LATE SURRENDER EoR?s
DEALER TEN
16 15 14 13 12
A 0.283 -0.046 -0.070 -0.081 -0.093
2 0.929 0.451 0.182 0.182 0.216
3 1.377 0.890 0.423 0.164 0.164
4 2.318 1.318 0.906 0.450 0.153
5 3.068 2.253 1.406 0.952 0.465
6 -0.740 3.133 2.494 1.617 1.184
7 -0.509 -0.683 3.028 2.368 1.472
8 -0.772 -0.914 -1.064 2.612 1.918
9 -1.013 -1.125 -1.292 -1.474 2.171
T -1.235 -1.319 -1.503 -1.698 -1.912
m 4.066 0.510 - 3.249 -7.286 1.578
ss 26.155 25.826 30.241 29.926 26.905
DEALER ACE ( S17)
16 15 14 13 12
A 0.147 -0.002 0.002 -0.002 0.025
2 0.902 0.179 -0.008 0.051 0.077
3 1.580 0.908 0.213 0.016 0.020
4 2.259 1.671 1.018 0.276 0.011
5 2.680 2.335 1.688 0.997 0.251
6 -0.631 2.963 2.579 1.934 1.250
7 -1.029 -1.197 2.360 1.938 1.256
8 -1.364 -1.557 -1.754 1.771 1.309
9 -1.647 -1.859 - 2.075 2.310 1.172
T -0.724 -0.861 -1.006 -1.168 -1.342
m 2.117 -1.622 -5.502 -9.596 -13.884
ss 23.744 28.159 27.582 22.499 13.501
DEALER ACE (H17)
16 15 14 13 12
A 0.119 -0.012 -0.011 -0.016 0.008
2 0.676 0.103 -0.067 -0.020 0.003
3 1.381 0.628 0.079 -0.101 0.106
4 2.064 1.393 0.653 0.050 -0.211
5 2.674 2.265 1.547 0.781 0.194
6 -0.951 2.594 2.135 1.410 0.641
7 -0.898 -1.052 2.487 2.010 1.263
8 -1.223 -1.398 -1.578 1.928 1.409
9 -1.489 -1.682 -1.882 -2.100 1.366
T -0.588 -0.710 -0.840 -0.986 -1.142
m 4.382 0.826 -2.892 -6.788 -10.871
ss 20.595 22.111 22.428 18.667 11.167
Checking the quality of the tables.
An EoR?s table is supousedly a fair one if:
Sum Ei* Pi = 0
That means that removing a single card times the probability of drawing it summed over
the 13 different values (tens shall be added 4 times) should be zero. Obviously, by rounding off
decimals, what you get is a final result close to zero. As long as this final result is no greater than
+/- 0.01 you have a fair one.
You will see, that the above tables are all within [-0.003 and +0.003] ad maximum.
E.g. 16 vs T
0.283*4/52 + 0.929*4/52 +?..+ (-1.235*16/52) = 0.001 quite accurate.
Entries, m and ss
All this is explained with detail in Griffin?s book, you have the same format here.
Entries = differences in expectations between surrendering and hitting
m = full deck favorability for surrendering
ss = sum of squares of the values
Basic Strategy answers.
Shall we late surrender T, 6 vs A with the H17 rule in effect?
A pocket calculator will suffice:
((0.119 + (? 0.951) + (-0.588))* 51/49 = -1.478 so we have:
4.382 + (-1.478) = 2.904 therefore you shall surrender the hand.
Note that 51/49 is a necessary refinement to adjust for the EoR?s of the full table.
Correlation of your point count system for the particular hand
For the above example use again Griffin formula:
C = (Sum Pi* Ei)/ sqr (SS*ss) where SS stands for sum of the squares of your point count
system.
The Hi-lo player can expect then:
16 vs A (h17) where we have SS = 10, the rest can be extracted from the table.
c = 8.077/ sqr (10*20.595) solving we get
c = .562820 (.562762 is the computed one), as the correlation for this play.
Extracting indexes with Arnold?s algebraic formula
(m/i)*p + (52/51)*t = count per deck.
The fraction 52/51 account for the removal of the dealer?s up card, Arnold didn?t used it,
but what the hell, more exact figures aren?t going to hurt us.
m = favorability, sign must be reversed (see Arnold?s paper for the explanation).
i = inner product of the 39 remaining point cards (assuming you?re a Hi-lo player).
p = sum of the squares of your total point count values. Hi-lo = 40
t = this is the point value of the removed dealer?s up card.
Example:
Shall we late surrender 14 vs A (s17)? If yes, at what count per deck?
m = -5.502 +0.002 = -5.500 reversing the sign m = 5.500
i = (4 * -0.008) + (4 * 0.213) + (4 * 1.018) + (4 * 1.688) + (4 * 2.579) + (-3 * 0.002)
+ (-16 * -1.006) = 38.05
Putting all the data into Arnold?s formula we have then:
(5.500/38.05) * 40 + (52/51)* -1 = 4.762258 as the count per deck to surrender 14 vs A.
I double checked this with Wong?s BCA where the true count given there is 5 for single deck,
the dealer standing on soft seventeen.
Note also here, that if you?re looking for specific two card combinations holding a 14,
you will need further refinements adjusting for the specific three cards been removed.
T, 4 vs A, here the t = 51/49 * (-1 +1 -1) and 3 removed cards shall be added to m also,
without forgetting the 51/49 multiplier again.
Easier and more accurate indexes can be extracted as follows:
?Please Mr. Wattenberger, could you run for me a full set of ?..??, and so on.
Approaching Thanksgiving, my best wishes for all the folks from DD.
Regards
Z
.
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