Zenfighter: ES10 under ENHC rules. Theoretical insights.

Zenfighter · 12-05-2004, 05:04 PM

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

Don Schlesinger · 12-05-2004, 07:17 PM

Zen,

As always, a beautiful and most useful piece of work! Thank you for gracing our pages here with your wonderful insights and research.

Now, if we could only find out who that New Yorker was, I'd probably put his remarks on p. 198 of BJA3! :-)

Don

Zenfighter · 12-06-2004, 02:59 AM

L`homme parle fran?ais correctement.

Jeopardizing the author? :-)

Zenfighter

Garry Baldy · 12-06-2004, 12:54 PM

Great! Wonderful! Many thanks Zengrifter.

Afraid to ask... What about ES against Ace?

Luck.

Garry Baldy.

Zenfighter · 12-06-2004, 02:28 PM

..... at least until January! The fact that very few players in the World can take advantage of this pearl called ESA, being you among the few fortunate ones, won?t prevent me to duplicate the work for the ace. What else can a father do, who?s both sons have Russian names? :-)

Glad to hear you liked it! Stay tuned.

Regards

Zenfighter

Zenfighter · 12-29-2004, 10:00 AM

6 dks, S17, DOA, DAS, SPL3, SPA1, ES10, ENHC

 

 

 

		                      Play-All Bets	Play-All Bets	BC 27% 16% 9%	BC 27% 16% 9% 

TC	TC Freq. EV%W/L	SE	SD	Optimal $	Practical $	Optimal $	Practical $ 

<=-1   44.89   -1.27	0	1.122	14,13,11	15,15,10	0	0 

0      27.77   -0.11	0.01	1.11	14,13,11	15,15,10	0	0 

1      11.26	0.51	0.01	1.104	42,42,42	40,40,25	0	0 

2	7.38	1.07	0.01	1.098	89,89,89	100,100,50	0	0 

3	3.49	1.6	0.01	1.096	113,133,133	120,125,125	168,145,135	200,150,135 

4	2.45	2.19	0.02	1.097	113,151,176	120,180,160	182,182,184	200 

5	1.11	2.84	0.03	1.101	113,151,176	120,180,160	234,235,237	200 

6	0.81	3.43	0.03	1.102	113,151,176	120,180,160	283,283,286	300 

7	0.34	4.27	0.05	1.102	113,151,176	120,180,160	335,352,356	400 

8	0.26	4.8	0.05	1.099	113,151,176	120,180,160	335,399,403	400,450,500 

9	0.1	5.34	0.09	1.095	113,151,176	120,180,160	335,434,451	400,450,500 

10	0.08	5.81	0.1	1.092	113,151,176	120,180,160	335,434,459	400,450,500 

11	0.03	6.51	0.17	1.088	113,151,176	120,180,160	335,434,459	400,450,500 

>=12	0.04	7.29	0.15	1.081	113,151,176	120,180,160	335,434,459	400,450,500

 

Bet Spread      Ke.B   Avg.B	%W/L	WinRate	$/100	SD/100	ROR	  N0	 DI	SCORE 

PA Opt. (1-8)	706	31.44	0.79	1.745	24.75	491.43	13.5	40,464	4.97	24.72 

PA Pract.(1-8)	667	33.23	0.79	1.76	26.4	531.41	15.4	40,518	4.97	24.67 

PA Opt. (1-12)	797	32.88	0.99	2.595	32.56	591.36	13.5	30,728	5.7	32.54 

PA Pract.(1-12)	667	36.53	0.98	2.396	35.94	633.18	16.6	31,038	5.68	32.22 

PA Opt. (1-16)	911	33.04	1.13	3.404	37.38	612.71	13.5	26,776	6.11	37.35 

PA Pract.(1-16)	1,000	26.47	1.17	3.104	31.04	516.3	 9.7	27,667	6.01	36.15 

BC Opt. (1-2)	60     207.15	2.68	0.288	48.22	696.02	13.3	20,694	6.94	48.22 

BC Pract.(1-2)	50     228.6	2.67	0.265	53.06	768.4	16.5	21,020	6.9	47.68 

BC Opt. (1-3)	69     203.47	2.79	0.342	49.43	705.43	13.6	20,235	7.03	49.43 

BC Pract.(1-3)	67     211.5	2.8	0.344	51.61	736.65	14.7	20,381	7.01	49.08 

BC Opt. (1-4)	87     201.48	2.83	0.431	49.56	704.72	13.5	20,215	7.04	49.55 

BC Pract.(1-4)	80     208.38	2.87	0.417	52.1	743.75	15.2	20,359	7.01	49.07

It is now, when DD's readers have in their hands the best ES10 article ever published.
Under the umbrella of this programming wizard, called Norm, I feel obliged for this statement.

Enjoy!

Zenfighter