For Gramazeka (HO2, AO2, BRH-0, EBJ2)

[Cacarulo]

This thread has a good summary of SCORE. And I think SCORE is the best tool to compare different counting systems.

https://www.blackjackinfo.com/commun...e-or-ce.17256/

Yes, SCORE or DI or N0, any of them.

[Cacarulo]

A) RPC
 
 play-all | rounds played = 100.00%
 spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly
 ------------------------------------------------------------------------------
 1 -  1 -0.336 11.592
 1 -  2 -0.336 11.592
 1 -  3  0.280 20.389  13.53  531735  1.37   1.88  1486.74 1.525   6.726  1.000
 1 -  4  0.556 24.020  13.53  186960  2.31   5.35  1038.58 1.692   9.628  1.000
 1 -  5  0.812 27.467  13.53  114312  2.96   8.75   928.66 1.832  10.768  1.000
 1 -  6  1.062 30.952  13.53   84985  3.43  11.77   902.32 1.966  11.083  1.000
 1 -  7  1.279 33.749  13.53   69577  3.79  14.37   890.21 2.068  11.233  1.000
 1 -  8  1.507 36.965  13.53   60164  4.08  16.62   906.69 2.186  11.029  1.000
 1 -  9  1.703 39.522  13.53   53848  4.31  18.57   917.10 2.275  10.904  1.000
 1 - 10  1.909 42.399  13.53   49318  4.50  20.28   941.59 2.377  10.620  1.000
 1 - 11  2.102 45.047  13.53   45934  4.67  21.77   965.45 2.469  10.358  1.000
 1 - 12  2.285 47.545  13.53   43291  4.81  23.10   989.23 2.555  10.109  1.000
 1 - 13  2.475 50.213  13.53   41177  4.93  24.29  1018.93 2.647   9.814  1.000
 1 - 14  2.668 53.000  13.53   39455  5.03  25.35  1052.75 2.744   9.499  1.000
 1 - 15  2.835 55.286  13.53   38022  5.13  26.30  1078.02 2.822   9.276  1.000
 1 - 16  3.007 57.684  13.53   36805  5.21  27.17  1106.64 2.903   9.036  1.000
  
B) EBJ-2
 
 play-all | rounds played = 100.00%
 spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly
 ------------------------------------------------------------------------------
 1 -  1 -0.341 11.595
 1 -  2 -0.341 11.595
 1 -  3  0.274 20.580  13.53  562502  1.33   1.78  1543.49 1.540   6.479  1.000
 1 -  4  0.550 24.224  13.53  193852  2.27   5.16  1066.56 1.706   9.376  1.000
 1 -  5  0.805 27.648  13.53  117851  2.91   8.49   949.13 1.845  10.536  1.000
 1 -  6  1.053 31.128  13.53   87449  3.38  11.44   920.51 1.980  10.864  1.000
 1 -  7  1.276 34.121  13.53   71482  3.74  13.99   912.25 2.091  10.962  1.000
 1 -  8  1.494 37.142  13.53   61783  4.02  16.19   923.19 2.201  10.832  1.000
 1 -  9  1.700 39.956  13.53   55256  4.25  18.10   939.23 2.302  10.647  1.000
 1 - 10  1.908 42.924  13.53   50604  4.45  19.76   965.59 2.408  10.356  1.000
 1 - 11  2.094 45.440  13.53   47111  4.61  21.23   986.26 2.495  10.139  1.000
 1 - 12  2.286 48.170  13.53   44391  4.75  22.53  1014.91 2.591   9.853  1.000
 1 - 13  2.484 51.034  13.53   42226  4.87  23.68  1048.68 2.692   9.536  1.000
 1 - 14  2.655 53.403  13.53   40456  4.97  24.72  1074.12 2.774   9.310  1.000
 1 - 15  2.832 55.911  13.53   38979  5.07  25.66  1103.86 2.860   9.059  1.000
 1 - 16  3.013 58.522  13.53   37731  5.15  26.50  1136.75 2.951   8.797  1.000

Sincerely,
Cac

[Cacarulo]

Here are the SCOREs for wonging.

