Dynamic Insurance

[Cacarulo]

Hi to all,

This post is a continuation of a previous thread where I tried to explain how to take advantage of C-D indices
and where the result was not what I expected. That's why I took a little more time to analyze it.
After reviewing again the subject of what I have now baptized as "dynamic insurance" I've come to the conclusion that there was no error in the theory.
It only had to be modified a little and thanks to several simulations I realized what was happening.
It's basically a new concept on how to maintain a side count of aces but with minimal mental effort.
In the dynamic insurance method there is no need to adjust the RC for excess or deficiency of aces as in the old-fashioned method.
In fact the RC is never adjusted according to the aces that have come out.
The aces that come out are simply counted and depending on the amount that have come out, the index is adjusted according to a table.
For a better understanding I will explain it with some examples for Hi-Lo:

Single deck
Generic index: +2

Dynamic index:
2 or more aces came up: +1
3 or more aces came up: -3

Double deck
Generic index: +2

Dynamic index:
4 or more aces came up: +1
6 or more aces came up: 0/-1
7 or more aces came up: -2/-3

Six decks
Generic index: +3

Dynamic index:
12 or more aces came up: +2
17 or more aces came up: +1
19 or more aces came up: 0

Note that you do not need to know the entire table. One can cut it anywhere.
For example in DD if I saw four aces out I can now modify my index to +1 and continue with that index until the end.
This is always going to be better than continuing with the generic index.
That's all.

Enjoy!

Sincerely,
Cac

[Freightman]

I find this very interesting, especially as it pertains to the regaled FBM ASC. Essentially, insurance is recalculated from strike point upwards or downwards depending on density of both aces and intermediates. I think the simple method presented (simpler than mine) can be further refined to produce additional accuracy, both for FBM ASC as well as for the presented method which does not appear to take intermediate density into account. My interest is primarily for 6d.

[Cacarulo]

I find this very interesting, especially as it pertains to the regaled FBM ASC. Essentially, insurance is recalculated from strike point upwards or downwards depending on density of both aces and intermediates. I think the simple method presented (simpler than mine) can be further refined to produce additional accuracy, both for FBM ASC as well as for the presented method which does not appear to take intermediate density into account. My interest is primarily for 6d.

I'm glad you find it interesting. This is new ground and I'm sure it can be improved as long as the simplicity is not lost. It would even be ideal to find some formula to find these indices. At least some good approximation.
Also, the idea can be expanded to other plays, not just insurance.

Sincerely,
Cac

PS: BTW, what is FBM ASC? I have been away for several years and have missed several things in the meantime.

[Freightman]

Also, the idea can be expanded to other plays, not just insurance.

Ace sensitive plays such as 99 v 7, lowering threshold of 10 v 10 with ace surplus, double or non double of 11 v 10 etc.

Also, since you use the word “Dynamic”, consider effect of spread or expand the concept of spread on variable spreads per TC. Tip of iceberg.

[G Man]

I’m trying to figure out Cac’s concept.

Say four decks have been played and we have a RC of 6 with exactly 16 aces gone.
That means a TC of +3 and we would take insurance.

If in the same situation, only 12 aces have been seen.
Then our RC of 6 would be “made of” more 10s and I would think the insurance index should be higher, not lower … Simply said, the dealer has more chances to get an ace as a down card.

Am I missing something ?

[k_c]

I'm glad you find it interesting. This is new ground and I'm sure it can be improved as long as the simplicity is not lost. It would even be ideal to find some formula to find these indices. At least some good approximation.
Also, the idea can be expanded to other plays, not just insurance.

Sincerely,
Cac

Here is my present generic insurance data for HiLo single data for exactly 1,2,3,4 aces removed. It seems you are able to make better sense out of this type of data than I am.

exactly 1 ace played

Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Insurance Data (without regard to hand comp)
Side counted subgroup removals (no input defaults to minimum):
{1} (1 to 4): 1

**** Player hand: x-x ****
Cards   RC      TC ref

48      -1      -1.08
47      0       0.00
35      1       1.49
26      4       8.00
15      5       17.33

exactly 2 aces played

Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Insurance Data (without regard to hand comp)
Side counted subgroup removals (no input defaults to minimum):
{1} (1 to 4): 2

