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Thread: Fuzzy Math: Cacarulo

  1. #11
    Fuzzy Math
    Guest

    Fuzzy Math: Re: Insurance

    > I do use the updated count -considering all
    > the cards lying on the table- and then
    > decide whether to insure the hand or not.
    > For me it's the same as any other CD play.
    > T6vT and 97vT both have different indices
    > and when we stand we expect the dealer to
    > bust in order to win. Why I would then stand
    > on one hand but hit on the other? See the
    > analogy?

    If you were dealt those two hands at the same time, you would not ever stand on the first one but then hit the second one -- each will play out exactly the same. Why should insurance be any different?

    Let's look at what insurance really is: You get to place a side bet which pays 2:1 if the dealer has a ten in the hole. If he does, then the money you lost on your hand is then paid back to you for winning the insurance betn You lose your initial bet if the dealer has a BJ regardless of insurance -- insurance is simply a side bet whose winning payout happens to be the same as the amount of your losing bet. If the dealer has a BJ less than 1 time in 3 that you insure, then you are losing money. A counter attempts to use his knowledge of the remaining cards to determine if this is a positive-EV bet to take. You are advocating that it will be a positive-EV bet on one of your hands, but negative-EV on another hand -- at the same time!

    The thing is that in making your decision you are considering the composition of one hand, but only the total (count-wise) of the other hand. Then you reverse the situation. This could be compared to getting dealt A/4 and hitting to get A/5/6/3 (hard 15) and then trying to use a C-D index for T/5 to make your decision. That index would account for one less five in the pack, but it still could be improved if you could also account for the missing six.

    And finally, I leave you with a puzzle: You are playing doubledeck and put out two bets with a RC of 7. You get dealt A/A on one hand, and T/T on the other. You are asked if you want insurance. There are exactly 52 cards remaining to be dealt/seen. The count has now fallen to 2. Your indices for 2D are .46 for A/A and 3.16 for T/T. What would you do to reconcile this large difference -- Does the insurance side bet yield positive-EV?

  2. #12
    Zenfighter
    Guest

    Zenfighter: Re: A few sd data

    For single deck play I?ve got these figures off the top:
     
    Generic index = 1.4

    T, 5 vs A Insurance if TC=>2.31254

    9, 6 vs A Insurance if TC=>0.82297



    The problem is that when you removed the 5 cards at the same time you get:

    Insurance if TC=>1.73515 so the dreams for an ?early insurance? for the 9, 6 hand seem to evaporate.

    Given that both hands belong to the same player the independence of effects is dubious at least.
    .
    Hope this helps, also.

    Sincerely

    Z

  3. #13
    Cacarulo
    Guest

    Cacarulo: Please, answer my "Moreover" post *NM*


  4. #14
    Cacarulo
    Guest

    Cacarulo: See my "Moreover" post please *NM*


  5. #15
    Cacarulo
    Guest

    Cacarulo: Re: Insurance

    > If you were dealt those two hands at the
    > same time, you would not ever stand on the
    > first one but then hit the second one --
    > each will play out exactly the same. Why
    > should insurance be any different?

    This is the problem. You play each hand independently of the other. You could hit one and stand on the other based on the CD indices.

    > Let's look at what insurance really is: You
    > get to place a side bet which pays 2:1 if
    > the dealer has a ten in the hole. If he
    > does, then the money you lost on your hand
    > is then paid back to you for winning the
    > insurance betn You lose your initial bet if
    > the dealer has a BJ regardless of insurance
    > -- insurance is simply a side bet whose
    > winning payout happens to be the same as the
    > amount of your losing bet. If the dealer has
    > a BJ less than 1 time in 3 that you insure,
    > then you are losing money. A counter
    > attempts to use his knowledge of the
    > remaining cards to determine if this is a
    > positive-EV bet to take. You are advocating
    > that it will be a positive-EV bet on one of
    > your hands, but negative-EV on another hand
    > -- at the same time!

    I'm not advocating that. I say that insuring one hand but not the other (based on the CD indices) will make more money (EV) in the long run. The other alternatives are:

    2) Insure both hands
    3) Don't Insure any hand

    In the long run option 1) will come ahead.

    OTOH, when the index shows positive-EV it has a variance associated. The positive-EV is an average in which sometimes we have positive-EV and sometimes we have negative-EV depending on the composition of the pack.

    Sincerely,
    Cacarulo

  6. #16
    Cacarulo
    Guest

    Cacarulo: Your puzzle

    > And finally, I leave you with a puzzle: You
    > are playing doubledeck and put out two bets
    > with a RC of 7. You get dealt A/A on one
    > hand, and T/T on the other. You are asked if
    > you want insurance. There are exactly 52
    > cards remaining to be dealt/seen. The count
    > has now fallen to 2. Your indices for 2D are
    > .46 for A/A and 3.16 for T/T. What would you
    > do to reconcile this large difference --
    > Does the insurance side bet yield
    > positive-EV?

    Let's forget about CD indices for a moment and get
    back to the traditional use of a single generic index (+2.38). Since the "updated" TC is now +2 we don't insure any of the hands. Correct?

    Now, say we know the indices for each particular hand (+0.46 for AA and +3.16 for TT). According to what I advocate for we should insure AA but not TT.
    Your position is that we should either insure both hands or don't insure any. Correct?
    Well, if your answer is YES then what do you propose to do based on the info that we have?

    1) Should we go by the generic index and DON'T INSURE any of the hands
    2) Should we go by the TT index and DON'T INSURE any of the hands
    3) Should we go by the AA index and INSURE both hands?