                         
A) RPC
 
wong-in TC =   2 | rounds played = 26.27%
spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly
------------------------------------------------------------------------------
1 - 16  1.515 22.298  13.53   21671  6.79  46.15   328.25 0.764  30.465  1.000
 
B) EBJ-2
 
wong-in TC =   2 | rounds played = 27.00%
spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly
------------------------------------------------------------------------------
1 - 16  1.539 22.903  13.53   22155  6.72  45.14   340.89 0.793  29.335  1.000

Sincerely,
Cac

[Gramazeka]

When one compares one system with another, the correct thing to do is to do it through the SCORE or DI or N0, whichever you like best. When using these indicators, an optimal betting scheme is used in such a way that the ROR reached is 13.53% and the SCORE is maximized (or N0 minimized). In this process, the bets must be exact. One can choose integer bets but in that case the ROR would no longer be 13.53% and the comparison would not be fair. Perhaps in "system A" when using integer bets the ROR obtained is 12.57% and in "system B" it is 14.85%. This is not comparable.

Sincerely,
Cac

Now I understand where are the apples and where are the oranges)) Even though EBJ wins more units per 100 hands, RPC has a lower ROR, and according to the Score formula has more attractiveness, and so on...

p.s. What computer are you currently working on? What processor does it have, what monitor?

[Cacarulo]

p.s. What computer are you currently working on? What processor does it have, what monitor?

I usually have access to many computers, most running Linux, some virtual machines (VMWARE) and some desktops. The desktop ones are not very pretentious: AMD Ryzen 3, 8Gb of RAM. Others are Intel I7, 16Gb of RAM.

Sincerely,
Cac

[Gramazeka]

Halves..1.072%..0.003%..33.58..1.23%.....3.66
EBJ II....1.050%..0.003%..31.70..1.30%.....3.50
RPC.....1.057%..0.003%..31.91..1.06%.....3.37
Hilo.......1.024%..0.003%..30.15..1.31%.....3.34

In order not to be bored on the forum, I will ask one more question - due to what does the RPC system achieve such a small ROR 1.06 ?

[Cacarulo]

In order not to be bored on the forum, I will ask one more question - due to what does the RPC system achieve such a small ROR 1.06 ?

You are probably using a unit value less than half the optimal unit value. If it were just half, the ROR would be 1.83%.
Using half the unit also cuts the c-SCORE in half.

Hope this helps.

Sincerely,
Cac

[Gramazeka]

Ok, please your comments-

"EVs as a function of the TCs

System....TC1....TC2....TC3....TC4....SDH....Var

Halves....0.291..0.810..1.316..1.859..1.143..1.31
EBJII......0.317..0.815..1.324..1.891..1.148..1.32
RPC.......0.354..0.867..1.434..2.071..1.146..1.31
Highlow..0.317..0.832..1.339..1.925..1.145..1.31
Std.err....0.005..0.006..0.008..0.011

Theoretical Kelly bets for a 20000$ bankroll

Halves....44.43$....123.66$....200.92$....283.82$
EBJII......48.03$....123.48$....200.61$....286.53$
RPC.......54.05$....132.37$....218.93$....316.18$
Highlow..48.40$....127.02$....204.43$....293.89$

Practical Kelly bets for our 'green' player

Halves....50$....125$....200$....300$
EBJII.......50$....125$....200$....300$
RPC.......50$....125$....225$....325$
Highlow..50$....125$....200$....300$

Frequencies of the different TCs

System--TC1----TC2----TC3-----TC4----TC5 >--Total

Halves..11.64..6.70...3.86....2.67...2.95...27.82
EBJII....11.67..6.62...3.76....2.18...2.75...26.98
RPC.....11.78..6.50...3.59....2.02...2.37...26.26
Highlow11.81..6.50...3.69....2.10...2.57...26.67

That's all folks!

Epilog: It seems to me, that for PRACTICAL purposes, what we have here are seasoned apples.

When dealing with 6dks and 'monster' 8dks, every-
body is able to dream, being myself a halves player, I also have mine. I'm dreaming to buy me a winter house in southern California, but I don't know why, I've the terrible suspicion that I'm deceiving myself.

Regards
Z"

"In the card counting section of Richard's new e-book, I looked at the following table:

System.....c-Score

Halves.......32.33
EBJ II.........31.39
RPC..........30.89
Highlow.....29.76

The players as stated there, are spreading their bets (1-10) vs. 6dks, USA rules, S17, DAS and LS, but using only generic BS to play their hands.

Watching EBJ II scoring higher than RPC was admitedly a little surprise to me, but after looking at their respective betting correlations,
it soon vanished. Well I thought, you've to count
four 9s more for every pack, that's a little more
effort, up to everyone, of course.

