FULL ES FOR 6 DECKS AND ENHC RULES
A month ago, after looking for a while at the perspectives to find something interesting to be shared here with the readers, I was frankly demoralized. Our Slavic?s expert player Garry Baldy asked for a sort of duplication of the ES10?s article posted here last December. Meanwhile the temptation was to throw at him something like this: ?Hey man, forget it! Just play Basic Strategy. There is no necessity at all for a duplication here.? But that was before I envisioned the possibility to purchase the Casino Verite?s software, so as to extract a Chapter X ? like table, with the idea to enhance the practical value of the whole article. The reader should judge by himself, if it was a great idea, after all.
Basic Strategy
Hand Ace
17 esr
16 esr
15 esr
14 esr
13 esr
12 esr
7 esr
6 esr
5 esr
3-3 esr
6-6 esr
7-7 esr
8-8 esr
Expected values and Hilo correlations
Hand Standing Hitting Surrender Correlation
T,7 -.637314 -.500000
9,8 -.637333 -.500000
T,6 -.664664 -.500000 .784262
9,7 -.664743 -.500000 .783637
8-8 -.664681 -.500000 .783605
T,5 -.6419 -.500000 .826625
9,6 -.643279 -.500000 .828345
8,7 -.638858 -.500000 .828733
T,4 -.612684 -.500000 .724686
9,5 -.614002 -.500000 .726083
8,6 -.615494 -.500000 .725542
7-7 -.619978 -.500000 .731924
T,3 -.581896 -.500000 .677533
9,4 -.582688 -.500000 .679729
8,5 -.58814 -.500000 .679536
7,6 -.58954 -.500000 .678985
T,2 -.54997 -.500000 .687355
9,3 -.554926 -.500000 .689991
8,4 -.55504 -.500000 .690165
7,5 -.55511 -.500000 .68994
6-6 -.55642 -.500000 .686214
6,2* -.449692 -.500000 .584522
5,3* -.448654 -.500000 .58623
4-4* -.447678 -.500000 .587583
5,2 -.52693 -.500000 .753637
4,3 -.528359 -.500000 .752369
4,2 -.523787 -.500000 .824749
3-3 -.523778 -.500000 .824463
3,2 -.504418 -.500000 .813067
2-2* -.485981 -.500000 .734957
? *Do not surrender here, obviously. Note that the footnote (4) from BJA3, page 490,is for when the H17 rule is in effect.
Thanks heaven, very sparsely used when dealing with ENHC rules, where S17 is the standard one.
The big differences in expectation when holding 17 through 14, will serve us this time, to simplify the issue a little bit, and thus, we?ll consider basic strategy here, our only tool to deal with them. We can play this positive-expectation game through the negatives with impunity, which doesn?t mean on the other hand, that remembering atrocious negative indexes, while having our base bet on the betting circle, will enhance our expectation a little more. (Bizarre departures can be sometimes valuable, for cover purposes, other times they act as giveaways. A philosophical dilemma!)
The American readers can take advantage of the simple formulae provided by Cacarulo, where you can jump from the USA conditional expectations, to be founded in Appendix A from BJA3, to the European ones, with a simple pocket calculator.
EV = pbj*(-1) + ((1- pbj) * ce), where
pbj = probability of BJ
ce = conditional expectation
An example: T,6 vs. A
EV = (95/309)*-1 + (1 ? 95/309)* -.515800
Note that -.515800 is the hitting entry from Table A50, page 443.
Solving quickly we get:
EV = -.644664 matching perfectly the above printed one for ENHC rules.
A few practical EoR?s tables
4 5 6 7 8
A 0.8541 0.8012 0.8032 0.9558 1.2954
2 0.4452 0.4787 0.8157 0.8832 0.9889
3 0.4977 0.8265 1.1950 1.1030 1.0532
4 0.8532 1.2024 1.5709 1.1100 0.3869
5 1.1712 1.5485 1.6717 0.4795 0.3056
6 1.8920 2.0076 0.7136 0.7615 0.9917 7 1.4324 0.1716 0.1197 -0.1683 0.0128
8 -0.3611 -0.3898 -0.3849 -0.4631 -0.8523
9 -0.8496 -0.8482 -0.8408 -0.7199 -1.0387
T -1.4840 -1.4496 -1.4161 -0.9854 -0.7859
m(6) -1.6931 0.0911 1.8464 2.3048 -5.5805
The temptation to surrender our pair of deuces (2-2 vs. A) should be resisted. After removing these three cards,
our full-deck favorability for carrying the action, namely to surrender the hand, remains still negative, with m (6) = -1.4052. A bit of patience, please! A greater dose of it will be needed before surrendering our eight (e.g. 6,2 vs. A). We will see below its degree. And again, divide any entry by 311/51 if you want to know the appropriate figure for six decks. M (6) doesn?t need this, obviously.
Looking for BS departures, desperately.
Hand Algebraic Rounded Sim(floored)*
17 vs A esr
16 vs A esr
15 vs A esr
14 vs A esr
T,3 vs A -8.44716 -8.4 -8
9,4 vs A -8.34378 -8.3
8,5 vs A -8.90454 -8.9
7,6 vs A -9.07448 -9.1
T,2 vs A -5.36964 -5.4 -6
9,3 vs A -5.69292 -5.7
8,4 vs A -5.70599 -5.7
7,5 vs A -5.7153 -5.7
6,6 vs A -5.71413 -5.7
6,2 vs A 9.13943 9.1 10
5,3 vs A 9.27949 9.3
4,4 vs A 9.41001 9.4
5,2 vs A -3.46765 -3.5 -4
4,3 vs A -3.67602 -3.7
4,2 vs A -2.01256 -2.0 -2
3,3 vs A -2.01309 -2.0
3,2 vs A -0.227675 -0.2 0
2,2 vs A 1.56096 1.6 1
*precision sigma = 3.5 se
Along all these years, I?ve followed the recommendations that can be extracted by inference from Don?s IL18 article,
now almost 19 years old, and that?s to be practical with the employment of BS departures. Keeping our memory efforts within the boundaries of ?2 and +6, will get the money out of any multiple-deck game. There is always room for improvements, but the boundaries are sealed. Note that another BJ?s giant, Stanford Wong, do not differ too much:
As a practical matter, you do not really need a wide range of strategy numbers.
