Well ? Will I have to ask my friend Snyder? ))Originally Posted by Gramazeka
I don't think I fully understand the "perfect EORs", but I don't think I explained myself well. The concepts of Playing Efficiency and Betting Correlation as defined in Theory of Blackjack are dated and we currently have better ways to calculate them.
We know that the best theoretical (theoretical because you can't use a computer at BJ table) gain from card counting that could be achieved is using Combinatorial analysis, where a) pre-deal advantage is calculated based on the shoe composition b) the playing decision is recomputed at every step for the player based on the dealer up card, the player's hand composition and the shoe composition.
In order to quantify that advantage for a number of decks, a set of the rules and a given penetration. In order to compute playing efficiency, we can run 2 sims one using Combinatorial Analysis to recompute the playing strategy every time the player needs to make a decision, and one using indices for a given counting system. For betting strategy, we will use flat betting for both sims, because this way we can compute the gain from using Combinatorial Analysis solely to "different and better" playing decisions compared to the ones dictated by index play. Comparing the SCOREs of those two sims we will be able to compute the Playing Efficiency of the counting system which is by definition how well a system can handle changes in playing decisions.
Calculating betting correlation is bit trickier and cannot be calculated using the same method because we cant compute the pre-deal EV using one method and then use a different playing strategy. For example, we cant use Combinatorial analysis to compute the pre-deal EV and then play using Hi-Low indices. I will need to think a little bit more about computing betting correlation, but one method would be to calculate the pre-deal EV and compare it to expected EV using True Count units for that system for a given penetration.
As far as the sims, you are right they are really slow, your best bet is to use heavy parallel computing, in the sim for 1 million shoes (not nearly enough shoes of course to get a good quantitative number), i ran on 256 cores for about 8 days! I would like to port the code to CUDA to run it on GPU, but really dont have a lot of time for BJ and would like to spend the free time to do something with higher return
Chance favors the prepared mind
You explained yourself perfectly and the method you are proposing is the correct way to do it. But the problem with that method is that it is unfeasible. A million shoes is too little to get a meaningful sample and that only took you 8 days using 256 cores!I don't think I fully understand the "perfect EORs"
We know that the best theoretical (theoretical because you can't use a computer at BJ table) gain from card counting that could be achieved is using Combinatorial analysis, where a) pre-deal advantage is calculated based on the shoe composition b) the playing decision is recomputed at every step for the player based on the dealer up card, the player's hand composition and the shoe composition.
In order to quantify that advantage for a number of decks, a set of the rules and a given penetration. In order to compute playing efficiency, we can run 2 sims one using Combinatorial Analysis to recompute the playing strategy every time the player needs to make a decision, and one using indices for a given counting system. For betting strategy, we will use flat betting for both sims, because this way we can compute the gain from using Combinatorial Analysis solely to "different and better" playing decisions compared to the ones dictated by index play. Comparing the SCOREs of those two sims we will be able to compute the Playing Efficiency of the counting system which is by definition how well a system can handle changes in playing decisions.
Calculating betting correlation is bit trickier and cannot be calculated using the same method because we cant compute the pre-deal EV using one method and then use a different playing strategy. For example, we cant use Combinatorial analysis to compute the pre-deal EV and then play using Hi-Low indices. I will need to think a little bit more about computing betting correlation, but one method would be to calculate the pre-deal EV and compare it to expected EV using True Count units for that system for a given penetration.
As far as the sims, you are right they are really slow, your best bet is to use heavy parallel computing, in the sim for 1 million shoes (not nearly enough shoes of course to get a good quantitative number), i ran on 256 cores for about 8 days! I would like to port the code to CUDA to run it on GPU, but really dont have a lot of time for BJ and would like to spend the free time to do something with higher return
Regarding the use of EORs, one can obtain very good approximations to what would be the perfect values obtained with CA and in such a reasonable time that it could even be run on my "humble computer"
I am sure that the results obtained by the EORs method would be as satisfactory as those obtained by CA.
Sincerely,
Cac
Finally I took some time to analyze Halves with a side count of tens for insurance.
The results are quite good, although it still fails to overcome HO2/A.
Let's look at the SCORES for 6D,S17,DOA,DAS,SPA1,SPL3,NS,4.5/6 and R22:
1) Halves alone:
1-12: 23.55
1-16: 27.65
2) Halves/Ten:
1-12: 24.99
1-16: 29.14
The ten side count for insurance improves the system 5.4%.
However, HO2/A continues to lead the ranking:
3) HO2/A:
1-12: 25.53
1-16: 29.74
Sincerely,
Cac
What could be simpler than Freightman’s Rule of 9 (sometimes 8)
Using 6 deck hi lo, strike point is 33.33333% 10 value cards remaining.
By 1/2 decks
5.5 decks 286 cards 96-10 33.33%
5.0 decks 260 cards 87-10 33.46% reduced 9 cards
4.5 decks 234 cards 78-10 33.33% reduced 9 cards
4.0 decks 208 cards 70-10 33.65% reduced 8 cards
3.5 decks 182 cards 61-10 33.51% reduced 9 cards
3.0 decks 156 cards 52-10 33.33% reduced 9 cards
2.5 decks 130 cards 44-10 33.84% reduced 8 cards
2.0 decks 104 cards 35-10 33.65% reduced 9 cards
1.5 decks 78 cards 26-10 33.33% reduced 9 cards
1.0 decks 52 cards 18-10 34.61% reduced 8 cards
0.5 decks 26 cards 9-10 34.61% reduced 9 cards
Mostly a reduction of 9 (sometimes 8) 10 value cards per 1/2 deck starting from 5.5 decks. Note, no 10 value cards appear in first 1/2 deck in order for insurance to be justified at 5.5 decks.
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