Vegas Strip rules

EBJ II.........BC = .989
RPC..........BC = .986

I wanted to check the above numbers under more
'realistic'circumstances, that's four card counters using a full IL 18 table of indexes to
vary the play of their hands and the somehow more agressive betting spread (1-16).

Here are the conditions for the sims:

1)5000 million hands for every count.
2)6dks., USA HC, S17, DAS and SP3
3)Penetration was set to 234 cards (4.5/6)
4)Total bankroll = 150 times max. bet
5)IL 18 appropriate indexes for each one.
6)Betting ramp as follows:

TC<2=0
TC-2=1
TC-1=1
TC 0=1
TC 1=4
TC 2=8
TC 3=12
TC4 or >=16

Under the above conditions I've got these:

System..Win rate..SE....Score...ROR....Uns.won/100

Halves..1.072%..0.003%..33.58..1.23%.....3.66
EBJ II....1.050%..0.003%..31.70..1.30%.....3.50
RPC.....1.057%..0.003%..31.91..1.06%.....3.37
Hilo.......1.024%..0.003%..30.15..1.31%.....3.34

I would like to hear your comments, suggestions
and opinions as well, after all, that's the main
reason we're all around here, to learn a little
more every day in this BJ "shelter" called
BJ math.

Regards
Z"

Here is the original research by Zenfighter.

[Gramazeka]

System..Win rate..SE....Score...ROR....Uns.won/100

Halves..1.072%..0.003%..33.58..1.23%.....3.66
EBJ II....1.050%..0.003%..31.70..1.30%.....3.50
RPC.....1.057%..0.003%..31.91..1.06%.....3.37
Hilo.......1.024%..0.003%..30.15..1.31%.....3.34

I'm surprised by the difference in ROR between systems. What will be your version of ROR systems? Due to what two-level RPC system gives a much smaller ROR than EBJ 2? I understand that I need to look at Griffin's book, but can you explain to me?

[Cacarulo]

I'm surprised by the difference in ROR between systems. What will be your version of ROR systems? Due to what two-level RPC system gives a much smaller ROR than EBJ 2? I understand that I need to look at Griffin's book, but can you explain to me?

In post #54 I already showed you what the true c-SCORE was. What happens with your calculations is that they are not optimal and that is why you have a difference in RORs.
If for example, for a bankroll of $10,000, instead of an ROR of 13.53% you would like an ROR of 1.83%, you can simply divide your unit by two. The c-SCORE will also be divided by two.
Now, if you want to keep the ROR at 1.83% but with the previous c-SCORE, you will have to double your bankroll and return the unit to the previous value. That's all the magic.

RPC example (from post #54):

1 - 16 3.007 57.684 13.53 36805 5.21 27.17 1106.64 2.903 9.036 1.000

The unit is 9.036, the c-SCORE is 27.17, and the ROR is 13.53% for a $10,000 bankroll.
If you keep your bankroll at $10,000 and use half of your unit (4.518) with the same betting scheme, the ROR will be 1.83% but your c-SCORE will be 13.585.
To continue to maintain the c-SCORE at 27.17, with an ROR of 1.83% you will need to bring your bankroll to $20,000 and your unit back to 9,036.

Hope this helps.

Sincerely,
Cac

[Gramazeka]

To rephrase my question - due to what construction of tags does the RPC system generate a smaller ROR ? Because of the nine ( 9 ) that Halves and EBJ 2 use?

[Cacarulo]

To rephrase my question - due to what construction of tags does the RPC system generate a smaller ROR ? Because of the nine ( 9 ) that Halves and EBJ 2 use?

The problem with that question is that I don't see a relationship between the ROR and the tags. However, the tags can affect the SCORE, damaging important plays such as insurance.
The difference you see is because your betting scheme is not optimal.

Sincerely,
Cac

[Norm]

Really cannot boil down blackjack to a couple handfuls of numbers (EORs) and any particular stat. Everything affects everything and everything must be as close to apples and apples as you can get. SCORE, which assumes optimal betting, solves much of this. But, we still have the problem that different systems have different sweet spots in penetration, and differing kinship with different rules. That's why I once tried running lots of rule combinations with a bunch of strategies over all reasonable penetrations combining them for an overall SCORE. But, even that doesn't get you all the way.