?..ignore all strategy numbers smaller than ?1 and larger than +6.
Summarizing our findings. Simplified and practical table
Hand 8 9 T A
17 6 esr
16 4 -1 esr esr
15 2 esr esr
14 5 -1 esr
13 3 esr
12 esr
7 esr
6 -2
5 0
4 1
Basic Strategy expectation for two different rules.
a) 6dks, s17, doa, das, spl3, nrsa, es and enhc
BSE = 0.114%
b) 6dks, s17, doa, das, spl3, rsa, es and enhc
BSE = 0.183%
Chapter X ? like table
4.5/6 S17 DOA DAS SPL3 SPA1 ES ENHC
Play-All Bets BC 27% 15% 8%
TC TC Fr. %W/L Sd. Opt. $ Pract. $ Opt.$ Pract. $
<=1 44.93 -0.92 1.105 26,21,18 25,20,20 0 0
0 28.37 0.35 1.092 29,29,29 25 0 0
1 11.42 1.06 1.090 89,89,89 50 141,124,111 150,125,100
2 6.90 1.70 1.086 144,144,144 125 144,144,144 150
3 3.25 2.33 1.082 199,199,199 200 199,199,200 200
4 2.51 2.97 1.079 211,254,255 200,240,300 255,255,255 300
5 1.16 3.70 1.078 211,254,293 200,240,300 283,318,318 300
6 .72 4.55 1.075 211,254,293 200,240,320 283,372,395 300,375,400
7 .30 5.20 1.070 211,254,293 200,240,320 283,372,444 300,375,400
8 .24 5.99 1.064 211,254,293 200,240,320 283,372,444 300,375,400
9 .10 6.63 1.058 211,254,293 200,240,320 283,372,444 300,375,400
10 .06 7.67 1.054 211,254,293 200,240,320 283,372,444 300,375,400
11 .02 7.97 1.048 211,254,293 200,240,320 283,372,444 300,375,400
>=12 .03 9.46 1.046 211,254,293 200,240,320 283,372,444 300,375,400
Kb Avg.b %W/L $/100 SD/100 ROR NO DI SCORE
PA Opt.(1-8) 379 57.59 1.32 75.87 858.62 13.5 13176 8.71 75.91
PA Pract.(1-8) 400 49.40 1.36 66.99 778.43 10.9 13498 8.61 74.05
PA Opt.(1-12) 472 57.44 1.51 86.45 921.84 13.5 11564 9.30 86.46
PA Pract.(1-12) 500 49.22 1.56 76.85 835.52 11.0 11823 9.20 84.59
PA Opt.(1-16) 547 57.21 1.62 92.45 946.06 13.5 10823 9.61 92.39 PA Pract.(1-16) 500 52.58 1.71 90.10 954.52 13.8 11223 9.44 89.09
BC Opt.(1-2) 71 173.49 2.20 102.07 1008.29 13.4 9810 10.10 102.07
BC Pract.(1-2) 67 184.95 2.22 109.35 1083.75 15.3 9822 10.09 101.81
BC Opt.(1-3) 81 172.51 2.35 108.39 1042.47 13.4 9231 10.41 108.39
BC Pract.(1-3) 80 178.25 2.36 112.15 1079.75 14.5 9273 10.39 107.89
BC Opt.(1-4) 90 169.81 2.45 110.96 1052.72 13.4 9013 10.53 110.96
BC Pract.(1-4) 100 169.00 2.46 111.07 1059.20 13.7 9089 10.49 109.95
We should not forget the kind of game we?re dealing with. Here a play-all approach seems to be dynamite against this positive-expectation
game. A huge SCORE with a reduced variance at the same time. We have already heard this statement before, didn?t we? If you were to back-count this game, then entering with confidence at TC =1 looks clearly optimal.
Hopefully the readers will find it a valuable tool. Theoretical insights are fine, but let?s be realistic, our main concern is to attack successfully any given game offered by the casinos. For this given purpose, there isn?t a better advice, that inside one of these tables.
I?m indebted to Norm Wattenberger, for his time and for his ready-to-help-hand. Without his aid, this Chapter 10?like table for these specific set of rules, will not be posted here. We got a couple of unexpected problems; believe it. The ?exotic? rule called ES was the responsible of them. Ditto for Don. When facing difficulties, his opinion and advice are priceless for me. No matter casino-comportment and/or technical questions. This guy seems to know the facts by intuition, with an exasperating easiness added.
Nobody ignores the fact, that the Russian casinos are offering probably the best rules in the World. For BJ?s travellers, the link below, seems to be a good place to have a look at.
Russian Casinos
From Russia with Love? Absolutely, why not? Well, and what if you are going to be kicked out? Nothing at all. Melodramas are senseless. You will still have The Red Square, The Bolshoi, The Vodka and The Caviar. The beautiful Russian ladies are for singles, make no mistakes here.
Sincerely, enjoy!
Zenfighter
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