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

[aceside]

0.5 % is a rule of thumb for Hi-Lo. It's not uniform. Let's take 6D,S17 with 22 indices as an example:

Hi-Lo

  10      0.000476488880      0.061209382263
   9      0.000962523080      0.054479161165
   8      0.001894033079      0.047515923006
   7      0.003549913439      0.040629630113
   6      0.006461209698      0.033793818826
   5      0.011887739096      0.027073550933
   4      0.021078035653      0.020736322732
   3      0.036924567448      0.014957618139
   2      0.065058029179      0.009545233196
   1      0.118179208902      0.004229703977
   0      0.267033329275     -0.001757881127
  -1      0.188816929980     -0.006267781336
  -2      0.123654982060     -0.010779987732
  -3      0.067056553499     -0.015782591178
  -4      0.038778760688     -0.020796967604
  -5      0.021111953793     -0.026068963357
  -6      0.012343745076     -0.031574742307
  -7      0.006673581358     -0.037552766121
  -8      0.003759524559     -0.043790938820
  -9      0.001920320239     -0.050448226281
 -10      0.001009002920     -0.057649010570

RPC

  10      0.006372829899      0.027301855334
   9      0.008569372839      0.024063123854
   8      0.011653612678      0.020926467757
   7      0.015385171578      0.017679132702
   6      0.020620626037      0.014609527830
   5      0.027652105676      0.011741223029
   4      0.037335565274      0.008935352324
   3      0.049935327772      0.006160542519
   2      0.067904886609      0.003336525709
   1      0.094138976165      0.000473857076
   0      0.162769829314     -0.002723333936
  -1      0.109741408322     -0.005086927518
  -2      0.098787306224     -0.007418290243
  -3      0.070139308069     -0.009979178426
  -4      0.052547268312     -0.012487106009
  -5      0.037899048414     -0.015071285529
  -6      0.028790138055     -0.017582050108
  -7      0.021189757057     -0.020216572978
  -8      0.016134736997     -0.022816386161
  -9      0.011748251658     -0.025605774264
 -10      0.008891312039     -0.028480907976

Calculate the difference between one TC and the next, multiply it by 100 and see what result you get.

Sincerely,
Cac

Can you use the truncation function to find the TC numbers (1st column), find the TC frequencies (2nd column), and then calculate these EV numbers (3rd column)? I just do not see any math justification for using the floor function here.

[Cacarulo]

Sorry i have a bad habit of not indicating the count used when i think of Hi-Lo
As far as the floored TC count, please note that this study was done at the 1/4 deck removed from the deck. So the TV divisor would be 0.75. And the missing TC counts are a result of flooring. For example a TC of -5 will never be possible.

No problem, I assumed it was Hi-Lo. However, I keep thinking there's something about those "gaps" that's not right.
Removing the first 13 cards randomly doesn't change the situation either.
What am I missing?

Sincerely,
Cac

[Gramazeka]

Give me a raise in EBJ, chart.

[Cacarulo]

Can you use the truncation function to find the TC numbers (1st column), find the TC frequencies (2nd column), and then calculate these EV numbers (3rd column)? I just do not see any math justification for using the floor function here.

Again I see that you propose another topic different from the one that is being discussed.
What you can do to get rid of the doubt is to run a simulation with CVDATA, in which you have to calculate truncated indices, and then see what happens with the frequencies and expected values at each TC.

Sincerely,
Cac

[Gramazeka]

Again I see that you propose another topic different from the one that is being discussed.
What you can do to get rid of the doubt is to run a simulation with CVDATA, in which you have to calculate truncated indices, and then see what happens with the frequencies and expected values at each TC.

Sincerely,
Cac

Do not pay attention. This is 99% trolling. This is a hired person to destroy the site.

[iCountNTrack]

No problem, I assumed it was Hi-Lo. However, I keep thinking there's something about those "gaps" that's not right.
Removing the first 13 cards randomly doesn't change the situation either.
What am I missing?

Sincerely,
Cac

All my CA calculations are done at the 39 cards remaining in the deck. If you remove 13 cards from a deck you will get unique possible 286,550 remaining 39-card Blackjack slugs (irrespective of suit and rank from 10 to K). For each of these 39-card slugs a CA computation is done to compute the pre-deal EV.

To calculate the True Count for these slugs, you will take the Running Count of the slug and divide it by the number of remaining decks which is 0.75 deck because we are at the 13-card removed mark. Certain true counts are not possible because of this divisor. a TC of -5 is not possible because with an RC of -3 the TC will be -4, with an RC of -4 the TC will be -5.333 which floors to -6, RC of -5 the TC will be -6.3333 which floors to -7.

Again the key is that the analysis is done for a single deck at exactly 13 cards removed mark.

[DSchles]

TCs of +3 and +7 aren't possible either.

Don

[Cacarulo]

Again the key is that the analysis is done for a single deck at exactly 13 cards removed mark.

AHA! this was the missing key.
What I am doing is, once I have reached the desired penetration (39 cards remaining or 13 cards removed), I play until there are 20 cards remaining. Between the remaining 39 and 20 cards, the gaps are filled without any problem.
To get the same scenario as you, I would only have to play one round. Instead of playing until there are 20 cards left, I would be playing until there are 39 cards left. In other words, one round.

Sincerely,
Cac

[Cacarulo]

TCs of +3 and +7 aren't possible either.

Don

Yes. Anyway, I think if we're talking about an estimated value of 0.5% per TC (which is sometimes more and sometimes less),
it's something that comes from a game that starts with a deck and ends when a certain penetration is reached.

Sincerely,
Cac

[iCountNTrack]

AHA! this was the missing key.
What I am doing is, once I have reached the desired penetration (39 cards remaining or 13 cards removed), I play until there are 20 cards remaining. Between the remaining 39 and 20 cards, the gaps are filled without any problem.
To get the same scenario as you, I would only have to play one round. Instead of playing until there are 20 cards left, I would be playing until there are 39 cards left. In other words, one round.

Sincerely,
Cac

Right! So really I did no sim at all. Just randomly removed 13 cards, calculated the pre-deal EV of every possible slug and grouped them by True Count and then calculated the average EV per True Count based on a locally weighted slug frequency. This approach is sub-optimal of course because in a game of blackjack cards are not drawn out randomly because of a fixed dealer playing strategy, this could result into deck compositions with zero or different probability which can skew the results

[Cacarulo]

Give me a raise in EBJ, chart.

EBJ-2

  10      0.007050076039      0.025289557019
   9      0.009319698018      0.022345939702
   8      0.012502821997      0.019253294176
   7      0.016216637137      0.016466660609
   6      0.021423489836      0.013637142323
   5      0.028432105994      0.010966459537
   4      0.037838803712      0.008408597490
   3      0.049890951730      0.005752483967
   2      0.066880707887      0.003073161999
   1      0.091255963902      0.000352760068
   0      0.156167824989     -0.002731765522
  -1      0.105588843979     -0.004978378492
  -2      0.096498664521     -0.007203926534
  -3      0.069467927806     -0.009737673790
  -4      0.052726855489     -0.012140132650
  -5      0.038557602552     -0.014596373805
  -6      0.029654868034     -0.017042257929
  -7      0.022131062216     -0.019475985640
  -8      0.017076319777     -0.022075362540
  -9      0.012621103577     -0.024702053036
 -10      0.009694247798     -0.027297584656

Sincerely,
Cac

[Gramazeka]

There is no one number.

ENHC, Sur 10, DAS, Spl 3, RSA

Yes, its Stay 17 ))