Insurance to lower volatility

I've read that one reason someone might take insurance is to reduce the variance in Blackjack since it's not correlated with the main bet. So always taking insurance raises the house edge by about 30 basis points. But I just ran a calculation and the standard deviation came out .02 higher always taking insurance. Can someone explain how this reduces variance ?

taking insurance ALWAYS get you even money if you have a BJ
Variance is zero.
So the phrase "to reduce variance" only applies when you have a BJ.

if you are not having a BJ then you are betting 3:1 that the hole card is a 10. that's why the variance is higher.

Your insurance bet isn't directly correlated to your blackjack bet, but both bets are correlated to your bankroll. This will increase bankroll variance because you're betting more. Anytime you're betting more you'll see more variance (your standard deviations will grow). As you correctly pointed out always taking insurance is a horrible idea and as was also pointed out would take away the BJ players biggest advantage: the 3:2 on blackjacks.

I've said it before and I'll say it again, it is *not* true that BJ has high variance as a game. Card counters experience high variance because of the bet spread they employ.

Don't agree with me? Sorry, this is a known value. The standard deviation is 1.15 [varies depending on rules] according to the Wizard. https://wizardofodds.com/gambling/house-edge/

Generally speaking, this means that notions to decrease the variance are generally misplaced; the recreational flat-betting BJ player desperately needs more variance - yet players come up with ideas all the time to reduce it, like not doubling each and every time it is recommended.

Taking Insurance will reduce Variance for Hands that you are likely to win if the dealer does not have BJ, like 20 v A.
And it will increase Variance for Hands that you are likely to lose if the dealer does not have BJ, like 17 v A.

A quick calculation shows variance for 20 v A dropping from around 0.85 to 0.27 AND
For 17 v A increasing from around 0.46 to 0.61

Without insurance your possible outcomes are 1,0,-1.
With insurance they are 0.5, 0 , -0.5, -1.5

With Bad Hands the effect of the -1.5 (ie delear wining without BJ) has more effect on increasing variance as it is more likely.

Quote: Romes

Your insurance bet isn't directly correlated to your blackjack bet.

The insurance bet is directly correlated to the BJ Bet.
If the 10 comes, that is 30% of the time the dealer will have BJ and your BJ bet will lose and the insurance bet win. (of course depending on your hand the BJ bet will lose additionally to this 30%)
Say in a rich 10 remaining decks this prob increases to 40%, then the above 30% increases to 40% for both BJ and insurance bet.
For the event of a 10 coming the correlation is 100% (1 wins and 1 loses 100% of the time)

And there is correllation if the 10 does not come. Then the Insurance bet loses 100% of the times and the BJ bet wins a high % of the time (which is higher for better hands like 20). The corellation is not 100%, it is less than 100%, but there is corellation.

I’m wondering how to calculate the combined variance between the Blackjack main bet and side insurance bet. Let’s use a 6-deck, Hit-17, double-after-split, no surrender, and no aces-re-split game as an example. Wizard has posted the expected value (EV) and Variance of this main game, as follows:

EV = -0.628%; Variance = 1.346.

If taking insurance with one unit of bet, these insurance numbers are

EV = -7.395%; Variance = 1.921.

However, insurance bet amount in blackjack is 0.5 unit only, so with this restriction, the variance of a 0.5 unit bet on insurance becomes

Variance_0.5 = 1.921/4 =0.480.

If a player takes insurance whenever it is available, what is the combined variance per hand of playing both? Just to remind, a player takes insurance only 1/13 of the hands, so the variance should be averaged over all main bet hands.

Thank you in advance!

Quote: aceside

I’m wondering how to calculate the combined variance between the Blackjack main bet and side insurance bet. Let’s use a 6-deck, Hit-17, double-after-split, no surrender, and no aces-re-split game as an example. Wizard has posted the expected value (EV) and Variance of this main game, as follows:

EV = -0.628%; Variance = 1.346.

If taking insurance with one unit of bet, these insurance numbers are

EV = -7.395%; Variance = 1.921.

However, insurance bet amount in blackjack is 0.5 unit only, so with this restriction, the variance of a 0.5 unit bet on insurance becomes

Variance_0.5 = 1.921/4 =0.480.

If a player takes insurance whenever it is available, what is the combined variance per hand of playing both? Just to remind, a player takes insurance only 1/13 of the hands, so the variance should be averaged over all main bet hands.

Thank you in advance!
link to original post

You basically have to calculate it from scratch. The splits and doubles make it difficult to back out. This is because (for example) changing a result from +2 to +1.5 has a bigger effect on variance than changing a +1 to a +0.5.

I’m so glad you are interested in this topic of history. The ultimate goal of this calculation is to find the covariance between the main and insurance bets. Toward this goal, I have to calculate a combined variance when assuming they are completely independent, as a first step.

Actually, let me provide a calculation first. Consider playing 13 hands of the main game, one of which includes an insurance side bet. So, the total variance of these 13 hands is

Variance_total = 1.346x13+1.921/4=17.978.

Therefore, the variance per hand of playing both is

Variance_per hand = 17.978/13=1.383.


Is this correct? Please check!

For practical use (no calculations) I recall it was Snyder who came up with an insurance scheme for counters, and if you take insurance on anything but a minimum bet it provides cover, it provides insurance, and the loss in EV compared to a precise insurance index using a typical single parameter count is negligible.

Quote: AutomaticMonkey

For practical use (no calculations) I recall it was Snyder who came up with an insurance scheme for counters, and if you take insurance on anything but a minimum bet it provides cover, it provides insurance, and the loss in EV compared to a precise insurance index using a typical single parameter count is negligible.
link to original post

There’s also one (I forget which book) to always take even money on BJ as a cover play.

If taking insurance every hand, the new EV becomes

EV_per hand = (-0.00628x13-0.07395x0.5)/13=-0.00912 = -0.912%.

That’s a drop from the original -0.628%.