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Modern Blackjack nth Edition

Fractional Insurance Index

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Nearly everyone uses integer indices these days as attempting to use indices like +1.4 provide little additional gain. This isn’t just because indices aren’t that sensitive. It is also because such theoretic indices aren’t even correct. The advantage over increasing counts for a decision is not a simple linear relationship. A decision may make sense at a count of 1.3 and 1.5 but not 1.4. When we focus in more closely and look at the advantage chart between two integer counts, we no longer see a smooth curve; but see a choppy mess.

Griffin tells us that there is an exception. Insurance is the only linear play in Blackjack. This is because insurance is based on a very simple relationship between tens and non-tens, does not depend on dealer draws, and does not depend on multiple player draws. So, some percentage of players do use non-integer indices for insurance. For example, we are told that the HiLo insurance index for double-deck is +2.4.

So, what is the floored insurance index for HiLo double-deck? Oddly, it is +3, not +2. The problem is that insurance is only linear theoretically. For a human, it is not linear. This is because humans do not calculate true count using the exact number of cards remaining. Instead, they typically estimate the remaining cards in increments of quarter, half or full decks. This estimation method destroys linearity.

Below is a chart of theoretic true counts. The x-axis is un-dealt cards. The y-axis is the true count. The lines are running counts of 5 through 50. For example, the red line is a running count of +5. With 13 cards remaining, the true count is 20. 5 divided by one-fourth remaining decks. What we see are nice smooth lines.

The second chart is the same, except that we estimate remaining cards by quarter-decks. The smooth lines are gone. We now have jerky lines. Linearity is gone when we calculate true counts as a human calculates them. If the linearity is gone in this calculation, then linearity must also not exist in the indices.

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Updated 04-25-2012 at 04:53 AM by Norm

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  1. Three's Avatar
    I sometimes keep a count of the cards played as long as I can. It is low priority and gets dropped a lot because I am not focused enough to be accurate on that count, but I find myself extrapolating the equations to determine TC while I have an exact number of cards played to get a linear curve. Is this something I shouldn't be doing. It is not really done consciously but math just flows in my brain so it is natural to use all information available. If I know the exact number of cards played is this predisposition to extrapolate exact fractional surplus of aces in particular and TC as well? I mean if you expect to have seen 5.5 aces you know you will not have seen that half of an ace. I always assumed the true curve is smooth and only becomes stepped from the way people implement the math.
  2. Norm's Avatar
    If it comes natuarally, why not? I have a chart somewhere that shows the gain from exact count of the cards. No idea where. But, it's not great unless you can find a well-dealt single-deck game.
  3. stopgambling's Avatar
    So ,what should we do??If I buy insurance at approximately tc 2.4 -3 .Would i be making some costly mistakes then??
  4. Norm's Avatar
    No, that's fine.
  5. simple man's Avatar
    In "close call" insurance situations, I tend to base my ultimate decision upon the strength of my hand. For instance: the TC is roughly +5.3 to +5.6 (using Omega II), and the published Ins. index is, of course, +6 (although, for many games, the non-RA CVDATA-generated index is +5), and my hand is stiff - say, 15 (7,8). In this instance I feel, strangely, quite comfortable NOT insuring - positive TC, a hand likely to break, my reluctance to potentially "take my own ten" - while on the other hand, were I to hold 20, or even 19, I would certainly and pointedly place my insurance bet.

    My question consists of two parts: (a) Is there any logic to considering hand strength in addition to a "close" index for an insurance decision? And, (b) If allowed, is insuring for less at all logical? (Perhaps a sort of "dynamic" insurance bet, as a function of the range of distance between the TC and the index, as well as the strength [EV] of the hand?)

    Thank you for your time, and I appreciate any help and/or insight you might be willing to provide.
  6. Norm's Avatar
    The answer to both questions is that there are risk-aversion aspects involved. If you are taking insurance, the count is high, and that means you probably have a large bet out, and Insurance increases the money on the table. MathProf investigated this in detail some years back. Personally, I don't think the calculations are worth the rouble, but have never studied it myself. I'd rather use cover considerations when using partial insurance.

    I should add that insuring all Blackjacks serves both the purposes of cover and reduced variance.
    Updated 05-02-2012 at 07:37 AM by Norm
  7. simple man's Avatar
    Thank you for the expedient and helpful response, Norm.

    I was actually hoping for the very answer you provided. Insurance, to me, is an important "tool" that is often under-utilized, misunderstood, and/or overlooked entirely by many otherwise capable players. The statement about insuring naturals for cover and reduced variance supports such a claim, in addition to opening my eyes to supplemental cover tactics in general. (It had never occured to me before now to take even money as a cover play. Actually, until now, I narrowly viewed cover as simply an occasional strange play, or - gulp! - an odd bet, in addition to the acting and interpersonal aspects, of course.)

    I am wondering what you meant, precisely, in stating, "I'd rather use cover considerations when using partial insurance." Does that mean you wouldn't partially insure? Can you elaborate, please?

    Again, thanks for your time, knowledge and help, Norm. Much appreciated!
  8. Norm's Avatar
    See Modern Blackjack pages 141-143. The last page mentions using Partial Insurance for cover.
  9. Three's Avatar
    If it is a positive EV bet take full insurance. If it is not you are insuring for cover or risk aversion on a good hand like 20 or BJ. This is were it makes sense to partially insure. For strickly cover insure for a small fraction of your bet.
  10. Blackriver's Avatar
    Tthree, I know you like learning obscure nuances to improve your edge (ive even tried finding middle ground on the 7ish counting)but from a biological perspective your taxing your brains oxygen and glucose to do things. I imagine these are nearly reflexive and internalized now that might even require MORE effort to unlearn in the short term, but I think it's worth it.

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