**** Player hand: x-x ****
Cards   RC      TC ref

48      -2      -2.17
47      -1      -1.11
35      0       0.00
26      2       4.00
18      3       8.67
6       4       34.67
5       3       31.20
4       4       52.00
3       3       52.00

exactly 3 aces played

Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Insurance Data (without regard to hand comp)
Side counted subgroup removals (no input defaults to minimum):
{1} (1 to 4): 3

**** Player hand: x-x ****
Cards   RC      TC ref

48      -3      -3.25
47      -2      -2.21
35      -1      -1.49
26      0       0.00
21      1       2.48
10      2       10.40

exactly 4 aces played

Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Insurance Data (without regard to hand comp)
Side counted subgroup removals (no input defaults to minimum):
{1} (1 to 4): 4

**** Player hand: x-x ****
Cards   RC      TC ref

48      -4      -4.33
47      -3      -3.32
35      -2      -2.97
23      -1      -2.26
12      0       0.00
3       1       17.33
2       0       0.00
1       1       52.00

k_c

[Zenfighter]

I’m trying to figure out Cac’s concept.

Say four decks have been played and we have a RC of 6 with exactly 16 aces gone.
That means a TC of +3 and we would take insurance.

If in the same situation, only 12 aces have been seen.
Then our RC of 6 would be “made of” more 10s and I would think the insurance index should be higher, not lower … Simply said, the dealer has more chances to get an ace as a down card.

Am I missing something ?

Your example is for the reversal situation. Off the top removing three tens I get:

INS if TC >3.67073 in other words 3.7

But removing three aces (let call both, artificial faked shoes):

INS if TC > 2.33008 take it at 2.4

When you´re sure an excess of aces is gone, then the index sinks. This seems to be the foundation of Cac´s derivations, IMO.
Is it clearer now?

Regards,

Zenfighter

[Freightman]

PS: BTW, what is FBM ASC? I have been away for several years and have missed several things in the meantime.

https://www.blackjacktheforum.com/sh...ine-by-request

Missed your inquiry. Post 1 of this linked thread gives a good outline. The masses don’t seem to have grasped the concepts, and that’s fine. In simple terms, your insurance thoughts revise index strike point based on ace density. You’ll note similarities with the link.

[Cacarulo]

I’m trying to figure out Cac’s concept.

Say four decks have been played and we have a RC of 6 with exactly 16 aces gone.
That means a TC of +3 and we would take insurance.

If in the same situation, only 12 aces have been seen.
Then our RC of 6 would be “made of” more 10s and I would think the insurance index should be higher, not lower … Simply said, the dealer has more chances to get an ace as a down card.

Am I missing something ?

Perhaps posting the table below explains the concept better than trying to do it in words.
It is easy to see but difficult to explain. Basically you have to distribute the expected value between aces that have come out and TCs.
In the first part of the table you can see the frequency and the expected value when "n" aces came out for each TC.
In the second part you can see the accumulated of the first. The first line corresponds to the generic value of the index since it is
the accumulated value from the first to the last ace. Here we see that the expected value becomes positive for a TC equal to +3.
The second line of the second part shows the accumulated when two or more aces have come out and the twelfth line shows
the accumulation of twelve or more aces. We can clearly see that the expected value is positive for a TC equal to +2.

But there are still more that make the concept more powerful. If you look closely at the first table, when we're at the generic index (+3),
even though the overall expectancy value is positive, most of the time we're playing with negative EV. The EV starts to be positive only
when twelve aces have gone! and for a TC of +4 only when four aces have gone.

Enjoy.