    Which decision is MORE correct? We don't have the index for AATT v A so we have to decide only on what we have (a pair of indices or a generic index).

    The index that we don't have is +1.11. So, if we knew this index apriori we would insure BOTH hands being that the correct decision.
    Aren't we better then insuring at least one hand rather than any?

    Sincerely,
    Cacarulo

  7. #17
    Fuzzy Math
    Guest

    Fuzzy Math: Re: Your puzzle

    I believe I understand your point now -- insuring only one hand in certain situations (that is, always following the C-D indices) would be better in the long run than simply going by the generic index in those situations.

    My point has simply been that this play is not optimal -- accurately considering both of your hands (or for that matter, any/all other hands since the last shuffle) would yield better long-term results than just using the single-hand CD indices.

    You could say that the generic index has an EV of X, your single-hand CD indices have an EV of Y, and considering the composition of more than one hand has an EV of Z. So X < Y < Z. You are discussing Y. I am discussing Z. Hopefully we each understand each other now.

  8. #18
    Cacarulo
    Guest

    Cacarulo: Re: Your puzzle

    > I believe I understand your point now --
    > insuring only one hand in certain situations
    > (that is, always following the C-D indices)
    > would be better in the long run than simply
    > going by the generic index in those
    > situations.

    Going by the CD indices is always better than going by the generic.

    > My point has simply been that this play is
    > not optimal -- accurately considering both
    > of your hands (or for that matter, any/all
    > other hands since the last shuffle) would
    > yield better long-term results than just
    > using the single-hand CD indices.

    And I agree that it's not optimal but as I said we don't have those indices (Z) and we don't want them either. We have Y that is better than X.

    > You could say that the generic index has an
    > EV of X, your single-hand CD indices have an
    > EV of Y, and considering the composition of
    > more than one hand has an EV of Z. So X < Y < Z. > You are discussing Y. I am discussing Z.
    > Hopefully we each understand each other now.

    We do now

    Sincerely,
    Cacarulo

  9. #19
    Cacarulo
    Guest

    Cacarulo: Re: A few sd data

    > For single deck play I?ve got these figures
    > off the top:
    > Generic index = 1.4
    > T, 5 vs A Insurance if TC=>2.31254
    > 9, 6 vs A Insurance if TC=>0.82297

    > The problem is that when you removed the 5
    > cards at the same time you get:
    > Insurance if TC=>1.73515 so the dreams
    > for an ?early insurance? for the 9, 6 hand
    > seem to evaporate.
    > Given that both hands belong to the same
    > player the independence of effects is
    > dubious at least.

    My figures are:

    Generic = 1.416667
    T5vA = 2.357333
    96vA = 0.840136
    T596vA = 1.770213

    which are very close to yours.
    Now, say the current TC is +1.5. If we go by the generic, we insure both hands (note that the correct choice would be to don't insure any of the hands).
    Going by the CD indices we would insure only one hand (96). So we lose less than with the generic.

    If the count were +2 the generic would be doing a good job but overall the CD indices are better.

    Sincerely,
    Cac

  10. #20
    Fuzzy Math
    Guest

    Fuzzy Math: Re: A few sd data

    Since insurance calculations are purely linear based simply on the ratio of tens, it occurs to me that each card known to the player can have a constant value used in calculating the proper index.

    I'll use the 2 deck data:

    A,A vs A = +0.46
    A,Z vs A = +1.02
    A,L vs A = +1.53
    T,T vs A = +3.16
    T,A vs A = +1.76
    T,Z vs A = +2.36
    T,L vs A = +2.86
    Z,Z vs A = +1.58
    Z,L vs A = +2.09
    L,L vs A = +2.60

    Each ace that the player sees lowers the index by about 1.0 (which I will refer to as -1.0). Z is -.4, T is +.4, L is about +.1

    We can then look at the chart this way (with all numbers rounded for simplicity -- we'd like to be able to use this at the table):

    Generic Index = +2.38 (+2.4)

    A,A vs A = +0.46 (2.4 - 1.0 - 1.0 = +0.4)
    A,Z vs A = +1.02 (2.4 - 1.0 - 0.4 = +1.0)
    A,L vs A = +1.53 (2.4 - 1.0 + 0.1 = +1.5)
    T,T vs A = +3.16 (2.4 + 0.4 + 0.4 = +3.2)
    T,A vs A = +1.76 (2.4 + 0.4 - 1.0 = +1.8)
    T,Z vs A = +2.36 (2.4 + 0.4 - 0.4 = +1.4)
    T,L vs A = +2.86 (2.4 + 0.4 + 0.1 = +2.9)
    Z,Z vs A = +1.58 (2.4 - 0.4 - 0.4 = +1.6)
    Z,L vs A = +2.09 (2.4 - 0.4 + 0.1 = +2.1)
    L,L vs A = +2.60 (2.4 + 0.1 + 0.1 = +2.6)

    One immediate application of this is that we can learn just those four numbers as opposed to all 10 indices.

    Secondly, I would infer that this formula would continue to hold true with more than two cards. If the player had A/A and T/T, he would calculate an index of (2.4 - 1.0 - 1.0 + 0.4 + 0.4 = 1.2). The index that you had calculated for this scenario was 1.1, so it seems that this method has worked fairly well. The player in my example would then correctly insure both hands with the count being 2.

    The main problem I see with continuing this past 2 cards is that rounding could skew the results (this insurance-count is a balanced count though, so the rounding errors should mostly cancel out). If there are any other issues that I didn't think of, please correct me.

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