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Thread: Should you buy insurance at 0 EV?

  1. #40
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    Quote Originally Posted by Dog Hand View Post
    I believe the coefficient of Z in the first term should be 8/3, since it is 4/3+4/3.
    Thanks DH. I was pretty sure someone would catch a mistake somewhere in there if they took the trouble to check. My brain woke up slowly today.
    Quote Originally Posted by Dog Hand View Post
    In this case, the X² coefficient might in fact be positive. Since X (the wager) is much larger than Y (the EV), would that change your result?
    I makes it more likely but I think Z is far less than .50. I still the first addend it is negative.

  2. #41


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    Quote Originally Posted by DSchles View Post
    The problem with the above discussions is that they don't seem to take into account the correlation between the two wagers. Rather, they treat them as separate, independent wagers, which they aren't, for the purpose of variance. That is, if you win your insurance bet, you must, of necessity, either lose or tie your main bet. And, of course, if you lose your insurance bet, you may win or lose your main bet, and we know that to be a somewhat 50-50 proposition, once the dealer has verified that he doesn't have a natural. So, for example, losing your insurance bet but then winning the hand are offsetting outcomes (the result is +0.5 of a wager), as is winning the insurance bet and losing the primary hand (net of zero).

    It is in this context that you have to calculate the overall effect on total variance of insuring. To understand, suppose I make an even-money wager on team A for the game between team A and team B. Variance is 1. Now I make a second wager on team B. You tell me that variance is also 1, so this adds to my overall variance. But, of course, it doesn't, because the two wagers are -100% correlated, meaning that, by definition, I must win one and lose the other, guaranteeing a result of zero and zero variance.

    Don
    You're right, it's a good example, they shouldn't be treated separately.
    I tried to consider the main bet and the insurance bet as a whole, then I came up with the conclusion that when the Insurance bet has exactly 0 EV, the overall risk is the same, so it doesn't matter whether to take the insurance.

    Player's Action Ten Underneath Probability Effect on Total Wager Non-ten Underneath Probability Effect on Total Wager B*C+D*E
    Take Insurance 1/3 0 2/3 -0.5 (1/3)*0+(2/3)*(-0.5)=0.33
    Don't Take Insurance 1/3 -1 2/3 0 (1/3)*(-1)+(2/3)*0=0.33

    Does this make any sense?

  3. #42
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    Quote Originally Posted by San Jose Bella View Post
    You're right, it's a good example, they shouldn't be treated separately.
    I tried to consider the main bet and the insurance bet as a whole, then I came up with the conclusion that when the Insurance bet has exactly 0 EV, the overall risk is the same, so it doesn't matter whether to take the insurance.

    Player's Action Ten Underneath Probability Effect on Total Wager Non-ten Underneath Probability Effect on Total Wager B*C+D*E
    Take Insurance 1/3 0 2/3 -0.5 (1/3)*0+(2/3)*(-0.5)=0.33
    Don't Take Insurance 1/3 -1 2/3 0 (1/3)*(-1)+(2/3)*0=0.33

    Does this make any sense?
    I think Don meant to consider the covariance between the two wagers. Total variance must factor in covariance. 1/3rd of the time you win the insurance bet and covariance is the max negative it can be and total variance is 0. When you lose the insurance bet covariance on bad hands is high but on good hand it is also most likely negative. When you insure a BJ total variance is 0. This covariance relationship is the basis of RA insurance.

  4. #43
    Senior Member Joe Mama's Avatar
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    Quote Originally Posted by Dog Hand View Post
    Joe Mama,

    You are incorrect.
    Not the first time, nor will it be the last time.

  5. #44


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    Quote Originally Posted by Joe Mama View Post
    Not the first time, nor will it be the last time.
    Babe Ruth was the home run king. He was also a strikeout leader.

  6. #45


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    Back to the original topic, if I may. There's a fascinating anecdote on p 236 and 237 of The Theory of Blackjack in which the player is betting a perfect Kelly bet, dividing his 41% edge on the next hand by 1.77 and betting exactly 23% of his entire bankroll on the next hand. He's dealt a natural with dealer showing Ace. Insurance is a negative expectation, but he attempts to insure for less (39% of his original bet). The floor tells him his choice is full insurance or nothing, so he takes even money.

    I don't fully understand the math behind this play, but my understanding was that by taking insurance, he reduced his EV slightly (32% of the deck was 10s) in exchange for reducing his volatility a lot.

    This makes logical sense to me - every bet we make is a compromise between more EV and less volatility. Insurance is a separate bet but has covariance with your main bet. Taking insurance when you have a BJ or another good hand, even at 0 EV or less than 0, may be the optimal strategy in a situation like this.

    Anyone else read that anecdote that can dumb down the math a bit for me?

  7. #46


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    Plain English: Sometimes it's worth making a negative expectation bet if it sufficiently reduces your variance compared to not making the play. Insuring a natural with a large bet guarantees an even money payoff -- therefore ZERO variance. You WILL get paid. Not insuring has a higher expectation, but comes with the risk of pushing and therefore not winning anything at all.

    The proper play in such a situation may be to bet a portion of the full insurance amount -- and that was the case in Griffin's example -- but to make things more interesting, he stipulated that partial insurance wasn't permitted. Hence, the lesser of two evils was to take the even money.