Sincerely,
Cac

6D, 4.5/6 pen, TCs are floored and exact

 
     +------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
     |           -3           |           -2           |           -1           |            0           |            1           |            2           |            3           |            4           |
     +------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
     |     p           ev     |     p           ev     |     p           ev     |     p           ev     |     p           ev     |     p           ev     |     p           ev     |     p           ev     |
     +------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
   1 |  0.000035   -0.163799  |  0.001211   -0.120682  |  0.026648   -0.083958  |  0.025203   -0.070106  |  0.002364   -0.052886  |  0.000287   -0.037887  |  0.000037   -0.022660  |  0.000005   -0.010206  |
   2 |  0.000217   -0.158388  |  0.003728   -0.116749  |  0.023941   -0.085401  |  0.022565   -0.067549  |  0.004335   -0.050342  |  0.000824   -0.034854  |  0.000143   -0.020080  |  0.000025   -0.006550  |
   3 |  0.000664   -0.153398  |  0.006304   -0.114557  |  0.020876   -0.085599  |  0.020227   -0.066013  |  0.005766   -0.048587  |  0.001480   -0.032761  |  0.000330   -0.017571  |  0.000072   -0.002384  |
   4 |  0.001393   -0.148804  |  0.008186   -0.112854  |  0.018147   -0.085419  |  0.018190   -0.065145  |  0.006758   -0.047052  |  0.002155   -0.030631  |  0.000588   -0.015122  |  0.000153   -0.000122  |
   5 |  0.002298   -0.145555  |  0.009325   -0.111555  |  0.015872   -0.085065  |  0.016501   -0.064693  |  0.007341   -0.045524  |  0.002776   -0.028760  |  0.000897   -0.013065  |  0.000273    0.001951  |
   6 |  0.003227   -0.142714  |  0.009854   -0.110449  |  0.014025   -0.084936  |  0.015144   -0.064185  |  0.007582   -0.044084  |  0.003310   -0.027223  |  0.001233   -0.011197  |  0.000430    0.004172  |
   7 |  0.004062   -0.140540  |  0.009942   -0.109482  |  0.012539   -0.084783  |  0.014001   -0.063758  |  0.007612   -0.043251  |  0.003748   -0.025825  |  0.001575   -0.009248  |  0.000618    0.006225  |
   8 |  0.004742   -0.138727  |  0.009762   -0.108840  |  0.011318   -0.084589  |  0.012989   -0.063357  |  0.007538   -0.042388  |  0.004091   -0.024653  |  0.001906   -0.007875  |  0.000832    0.008220  |
   9 |  0.005252   -0.137262  |  0.009451   -0.108308  |  0.010262   -0.084180  |  0.012081   -0.063026  |  0.007396   -0.041541  |  0.004346   -0.023409  |  0.002213   -0.006340  |  0.001061    0.009578  |
  10 |  0.005600   -0.135982  |  0.009070   -0.107836  |  0.009322   -0.083801  |  0.011269   -0.062959  |  0.007191   -0.040748  |  0.004521   -0.022241  |  0.002488   -0.004820  |  0.001297    0.011580  |
  11 |  0.005807   -0.134901  |  0.008646   -0.107203  |  0.008473   -0.083385  |  0.010540   -0.062626  |  0.006932   -0.040019  |  0.004623   -0.021172  |  0.002723   -0.003357  |  0.001531    0.013519  |
  12 |  0.005897   -0.133734  |  0.008196   -0.106597  |  0.007699   -0.082755  |  0.009867   -0.062313  |  0.006645   -0.039055  |  0.004657   -0.019722  |  0.002912   -0.001613  |  0.001749    0.015692  |
  13 |  0.005881   -0.132443  |  0.007725   -0.105824  |  0.006972   -0.081816  |  0.009230   -0.061574  |  0.006322   -0.037759  |  0.004619   -0.017702  |  0.003044    0.000564  |  0.001933    0.019332  |
  14 |  0.005761   -0.130569  |  0.007227   -0.104529  |  0.006265   -0.080191  |  0.008583   -0.059977  |  0.005950   -0.035747  |  0.004481   -0.014191  |  0.003093    0.004851  |  0.002048    0.024941  |
  15 |  0.005510   -0.127154  |  0.006670   -0.101994  |  0.005527   -0.076401  |  0.007838   -0.055988  |  0.005490   -0.032014  |  0.004189   -0.007912  |  0.003012    0.011469  |  0.002046    0.034091  |
  16 |  0.005064   -0.121029  |  0.005989   -0.096882  |  0.004689   -0.069741  |  0.006868   -0.048988  |  0.004881   -0.024761  |  0.003687    0.002144  |  0.002748    0.022386  |  0.001878    0.046964  |
