2 -1.80550% 0.32345% 3 -1.67910% 0.44985% 4 -1.52358% 0.60537% 5 -1.33868% 0.79027% 6 -1.74142% 0.38753% 7 -2.08511% 0.04384% 8 -2.27057% -0.14162% 9 -2.28984% -0.16089% T -2.54035% -0.41140%
k_cCode:Rem Overall EV EOR A -2.58479% -0.10646% 2 -2.42176% 0.05657% 3 -2.40184% 0.07649% 4 -2.37724% 0.10109% 5 -2.34764% 0.13069% 6 -2.42439% 0.05394% 7 -2.47951% -0.00118% 8 -2.50513% -0.02680% 9 -2.50451% -0.02618% T -2.54286% -0.06453%
Interesting. I see that we coincide on the EoRs of 6 decks but not on those of single deck. That means that for single deck there are some CD plays that don't follow the general strategy.
I'm using the same strategy in both cases. What would those different CD plays be? Thanks.
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
I made a file of CD basic strategy for single deck, no dealer cards known, same rules as in this thread. File is too big to upload so I uploaded to my website. Order of ranks in file is T,9,8,7,6,5,4,3,2,A.
www.bjstrat.net/Downloads/playerHands.zip
k_c
Last edited by k_c; 03-04-2024 at 06:08 PM.
Thanks for the file, although generally when we talk about CD, we usually limit it to the player's first 2 cards and then TD for the rest.
It should be something we can remember when playing. It doesn't mean it's wrong, and it's surely more accurate.
I used TD for both cases. TD is what is used in a simulator, although sometimes we can add some 2-card CD plays to it.
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
I think there are several hands of hard 14 where CD basic strategy is stand rather than hit for single deck.
I added hand total of each entry and flagged each instance of hard 14 with a strategy of stand with an asterisk.
www.bjstrat.net/Downloads/playerHands.zip
k_c
Okay, what I don't see is any change of strategy in the first two cards of the player, unless I'm missing something.
So in this case, there wouldn't be any difference between 2-card CD and TD.
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
What I would say is that there may not be a change in the strategy of the first 2 cards. However, EV is affected. Order makes a difference.
Hand 443: 9-2-A-A-A
9 first: hand will not occur
2 first: hand will occur only if 9 is not second
A first: hand will occur only if 2 is second
k_c
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