Peter A. Griffin analyzes the cost of insurance on a good blackjack hand as card counting camouflage.
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Blackjack Insurance on Good Hands Part II

 
Peter A. Griffin analyzes blackjack insurance and card counting camouflage
 
ANALYSIS & THEORY OF BLACKJACK
Blackjack Strategy Insure a Good Hand? Part I
    By Marvin L. Master
The Easiest Professional Level Card Counting System Excerpt from Beat the 6-Deck Game
    How to Use Frequency Distributions to
    Determine Your Win Rate and
    Fluctuations
    By Arnold Snyder
Best Opportunities Right Now for Blackjack Players The Hi-Lo Lite and Rounding Indices:
    Why All Those Index Numbers Card
    Counters Have Been Learning For
    Years Never Really Mattered
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How Professional Gamblers Win How True is Your True Count?
    By Arnold Snyder w/ Dr. John Gwynn Jr.
Card Counting Reality Blackjack Side Counts
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Blackjack Strategy The "Best" Card Counting System
    By Arnold Snyder
Card Counting Reality The "Best" Card Counting System:
    A Comparison of the Red Seven, KO,
    and Hi-Lo Counts (And How Blackjack
    Systems Are Best Compared)
    By Arnold Snyder
    with computer sims by John Auston
Blackjack Strategy Surrender: When It Pays to Say
    "Uncle!"
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Blackjack Strategy Algebraic Approximations of Optimum
    Blackjack Strategy (Revised)
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Blackjack Strategy Man vs. Computer: Does Casino
    Blackjack Differ from Computer-
    Simulated Blackjack?
    By Dr. John M. Gwynn, Jr. and Arnold
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Card Counting Reality Ruffled by the Shuffle
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Blackjack Strategy Shoehenge…Probing the Multi-Deck
    Mysteries
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Card Counting Reality Improving Your Insurance Decisions:
    The Victor Insurance Parameter
    By Rich Victor
Blackjack Strategy So You Think You're A Blackjack
    Expert?
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Card Counting Reality Late Surrender & Blackjack Statistics
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Blackjack Strategy Bad Player at the Blackjack Table:
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    By Arnold Snyder
Card Counting Reality The Blackjack Insurance Bet
    By Arnold Snyder
 
 

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Blackjack Insurance on Good Hands May Be A Good Idea After All

By Peter A. Griffin
(From Blackjack Forum Volume VIII #2, December 1988)
© Blackjack Forum 1988

[Note from Arnold Snyder: In the December issue of Blackjack Forum (Vol. VII #4), Marvin L. Master conjectured that if your card counting system indicated that the insurance bet was dead even, it may be advisable to insure a "good" hand, since this play would tend to reduce fluctuation. Marvin's logic is clear. If the dealer does have a blackjack, then you will lose a bet you expected to win. Taking insurance would save this bet on one third of these hands, and on those hands where the insurance bet loses, you still expect to win your initial "good" hand. Thus, bankroll fluctuations are reduced.

Here now, to lay this controversy to rest, is Peter Griffin's final word on whether and when you should take insurance on "good" blackjack hands. More probably, this article will give nightmares to players who consider attempting to work out Griffin's insurance formula when playing.

Griffin shows that it is sometimes advisable to insure good hands—in order to reduce fluctuations—even when the insurance bet has a negative expectation! Unfortunately, most dealers only allow a couple of seconds for the insurance decision. So, the simplest answer is: Marvin was right! Insure your good hands when it's a dead even bet.]

Marvin L. Master asks the question: Should you, to reduce fluctuations, insure a good hand when precisely one third of the unplayed cards are tens?

The answer depends upon what criterion for "reducing fluctuations" has been adopted. Griffin, in his monumental epic The Theory of Blackjack, shows that there are occasions when a Kelly proportional bettor would insure a natural with less than one third of the unplayed cards being tens.

Theoretically, this criterion could also be used to analyze whether to insure 20 and other favorable holdings. However, the answer is dependent upon both the fraction of capital bet and the distribution of the non-tens remaining in the deck.

An approximate calculation based upon what would seem a reasonable assumption in this regard suggested that 20 should be insured, but 19 not. Precise probabilities for the dealer were not computed, and the answer could well change if they were, or if a different fraction than assumed were wagered.

Another, more tractable, principle to reduce fluctuations also appears in The Theory of Blackjack: When confronted with two courses of action with identical expectations (the insurance bet here is hypothesized to neither increase nor decrease expectation), prefer that one which reduces the variance, hence average square, of the result.

This proves particularly easy to apply here. Let W, L and T stand for the probabilities of winning, losing, and tying the hand assuming insurance is not taken. In this case the average squared result is

ENx2 = 1 - T

If insurance is taken the average square becomes

EIx2 = 1/3 02 + W(1/2)2 + T(-1/2)2 + (L-1/3)(-3/2)2 = (W + T + 9L - 3)/4

Insurance will have a smaller average square if

W + T + 9L - 3 < 4 - 4T

Equivalently

W + 5T + 9L < 7

Or, subtracting

5(W + T + L) = 5

4L - 4W < 2

L - W < .5

L < W + .5

This will clearly be the case for player totals of 20, 19, 18, 11, 10, 9 and 8 if the dealer stands on soft 17. If the dealer hits soft 17, 18 would probably still be insurable, but not 8.

Returning to the Kelly criterion, the interested reader would be well advised to consult Joel Friedman's "Risk-Averse" card counting and basic strategy modifications. Among Joel's astute observations is that if a player confronts an absolute pick 'em hit-stand decision he should hit rather than stand. The reason is that he thereby trades an equal number of wins, (+1)2, and losses, (-1)2, for pushes, (0)2, thus reducing fluctuation. ♠


For complete information on the game of blackjack, from the value of each card, to the best strategy for insurance and surrender, to the history of the game and its players, see Arnold Snyder's Big Book of Blackjack.

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