  17 |  0.004352   -0.111087  |  0.005099   -0.087738  |  0.003715   -0.059169  |  0.005601   -0.038061  |  0.004049   -0.012905  |  0.002954    0.016431  |  0.002273    0.037268  |  0.001536    0.064099  |
  18 |  0.003370   -0.096814  |  0.003957   -0.073461  |  0.002649   -0.044779  |  0.004092   -0.022706  |  0.003004    0.003953  |  0.002074    0.034924  |  0.001644    0.056392  |  0.001080    0.084797  |
  19 |  0.002249   -0.078436  |  0.002664   -0.054707  |  0.001632   -0.026456  |  0.002567   -0.003553  |  0.001899    0.025106  |  0.001226    0.056482  |  0.000999    0.078732  |  0.000630    0.108449  |
  20 |  0.001229   -0.057050  |  0.001475   -0.032509  |  0.000830   -0.004770  |  0.001318    0.019012  |  0.000973    0.049548  |  0.000584    0.080789  |  0.000488    0.103856  |  0.000293    0.133972  |
  21 |  0.000521   -0.032946  |  0.000632   -0.007192  |  0.000329    0.019958  |  0.000523    0.044300  |  0.000381    0.076002  |  0.000213    0.107798  |  0.000182    0.132151  |  0.000103    0.162107  |
  22 |  0.000158   -0.007071  |  0.000194    0.020298  |  0.000094    0.046647  |  0.000149    0.070992  |  0.000106    0.105503  |  0.000055    0.134669  |  0.000048    0.161470  |  0.000026    0.190780  |
  23 |  0.000030    0.019383  |  0.000037    0.047358  |  0.000017    0.075658  |  0.000027    0.098525  |  0.000019    0.134205  |  0.000009    0.163741  |  0.000008    0.190168  |  0.000004    0.221064  |
  24 |  0.000003    0.048373  |  0.000003    0.080612  |  0.000001    0.103686  |  0.000002    0.126262  |  0.000002    0.170802  |  0.000001    0.195108  |  0.000001    0.214395  |  0.000000    0.250950  |
     +------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+
>= 1 |  0.073321   -0.127462  |  0.135346   -0.103977  |  0.211842   -0.081970  |  0.235375   -0.061281  |  0.110536   -0.036597  |  0.060909   -0.013380  |  0.034581    0.009819  |  0.019622    0.033252  |
>= 2 |  0.073286   -0.127444  |  0.134135   -0.103826  |  0.185194   -0.081684  |  0.210172   -0.060223  |  0.108172   -0.036241  |  0.060622   -0.013264  |  0.034545    0.009854  |  0.019617    0.033263  |
>= 3 |  0.073069   -0.127352  |  0.130407   -0.103457  |  0.161253   -0.081132  |  0.187607   -0.059342  |  0.103837   -0.035653  |  0.059798   -0.012966  |  0.034402    0.009978  |  0.019592    0.033315  |
>= 4 |  0.072405   -0.127114  |  0.124103   -0.102893  |  0.140377   -0.080468  |  0.167379   -0.058536  |  0.098071   -0.034892  |  0.058318   -0.012464  |  0.034072    0.010245  |  0.019520    0.033446  |
>= 5 |  0.071012   -0.126688  |  0.115917   -0.102190  |  0.122230   -0.079733  |  0.149189   -0.057730  |  0.091313   -0.033992  |  0.056163   -0.011767  |  0.033484    0.010690  |  0.019366    0.033712  |
>= 6 |  0.068714   -0.126057  |  0.106592   -0.101370  |  0.106357   -0.078937  |  0.132689   -0.056864  |  0.083972   -0.032984  |  0.053388   -0.010883  |  0.032588    0.011343  |  0.019093    0.034166  |
>= 7 |  0.065487   -0.125236  |  0.096738   -0.100446  |  0.092333   -0.078026  |  0.117545   -0.055921  |  0.076390   -0.031883  |  0.050078   -0.009804  |  0.031355    0.012230  |  0.018664    0.034856  |
>= 8 |  0.061425   -0.124224  |  0.086795   -0.099410  |  0.079794   -0.076965  |  0.103544   -0.054861  |  0.068778   -0.030624  |  0.046330   -0.008508  |  0.029780    0.013366  |  0.018046    0.035837  |
>= 9 |  0.056683   -0.123011  |  0.077033   -0.098216  |  0.068475   -0.075704  |  0.090555   -0.053643  |  0.061240   -0.029176  |  0.042239   -0.006944  |  0.027874    0.014818  |  0.017213    0.037172  |
>=10 |  0.051431   -0.121556  |  0.067583   -0.096804  |  0.058213   -0.074210  |  0.078474   -0.052198  |  0.053844   -0.027478  |  0.037893   -0.005055  |  0.025661    0.016642  |  0.016153    0.038984  |
