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Thread: Insurance Bet and Fluctuations

  1. #27
    Random number herder Norm's Avatar
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    No. It affects overall EV and SD, and therefore the main bets if you are betting optimally. Read the OP's question. The overall result of a strategy is what matters.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  2. #28
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    You are right. The original question is vague. It’s not a question a mathematician would ask.

  3. #29
    Random number herder Norm's Avatar
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    Ridiculous.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  4. #30


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    A few references might prove useful. Start with Grosjean, Beyond Counting, pages 11-12.

    But, the definitive work on everything having to do with insurance, risk aversion, variance, etc., is Michael Canjar's (MathProf) 32-page authoritative study on the subject:
    https://www.bjrnet.com/archive/AdvancedInsurancePlay_MichaelCanjar.pdf


    There's little point in discussing seat-of-the-pants stuff when such a compelling work exists.

    Don

  5. #31


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    Hi Everyone:

    I'm just getting back to this and thanks for all the replies. I'll work my way through them and if I have any comments I'll post them.

    Best wishes,
    Mason

  6. #32


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    Quote Originally Posted by Mr. Ed View Post
    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.

    Hi Mr. Ed:

    My inclination, when you put everything together, is that properly taking insurance is that properly taking insurance will lower the standard deviation.

    Best wishes,
    Mason

  7. #33


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    Quote Originally Posted by Norm View Post
    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.
    Hi Norm:

    You're correct in that the right way to look at a gambling problem is to take into account the relationship between EV and SD. However, if the EV goes up and the SD goes down, then it's a no-brainer.

    Best wishes,
    Mason

  8. #34


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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.

    This is an interesting result. If the SD would have been much smaller, it would imply that for players on a small bankroll that for survival purposes it would be correct to also take insurance in situations where the bet was still slightly negative. This result says no to that idea.

    Best wishes,
    Mason

  9. #35
    Random number herder Norm's Avatar
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    Small bankroll is always a problem and other rules, penetration, and decks will obviously affect this. Insurance is a valuable index for funded players. But these days, positive EV on an Insurance bet for a typical game available with a small bankroll is something like 1 in 200 hands. So the value to a small bankroll player who may be playing at a high risk of ruin may not be that valuable.

    Now we get to what kind of player. If the player with a small bankroll is attempting to build a bankroll (good luck), risk aversion is important and session sims would probably suggest Insurance, possibly even at a slightly lower index. If the small bankroll is replenishable, perhaps not. If the player just wants to enjoy himself for a time and has budgeted his bankroll, up to him. Devil is in the details.

    Of course, you can also look at which hands you insure. But, if it is a small bankroll player, probably better to not add any additional rules.

    Just had a bottle of wine with my trout and will look over my response in the morn.
    Last edited by Norm; 01-20-2022 at 06:03 PM.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  10. #36


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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.
    Hi Norm:

    I've been away from blackjack for some time. So let me clarify something you wrote. When you say "you bet with the same ramp instead of Kelly optimal" what kind of bet spread are you using, and how is this different from Kelly Optimal?

    Mason

  11. #37


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    Quote Originally Posted by MMalmuth View Post
    Hi Norm:

    I've been away from blackjack for some time. So let me clarify something you wrote. When you say "you bet with the same ramp instead of Kelly optimal" what kind of bet spread are you using, and how is this different from Kelly Optimal?

    Mason
    Whatever the spread, it's the same for both players in Norm's sim, whereas, if the insurance player were betting optimally, he'd be betting more than the non-insurance player, because he has a greater overall advantage by virtue of insuring when it's correct to do so. Those larger bets would, in turn, lead to a greater s.d. than the one for the non-insurance player, provided both bet optimally.

    Don

  12. #38
    Random number herder Norm's Avatar
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    Basically, if your playing strategy is improved with the same betting levels (i.e. it has a higher SCORE or balance between EV and SD), then your risk of ruin drops. So, you can increase your betting, and consequently EV, while bringing your risk back to the level of the inferior playing strategy. More money, same risk.

    Now, you mentioned buying Insurance at a different index than one that maximizes EV. That's where risk-averse indices come in. These maximize the balance between EV and SD. With Insurance, the index could vary by the hand as that could reduce SD as you've pointed out. Canjar's paper, linked to by Don, covers all this. Academically valuable as someone had to delve into the subject. But, I've never thought it mattered enough to warrant the increase in complexity.

    As for the small bankroll player. I suppose his aversion to risk matters. Gamblers generally like risk. Smaller bankrolls also mean less betting flexibility. It's more difficult to bet optimally with a smaller bankroll, and rules are commonly less favorable.
    Last edited by Norm; 01-21-2022 at 04:29 AM.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  13. #39


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    Now, you mentioned buying Insurance at a different index than one that maximizes EV.
    Not considering other factors which affect strike point, is there an available graph that displays % EV captured by True Count. I would be especially interested in either Hi Lo or Halves.

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