ES10 for 6 decks and ENHC rules
Basic strategy
For the sake of simplicity, lets assume Griffin?s definition as stated on page 12 of TOB:
The basic strategy is the strategy which maximizes the player?s average gain, or expectation, playing one hand against a complete pack of cards.
Table B13 from BJA3 gives us the following strategy:
9 T
16 esr esr
15 esr
14 esr
7,7 esr
8,8 esr
Testing the accuracy of the table.
1) Method one.
We are going to compare our expectation for hitting (and/or splitting when a pair is involved), versus the alternative of surrender the hand, which has a fixed negative expectation of -.500000, as we all know.
Hand Hitting Surrender
T,6 v T -.570817 -.500000
9,7 v T -.571478 -.500000
8,8 v T * -.57145 -.500000
T,5 v T -.542439 -.500000
9,6 v T -.543765 -.500000
8,7 v T -.538616 -.500000
T,4 v T -.504799 -.500000
9,5 v T -.505807 -.500000
8,6 v T -.507566 -.500000
7,7 v T -.514913 -.500000
T,6 v 9 ** -.504547 -.500000
9,7 v 9 ** -.504993 -.500000
8,8 v 9 ***
? * Splitting 8s under ENHC yields a horrible -.616 aprox. (Spl3 and das). The exact figures can be seen at bjmath.com. A courtesy of Cacarulo.
?
? ** EV?s from BJA3, Table A58, page 451.
?
? *** The spl3 w/das case yields EV = -. 389371 therefore do not surrender here, split the hand instead.
2) Method two.
Deconstructing ES10 with the aid of exact EoR?s for 6 dks and ENHC seems to be a good idea. These tables with their full-deck favourabilities included (m6, here), tends to act like real eye-openers. A travel to the core of the early surrender?s rule. Enjoy!
DEALER TEN
17 16 15 14 13
A -1.0563 -0.5795 -0.9368 -1.0149 -1.0980
2 0.7776 0.9314 0.4906 0.2467 0.2560
3 0.6833 1.3443 0.8990 0.4724 0.2242
4 0.6029 2.1761 1.2784 0.8845 0.4539
5 0.5036 2.8314 2.0818 1.3020 0.8980
6 0.8330 -0.6083 2.9014 2.3292 1.5568
7 0.6217 -0.4140 -0.5566 2.8253 2.2412
8 -0.9617 -0.6413 -0.7570 -0.8839 2.4679
9 -0.6398 -0.8518 -0.9425 -1.0838 -1.2406
T -0.3411 -1.0471 -1.1146 -1.2693 -1.4399
m(6) -3.6287 7.5355 4.2686 0.7569 -3.0218
ss 5.6843 21.8261 23.0536 25.5994 25.7026
DEALER 9
16 15 14
A -0.2805 -0.5466 -0.5926
2 0.4806 -0.0151 -0.2667
3 1.6830 0.8318 0.3563
4 2.5441 1.7589 0.9066
5 2.8161 2.6133 1.8308
6 -0.8507 2.7562 2.5460
7 -0.7972 -0.9294 2.6606
8 -0.6029 -0.7232 -0.8583
9 -0.8301 -0.9677 -1.1215
T -1.0406 -1.1945 -1.3653
m(6) 0.9114 -2.8561 -6.9124
ss 24.2885 26.5418 27.7342
DEALER 8
16
A -0.1503
2 0.9352
3 1.7631
4 2.4015
5 2.5858
6 -1.0579
7 -0.9904
8 -0.9268
9 -0.7312
T -0.9572
m(6) -4.1929
ss 23.6180
1) Despite the fact that 6 decks have been employed to extract this EoR?s tables,
the figures (Ace through Ten) have been normalized to one-deck values. The rationale behind this is to facilitate comparisons with other already extracted, which employ a standard 52 pack. So here, if you want to know what your truly figure is for removing a single denomination, just perform a division by 6 (dividing by 311/51 is the theoretical procedure and should be favoured) and you will get your 6 decks figure. E.g. 16 v T. What is the amount gained/lost by removing a single ten?
-1.0471/(311/51) = -0.1717 therefore our m (6) changes to:
7.5355 + (-0.1717) = 7.3638 a noticeable advantage for surrendering the hand.
