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Thread: Insurance Bet and Fluctuations

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    Insurance Bet and Fluctuations

    Hi Everyone:

    This is the first time I've posted on this forum.

    In my Gambling Theory book I argue that those strategies which increase expectation are usually accompanied by a higher standard deviation. However, this is not a hard and fast rule. Two examples where I know it doesn't hold are the ability to read hands well in poker and the surrender rule in blackjack. Both of these will increase your expectation and lower your fluctuations at the same time (which is nice).

    I'm now wondering about the insurance rule in blackjack. Assuming you're taking insurance at the appropriate times (according to the count) it will increase your expectation. But what does it do to the standard deviation?

    I have my opinion, but would like to hear what others think,

    Mason

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    About the insurance rule in blackjack, you will increase your expectation and decrease your deviation for shoe games.
    For infinite deck games, neither.

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    Quote Originally Posted by MMalmuth View Post
    Hi Everyone:

    This is the first time I've posted on this forum.

    In my Gambling Theory book I argue that those strategies which increase expectation are usually accompanied by a higher standard deviation. However, this is not a hard and fast rule. Two examples where I know it doesn't hold are the ability to read hands well in poker and the surrender rule in blackjack. Both of these will increase your expectation and lower your fluctuations at the same time (which is nice).

    I'm now wondering about the insurance rule in blackjack. Assuming you're taking insurance at the appropriate times (according to the count) it will increase your expectation. But what does it do to the standard deviation?

    I have my opinion, but would like to hear what others think,

    Mason
    Hi Mason,

    I enjoyed reading your book Blackjack Essays. I don't have any intuition about your question, but I can run a simulation in CVData. This simulation used 6 decks, 1 deck pen, Pennsylvania rules. Two players using the same Wong Halves (doubled tags) strategy. The "seat effect" is removed. Player 1 takes insurance at +7, whereas Player 2 never takes insurance.

    At the TCs below 7, they have the same standard deviation, but as the TC rises above TC 7, the player 1 who takes insurance has a relatively lower standard deviation than the player 2 who does not take insurance. Now what I don't get is that there is another standard deviation at the bottom summary which is larger for player 1.

    Mason Player 1.jpg


    Mason Player 2.jpg

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    Hmmm. I need to think about this. “Even Money” will reduce your sd, since now your payout is always 1 (I.e. 1 bet). Insuring a 20 reduces sd, since most of the time your payout +1/2 (instead of 1), or 0 instead of -1.

    But if you have a stiff hand, say 14, your payout will be zero instead of -1 about 1/3 of the time if he has BJ, but if he does not, your payout is most likely -1.5 instead of -1 if you lose the hand, and +0.5 instead of +1 if in the off chance you win. Sd is increased.

    So you have to look at insurance for all player hands to see if sd is increased or decreased overall. I don’t have the patience to do this, but I am a bit curious if insurance really reduces Sd, since it sure feels like it increases it.

    P.s. This might be nit-picking, but please don’t say, “opinion” when you are talking about math. You might be right, you might be wrong, but your opinion does not matter.

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    Random number herder Norm's Avatar
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    Unlike the summary, the SD per TC is not in dollars. The insurance player has a better EV. Therefore, the optimal bets are increased. This increases overall SD. Of course, it's SCORE that matters as it takes into account both EV and SD.

    Oh, and welcome to the site Mason.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Quote Originally Posted by Norm View Post
    Unlike the summary, the SD per TC is not in dollars.
    So if those standard deviations by true count are not calculated using dollars, what is being plugged into the formula?

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    Random number herder Norm's Avatar
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    The EV (IBA) of each round and the population size. Simple SD formula assuming that the same bet is always made at all TCs.

    Remember that to create optimal Kelly betting you need SD per TC. You cannot know what the SD is in $'s before you know the bet in $. Although, CVCX doesn't actually only use the Kelly formula as it isn't enough to support the simplification features and the fact that you can't bet in pennies and rounding after the calcs is inaccurate.
    Last edited by Norm; 01-19-2022 at 07:21 AM.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Random number herder Norm's Avatar
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    In answer to the original question, assuming you bet with the same ramp instead of Kelly optimal, the SD is lower for the insurance player. BUT, the difference is tiny. Running 25 billion hands each:

    No insurance SD/hour: $193.91
    Correct insurance SD/hour: $193.29

    This difference is so small, it might be reversed for another count.
    Last edited by Norm; 01-19-2022 at 06:06 AM.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Quote Originally Posted by Norm View Post
    In answer to the original question, assuming you bet with the same ramp instead of Kelly optimal, the SD is lower for the insurance player. BUT, the difference is tiny. Running 25 billion hands each:

    No insurance SD/hour: $193.91
    Correct insurance SD/hour: $193.29

    This difference is so small, it might be reversed for another count.
    Norm, is that for perfect insurance?
    Nice to see you here, Mr, Malmuth. I've also enjoyed your book.

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    Random number herder Norm's Avatar
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    That's for 6D HiLo using a +3 index. Using an insurance side count, it's $193.39. Insignificant difference.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Norm, HiLo sometimes overestimates the Ten Ratio and sometimes understimates the Ten Ratio
    It may err on both sides but I thought that overall it would be pretty much equal.
    Perfect insurance giving a slightly superior SD than HiLo, your sim seems to suggest that
    HiLo underestimates the Ten Ratio more often than it ovestimates it. Why is that?

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    Random number herder Norm's Avatar
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    Well, this will certainly be affected by the fact bets are different by TC. Also, any difference in a count's accuracy varies by depth, not even counting floating advantage. The most accurate answer to the OP's question, as with so many questions in blackjack, is: "it depends".
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    I agree with Norm, but there is some math involved that may help. First, and this is important and was also stated by Norm, if you want to do the comparison correctly, you would not be using the same bets at each true count, since the insurance player, with the greater overall advantage, would be making larger bets. This, in turn, is what accounts for the larger overall variance (s.d.) that you see in the bottom numbers. Long story short, if the game is played optimally, the insurance player has greater variance than the non-insurance player.

    But consider what happens at the first TC where insurance is involved (+7 in this case). If no insurance is taken, the average squared result of the hand is 1.131^2 = 1.279. If you make the same bet, which you shouldn't, but take insurance, then about 1/3 (slightly more) of the time, the dealer has blackjack and the average squared result of the hand is 0. But what happens when he doesn't have blackjack? You have now bet an extra 1/2 unit, and you lose both that and your original bet about half of the time. The average squared result is (-3/2)^2 = 9/4, and it happens 1/3 of the total time. The other 1/3 of the total time, you lose the insurance bet but win the main-hand bet, so the overall result is +1/2 unit, and the average squared result is 1/4. Adding, we get that, when you take insurance, the average squared result for the entire endeavor is the 0 from when the dealer has blackjack (1/3 of the time) + 1/3(9/4) + 1/3(1/4) = 5/6, which is lower than the normal average squared result for an uninsured hand.

    Again, the reason the bottom summary results show otherwise is because you're betting more for the game where insurance is involved.

    Don

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