>=11 |  0.045831   -0.119793  |  0.058512   -0.095094  |  0.048892   -0.072382  |  0.067205   -0.050394  |  0.046653   -0.025433  |  0.033372   -0.002727  |  0.023173    0.018946  |  0.014856    0.041377  |
>=12 |  0.040025   -0.117601  |  0.049866   -0.092995  |  0.040419   -0.070075  |  0.056665   -0.048119  |  0.039721   -0.022887  |  0.028749    0.000239  |  0.020450    0.021916  |  0.013325    0.044577  |
>=13 |  0.034128   -0.114814  |  0.041670   -0.090319  |  0.032720   -0.067092  |  0.046799   -0.045126  |  0.033076   -0.019639  |  0.024092    0.004098  |  0.017538    0.025823  |  0.011577    0.048940  |
>=14 |  0.028247   -0.111143  |  0.033945   -0.086791  |  0.025748   -0.063104  |  0.037569   -0.041085  |  0.026754   -0.015358  |  0.019472    0.009269  |  0.014495    0.031127  |  0.009644    0.054874  |
>=15 |  0.022486   -0.106166  |  0.026719   -0.081993  |  0.019483   -0.057610  |  0.028986   -0.035491  |  0.020805   -0.009527  |  0.014991    0.016281  |  0.011402    0.038254  |  0.007596    0.062944  |
>=16 |  0.016976   -0.099354  |  0.020049   -0.075340  |  0.013956   -0.050168  |  0.021148   -0.027895  |  0.015314   -0.001465  |  0.010802    0.025664  |  0.008390    0.047870  |  0.005550    0.073579  |
>=17 |  0.011913   -0.090142  |  0.014060   -0.066164  |  0.009267   -0.040265  |  0.014280   -0.017750  |  0.010433    0.009435  |  0.007115    0.037852  |  0.005642    0.060281  |  0.003672    0.087195  |
>=18 |  0.007560   -0.078085  |  0.008961   -0.053888  |  0.005552   -0.027616  |  0.008679   -0.004641  |  0.006384    0.023607  |  0.004161    0.053057  |  0.003369    0.075812  |  0.002136    0.103799  |
>=19 |  0.004190   -0.063020  |  0.005004   -0.038413  |  0.002903   -0.011959  |  0.004587    0.011474  |  0.003380    0.041073  |  0.002087    0.071074  |  0.001725    0.094327  |  0.001056    0.123236  |
>=20 |  0.001942   -0.045166  |  0.002341   -0.019872  |  0.001272    0.006646  |  0.002020    0.030573  |  0.001480    0.061559  |  0.000861    0.091847  |  0.000726    0.115782  |  0.000426    0.145098  |
>=21 |  0.000712   -0.024652  |  0.000866    0.001646  |  0.000442    0.028084  |  0.000701    0.052302  |  0.000508    0.084577  |  0.000277    0.115145  |  0.000238    0.140202  |  0.000133    0.169601  |
>=22 |  0.000191   -0.002079  |  0.000234    0.025475  |  0.000113    0.051791  |  0.000178    0.075833  |  0.000126    0.110501  |  0.000065    0.139327  |  0.000057    0.166068  |  0.000030    0.195410  |
>=23 |  0.000033    0.021785  |  0.000041    0.050106  |  0.000019    0.077856  |  0.000029    0.100680  |  0.000020    0.136971  |  0.000010    0.165961  |  0.000009    0.191908  |  0.000004    0.223081  |
>=24 |  0.000003    0.048373  |  0.000003    0.080612  |  0.000001    0.103686  |  0.000002    0.126262  |  0.000002    0.170802  |  0.000001    0.195108  |  0.000001    0.214395  |  0.000000    0.250950  |
     +------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+------------------------+

Total Ev = -0.073951
Rounds   = 100000000150

[Cacarulo]

I’m trying to figure out Cac’s concept.

Say four decks have been played and we have a RC of 6 with exactly 16 aces gone.
That means a TC of +3 and we would take insurance.

If in the same situation, only 12 aces have been seen.
Then our RC of 6 would be “made of” more 10s and I would think the insurance index should be higher, not lower … Simply said, the dealer has more chances to get an ace as a down card.

Am I missing something ?

Your example is for the reversal situation. Off the top removing three tens I get:

INS if TC >3.67073 in other words 3.7

But removing three aces (let call both, artificial faked shoes):

INS if TC > 2.33008 take it at 2.4

When you´re sure an excess of aces is gone, then the index sinks. This seems to be the foundation of Cac´s derivations, IMO.
Is it clearer now?

Regards,

Zenfighter

Correct!

Sincerely,
Cac