2) The entries as usual are differences in expectation for the two actions being contemplated here, namely surrender vs. hitting. The tables with positive m (6) values inform us that surrender is the favoured action to be taken, thus. A quick glance at all the m (6) and voil?, we have confirmed the exactitude of our BS chart.
3) As usual, TOB and Griffin?s comments are mandatory if you want to extract the most out of the tables. A masterpiece is Don?s introduction to the new EoR?s tables that are going to appear in the next soft cover edition of BJA3. A clear, concise and illustrative treatise. Don?t miss it!
Testing the Hilo accuracy. Playing correlations.
Hand Playing Correlations
T,7 v T .773296
9,8 v T .775935
T,6 v T .777098
9,7 v T .774658
8,8 v T .774603
T,5 v T .858083
9,6 v T .860034
8,7 v T .85964
T,4 v T .705731
9,5 v T .706764
8,6 v T .705999
7,7 v T .716504
T,3 v T .637199
9,4 v T .638846
8,5 v T .640377
7,6 v T .638938
T,6 v 9 .717304
9,7 v 9 .714518
T,5 v 9 .814052
9,6 v 9 .815241
8,7 v 9 .816024
T,4 v 9 .685344
9,5 v 9 .68602
8,6 v 9 .685569
7,7 v 9 .694255
T,6 v 8 .695154
9,7 v 8 .691655
Here the removal of the three cards 9,6 and T pop up our full-deck favorability until
4. 40795%. Its high correlation for surrender the hand should not raise eyebrows!
Algebraic and simulated Hilo indexes. Weapons to fight
Hand Algebraic derived Rounded Simulated (floored)
T,7 v T 5.8995 5.9 6
9,8 v T 6.1600 6.2
T,6 v T -6.3164 -6.3 -7
9,7 v T -6.4145 -6.4
8,8 v T -6.4121 -6.4
T,5 v T -3.4221 -3.4 -3
9,6 v T -3.3940 -3.4
8,7 v T -3.1277 -3.1
T,4 v T -0.5920 -0.6 -1
9,5 v T -0.5156 -0.5
8,6 v T -0.6973 -0.7
7,7 v T -1.4720 -1.5
T,3 v T 3.2126 3.2 3
9,4 v T 3.3057 3.3
8,5 v T 2.6420 2.6
7,6 v T 2.5793 2.6
T,6 v 9 -0.4126 -0.4 -1
9,7 v 9 -0.4550 -0.5
T,5 v 9 2.1039 2.1 2
9,6 v 9 2.2243 2.2
8,7 v 9 2.4782 2.5
T,4 v 9 6.2773 6.3 5
9,5 v 9 6.2890 6.3
8,6 v 9 6.1632 6.2
7,7 v 9 5.4428 5.4
T,6 v 8 4.3722 4.4 4
9,7 v 8 4.3650 4.4
From Hell to Heaven, with the aid of the ES10 rule.
We need only a pocket calculator and Table C1 from BJA3, to evaluate four typical games featuring this rule.
a) 6 dks, S17, DOA, DAS, SPL3, RSA, ES10, ENHC(lose all vs. Dealer?s BJ)
Base rules -.546
Enhc -.109
Das/Spl3 .142
Rsa .069
ES10 .241
BSE = -.203
b) 6 dks, S17, DOA, DAS, SPL3, NRSA, ES10, ENHC
BSE = -.272
c) 6 dks, S17, DB9, DAS, SPL3, RSA, ES10, ENHC
BSE = -.292
d) 6 dks, S17, DB9, DAS, SPL3, NRSA, ES10, ENHC
BSE = -.361
My suggestion is to read calmly Tables 10.51 and 10.52 (pages 240/41 from BJA3) for 6 decks and late surrender. (BSE = -.26)
You will have a very close idea of what to expect when dealing with these types of games.
A New Yorker told me recently, that Surrender is a sort of Holy Grail; while enhancing the expectation it decreases the variance at the same time!
It seems to me, that holiness and dollars are not contradictory ideals, not in our game, at least.
Want something new? Look at something old, then.
Best regards
Zenfighter
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