    How many of us with a quarter of a million dollars bet can say that we'd do otherwise?! :-)

    Don

  8. #47


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    That brings up another question I have: are there some doubles or splits whose added EV isn't worth the additional variance?

    I'm picturing something like this: you have a high count, large bet out, and you're dealt 8 v. 6. Best EV is to double, but this increases your variance.

    Similarly, suppose you're dealt 14 v. T with hi-low TC of +2 - surrender index is 3, so EV is best if you hit. But if you surrender, you reduce variance in exchange for very little EV.

    Is there some kind of formula for determining how much EV to "spend" on decreasing variance? I'm assuming there is, and that Griffin used it for that example.

  9. #48


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    Quote Originally Posted by DSchles View Post
    Plain English: Sometimes it's worth making a negative expectation bet if it sufficiently reduces your variance compared to not making the play. Insuring a natural with a large bet guarantees an even money payoff -- therefore ZERO variance. You WILL get paid. Not insuring has a higher expectation, but comes with the risk of pushing and therefore not winning anything at all.

    The proper play in such a situation may be to bet a portion of the full insurance amount -- and that was the case in Griffin's example -- but to make things more interesting, he stipulated that partial insurance wasn't permitted. Hence, the lesser of two evils was to take the even money.

    How many of us with a quarter of a million dollars bet can say that we'd do otherwise?! :-)

    Don
    Can't say until it happens.

    Also, welcome back!

  10. #49


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    Quote Originally Posted by Optimus Prime View Post
    That brings up another question I have: are there some doubles or splits whose added EV isn't worth the additional variance?

    I'm picturing something like this: you have a high count, large bet out, and you're dealt 8 v. 6. Best EV is to double, but this increases your variance.

    Similarly, suppose you're dealt 14 v. T with hi-low TC of +2 - surrender index is 3, so EV is best if you hit. But if you surrender, you reduce variance in exchange for very little EV.

    Is there some kind of formula for determining how much EV to "spend" on decreasing variance? I'm assuming there is, and that Griffin used it for that example.
    Interesting question. Your various reference books which give you tables, eg, Wong’s Professional Blackjack, will quote you strike points for numerous index plays. This includes both splits and doubles. These strike points are designed as EV maximizing doubles and splits.

    You specifically mentioned 8v6, but did not mention true count, so let’s deal with that. Basic 8v6 is hit. EV maximizing is double at plus 1. That is the strike point. All of your doubles at plus 1 will capture a smidgen over 50% of EV. Risk Averse doubles captures a far greater percentage if EV. RA for 8v6 is true 3. That captures, let’s say, 70% if EV. Too valuable to ignore.

    Players on shoe string bankrolls should practice RA strategy. Strong bankrolls, such as mine, will practice a combination of EV maximizing and Risk averse plays. Most, not quite all, of my risk averse plays are used for cover purposes, such as 8v6, as that frequency of occurrence is high enough to allow the pit additional data to pick me off.

    You also mentioned 14v10. My normal game is ES10, so, surrender is basic. Because of its frequency of occurrence, I choose to hit any single unit bet. This “error” is very low cost. In your case, surrender is obviously late surrender. I would tend to hit on late surrender at true 2, though you can certainly sim your preference, calculate the cost of this deviation, and make your best decision for yourself. There is a cost, but I would think fairly minor at true 2.

    Though it sounds counter intuitive, you can make more money using Risk Averse. The reasoning here is that reduction of variance by splitting or doubling at higher tc’s Versus strike point, you have 5he ability to increase max bet.

  11. #50
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    Quote Originally Posted by Optimus Prime View Post
    That brings up another question I have: are there some doubles or splits whose added EV isn't worth the additional variance?
    This is dependent on bet size relative to your BR and/or your risk tolerance. On bigger bets you want to be picker about being over the index rather than at the index. On little bets you can chase that extra penny with little affect on variance. Some plays by chance have a small increase in EV at the index because of the decimal index value. While other plays start with a reasonable increase in EV. Then some plays increase EV fast after the index is exceeded while other plays gain EV slowly after the index is exceeded. This is dependent on your count so to some degree it is count specific. I don't use Hilo so I assume my advice may not be the best for your count.

    I like to give up some EV on the riskier plays with a big bet out by waiting until the index is exceeded. Many just like to generate the most EV rather than worrying about the affects of higher variance when you have your biggest bets out. I generate plenty of EV and would like a more certain BR growth. But that is me. There is no right or wrong answer to this. With a big bet out I give up a little EV to surrendering early on crappy hands, I am more cautious about certain doubles and splits, and I insure good hands slightly below the index and poor hands slightly above the index. Remember you don't have to take full insurance. Each of these give up a little EV for lower variance and more certain BR growth. Many APs prefer to damn swings, variance, and certainty of BR growth to generate as much EV as possible. It is just a matter of personal preference.
    Quote Originally Posted by Optimus Prime View Post
    Is there some kind of formula for determining how much EV to "spend" on decreasing variance?
    See BJA3 pages 370-377.

  12. #51


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    "See BJA3 pages 370-377."

    Damn. You should be worried; you're starting to sound like me! :-)

    Don

  13. #52


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    Quote Originally Posted by DSchles View Post
    "See BJA3 pages 370-377."

    Damn. You should be worried; you're starting to sound like me! :-)

    Don
    Not only that, the resemblance is shocking.

    https://youtu.be/FuZI_7nZbJE

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