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Thread: Cacarulo: Optimal way of playing two hands (w/one other player at the table)

  1. #1
    Cacarulo
    Guest

    Cacarulo: Optimal way of playing two hands (w/one other player at the table)

    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

  2. #2
    chgobjpro
    Guest

    chgobjpro: Question

    Rules change. Many houses now play H17. Would that one change affect the conclusion about when to go back to 1 hand?

  3. #3
    Cacarulo
    Guest

    Cacarulo: Re: Question

    > Rules change. Many houses now play H17. Would that one
    > change affect the conclusion about when to go back to
    > 1 hand?

    Probably no but as you've seen the solution to this type of problems requires a lot of sims. Unfortunately, we cannot use one sim to determine the optimal entry point as we do with wonging problems.
    However, you cannot be so wrong using a TCX between [-1,-3]. After all, it's better than playing two hands all the time.

    Sincerely,
    Cac

  4. #4
    Zenfighter
    Guest

    Zenfighter: Re: Very interesting

    Very creative work and let me personally thank you for posting these essays here.

    From a practical point of view, I am afraid the stuff is not going to be of great value especially for U.S. players, where the general awareness regarding card counting techniques is high and the paranoia tend to arise pretty quick, That is, it is simple not worth the risk to change the numbers of hands played along any given session, sometimes because you are not going to be allowed to do this (nmse), and others because you will be spotted with easiness as an advantage player, without even having to check this fact with the surveillance department.

    But the World is ample and there a lot of places where doing this, as well as jumping bets, won?t raise any eyebrows at all.

    Again, congrats for this interesting comparative research.

    Sincerely,

    Zf


  5. #5
    Hunch Back of Black Jack
    Guest

    Hunch Back of Black Jack: Re: Optimal way of playing two hands (w/one other player at the table)

    > 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 1.00 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 1.00 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 1.00 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 1.00 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 1.00 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 1.00 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

    What is the reasoning behind placing a second bet in a negative situation? Is it because:

    1. You eat negative cards?

    2. Once you drop a hand you cannot go back to two?

    If number 2 is the reason then at some point you should still drop the second hand because if deep in the shoe and negative at some point the money invested in the second hand is wasted because the shoe won't come back to positive and allow the second hand to be bet in a positive situation.

    An example, I can see no reason to play 2 hands the last hand of the shoe if not positive expectation?

    Another question
    It appears that the decision to play two hands over one hand when playing all is correct even if you have to bet double table minimum? I assumed a $5 table minimum, so you would have to bet a minimum of $10 on two hands.

    Thank you for your time

  6. #6
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Optimal way of playing two hands (w/one other player at the table)

    > What is the reasoning behind placing a second bet in a
    > negative situation? Is it because:

    > 1. You eat negative cards?

    Yes.

    > 2. Once you drop a hand you cannot go back to two?

    No.

    > If number 2 is the reason then at some point you
    > should still drop the second hand because if deep in
    > the shoe and negative at some point the money invested
    > in the second hand is wasted because the shoe won't
    > come back to positive and allow the second hand to be
    > bet in a positive situation.

    It's not the reason.

    > An example, I can see no reason to play 2 hands the
    > last hand of the shoe if not positive expectation?

    Right.

    Don

  7. #7
    Cacarulo
    Guest

    Cacarulo: Answered by Don *NM*


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