Hi to All,
The answer to this problem is very interesting. Let's see what we get when playing solo and
what when playing two hands all the time. Remember that there are no other players
at the table and speed is not considered.
Conditions: 6D,S17,DOA,DAS,SPA1,SPL3,NS,5/6,Hi-Lo,C22 floored, 10000 million rounds.
1) Playing Alone
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 1.841 36.238 13.53 38735 5.08 25.82 713.21 2.147 14.021 1.000
1 - 12 2.752 46.665 13.53 28749 5.90 34.78 791.22 2.507 12.639 1.000
1 - 16 3.551 55.899 13.53 24785 6.35 40.35 880.02 2.821 11.363 1.000
Note that for 1:16 the betting pattern should be:
TC <= -1 ==> 1.00 u | $ 11.36
TC = 0 ==> 1.00 u | $ 11.36
TC = 1 ==> 2.90 u | $ 32.96
TC = 2 ==> 6.48 u | $ 73.62
TC = 3 ==> 10.07 u | $ 114.41
TC = 4 ==> 13.75 u | $ 156.22
TC >= 5 ==> 16.00 u | $ 181.81
2) Playing two hands all the time
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.730 60.143 13.53 26001 6.20 38.46 969.78 2.144 10.312 1.000
1 - 12 5.570 77.596 13.53 19408 7.18 51.53 1081.00 2.508 9.251 1.000
1 - 16 7.191 93.167 13.53 16784 7.72 59.58 1207.00 2.827 8.285 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 8.28
TC = 0 ==> 1.00 u | $ 8.28
TC = 1 ==> 2.91 u | $ 24.08
TC = 2 ==> 6.47 u | $ 53.62
TC = 3 ==> 10.10 u | $ 83.65
TC = 4 ==> 13.79 u | $ 114.28
TC >= 5 ==> 16.00 u | $ 132.56
It's obvious that under these considerations it's better to play two hands all the time.
But, what if we restrict our second hand to a particular TC? Say that our second bet will
be placed only if the TC is greater or equal to a certain TCX. The problem is now reduced to
determine what this TCX should be. The answer is not straightforward since we
need to determine this value by a trial and error process. Besides, it's
SPREAD related.
So here we go. I'm not going to post every single TCX, just the ones that matter for
optimal spreads lower or equal 1:16.
3) For TCX = -3
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.573 56.525 13.53 25032 6.32 39.95 894.31 2.026 11.182 1.000
1 - 12 5.304 73.555 13.53 19231 7.21 52.00 1020.01 2.374 9.804 1.000
1 - 16 6.825 88.590 13.53 16848 7.70 59.36 1149.86 2.674 8.697 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 8.70
TC = 0 ==> 1.00 u | $ 8.70
TC = 1 ==> 2.77 u | $ 24.11
TC = 2 ==> 6.16 u | $ 53.61
TC = 3 ==> 9.61 u | $ 83.59
TC = 4 ==> 13.12 u | $ 114.14
TC >= 5 ==> 16.00 u | $ 139.15
4) For TCX = -4
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.644 57.784 13.53 25147 6.31 39.77 916.33 2.066 10.913 1.000
1 - 12 5.431 75.193 13.53 19168 7.22 52.17 1041.02 2.425 9.606 1.000
1 - 16 6.964 90.086 13.53 16733 7.73 59.77 1165.28 2.725 8.582 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 8.58
TC = 0 ==> 1.00 u | $ 8.58
TC = 1 ==> 2.81 u | $ 24.08
TC = 2 ==> 6.25 u | $ 53.60
TC = 3 ==> 9.75 u | $ 83.69
TC = 4 ==> 13.30 u | $ 114.13
TC >= 5 ==> 16.00 u | $ 137.31
5) For TCX = -5
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.686 58.622 13.53 25293 6.29 39.54 932.29 2.093 10.726 1.000
1 - 12 5.501 76.162 13.53 19167 7.22 52.17 1054.42 2.457 9.484 1.000
1 - 16 7.048 91.052 13.53 16689 7.74 59.92 1176.25 2.757 8.502 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 8.50
TC = 0 ==> 1.00 u | $ 8.50
TC = 1 ==> 2.83 u | $ 24.08
TC = 2 ==> 6.31 u | $ 53.65
TC = 3 ==> 9.84 u | $ 83.63
TC = 4 ==> 13.43 u | $ 114.15
TC >= 5 ==> 16.00 u | $ 136.03
6) For TCX = -6
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.714 59.239 13.53 25439 6.27 39.31 944.83 2.113 10.584 1.000
1 - 12 5.533 76.653 13.53 19195 7.22 52.10 1061.99 2.474 9.416 1.000
1 - 16 7.105 91.768 13.53 16682 7.74 59.95 1185.24 2.781 8.437 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 8.44
TC = 0 ==> 1.00 u | $ 8.44
TC = 1 ==> 2.86 u | $ 24.09
TC = 2 ==> 6.36 u | $ 53.64
TC = 3 ==> 9.91 u | $ 83.65
TC = 4 ==> 13.54 u | $ 114.24
TC >= 5 ==> 16.00 u | $ 134.99
Conclusion: If we use a 1:12 spread we should go for a second hand at a TCX
of -4 and above. For 1:16 the TCX should be -6. Note that the
more we spread the lower the TCX is so, for a higher spread it's better to play
two hands all the time. Lower spreads also get TCXs higher.
Sincerely,
Cac
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