Let's see what happen to the two-hand problem when adding one player to the table.
As I did before, I'll first show the following scenarios:
1) Playing one hand only (remember that there is another player at the table playing all the time)
2) Playing two hands all the time
Note: Speed is not considered.
Conditions: 6D,S17,DOA,DAS,SPA1,SPL3,NS,5/6,Hi-Lo,C22 floored, 5000 million rounds.
1) Playing one hand only
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 1.866 36.159 13.53 37570 5.16 26.62 700.86 2.142 14.268 1.000
1 - 12 2.781 46.546 13.53 28017 5.97 35.69 779.09 2.501 12.836 1.000
1 - 16 3.596 55.975 13.53 24225 6.43 41.28 871.20 2.823 11.478 1.000
Note that for 1:16 the betting pattern should be:
TC <= -1 ==> 1.00 u | $ 11.48
TC = 0 ==> 1.00 u | $ 11.48
TC = 1 ==> 2.90 u | $ 33.28
TC = 2 ==> 6.43 u | $ 73.77
TC = 3 ==> 10.04 u | $ 115.20
TC = 4 ==> 13.86 u | $ 159.12
TC >= 5 ==> 16.00 u | $ 183.66
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 3.774 59.854 13.53 25154 6.31 39.76 949.29 2.133 10.534 1.000
1 - 12 5.622 77.241 13.53 18879 7.28 52.97 1061.28 2.495 9.423 1.000
1 - 16 7.246 92.708 13.53 16368 7.82 61.09 1186.08 2.813 8.431 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 8.43
TC = 0 ==> 1.00 u | $ 8.43
TC = 1 ==> 2.92 u | $ 24.58
TC = 2 ==> 6.44 u | $ 54.30
TC = 3 ==> 10.10 u | $ 85.16
TC = 4 ==> 13.77 u | $ 116.11
TC >= 5 ==> 16.00 u | $ 134.90
So, two hands all the time is better than one hand.
Now, let again restrict our second hand to a particular TC. Say that our second bet will be placed only if the TC is greater than or equal to a certain TCX which will be determined by a trial and error process.
I'm going to examine optimal spreads lower than or equal to 1:16.
3) For TCX = 0
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.452 50.094 13.53 21055 6.89 47.50 726.86 1.836 13.758 1.000
1 - 12 4.940 65.015 13.53 17323 7.60 57.73 855.70 2.130 11.686 1.000
1 - 16 6.289 78.780 13.53 15692 7.98 63.73 986.83 2.398 10.133 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 10.13
TC = 0 ==> 1.00 u | $ 10.13
TC = 1 ==> 2.40 u | $ 24.34
TC = 2 ==> 5.39 u | $ 54.59
TC = 3 ==> 8.43 u | $ 85.38
TC = 4 ==> 11.40 u | $ 115.54
TC = 5 ==> 14.59 u | $ 147.80
TC >= 6 ==> 16.00 u | $ 162.14
4) For TCX = -1
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.573 52.275 13.53 21401 6.84 46.73 764.73 1.900 13.076 1.000
1 - 12 5.161 67.886 13.53 17303 7.60 57.80 892.97 2.214 11.199 1.000
1 - 16 6.627 82.607 13.53 15540 8.02 64.35 1029.76 2.508 9.711 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 9.71
TC = 0 ==> 1.00 u | $ 9.71
TC = 1 ==> 2.53 u | $ 24.56
TC = 2 ==> 5.58 u | $ 54.22
TC = 3 ==> 8.77 u | $ 85.15
TC = 4 ==> 11.93 u | $ 115.89
TC = 5 ==> 15.21 u | $ 147.75
TC >= 6 ==> 16.00 u | $ 155.38
5) For TCX = -2
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.665 54.351 13.53 21995 6.74 45.47 806.05 1.963 12.406 1.000
1 - 12 5.345 70.626 13.53 17463 7.57 57.27 933.30 2.296 10.715 1.000
1 - 16 6.934 86.452 13.53 15543 8.02 64.34 1077.80 2.617 9.278 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 9.28
TC = 0 ==> 1.00 u | $ 9.28
TC = 1 ==> 2.66 u | $ 24.66
TC = 2 ==> 5.86 u | $ 54.35
TC = 3 ==> 9.18 u | $ 85.14
TC = 4 ==> 12.51 u | $ 116.08
TC = 5 ==> 15.95 u | $ 147.97
TC >= 6 ==> 16.00 u | $ 148.45
6) For TCX = -3
play-all | rounds played = 100.00%
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 8 3.715 55.866 13.53 22619 6.65 44.21 840.20 2.009 11.902 1.000
1 - 12 5.461 72.676 13.53 17709 7.51 56.47 967.11 2.356 10.340 1.000
1 - 16 7.058 88.308 13.53 15655 7.99 63.88 1104.89 2.675 9.051 1.000
Note that for 1:16 the betting pattern on each hand should be:
TC <= -1 ==> 1.00 u | $ 9.05
TC = 0 ==> 1.00 u | $ 9.05
TC = 1 ==> 2.72 u | $ 24.62
TC = 2 ==> 6.00 u | $ 54.32
TC = 3 ==> 9.41 u | $ 85.18
TC = 4 ==> 12.84 u | $ 116.19
TC >= 5 ==> 16.00 u | $ 144.81
Conclusions: If we use a 1:8 spread we should go for a second hand at a TCX
of 0 and up. For 1:12 the TCX should be -1 and for 1:16 the TCX should also be -1.
Sincerely,
Cac
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