Should you buy insurance at 0 EV?

[aceside]

I actually am not so sure about the math here. I post to consult experts here. Let me try another method for this calculation:

If we bet 2/3 unit on the main game blackjack, the variance=(2/3) x1.3;
if we bet 1/3 unit on the side bet insurance, the variance = (1/3) x2.
Therefore. The combined variance of betting both is
(2/3) x1.3 +(1/3) x2= 1.53

Still greater. We need a mathematician here!

[Old new guy]

We need a mathematician here!

Wow….

[Norm]

Washington Post, 25 October 1911, "Nor would a wise man, seeing that he was in a hole, go to work and blindly dig it deeper."

[iCountNTrack]

Washington Post, 25 October 1911, "Nor would a wise man, seeing that he was in a hole, go to work and blindly dig it deeper."

Norm you killed me with this hahahaha

[aceside]

A couple of problems here. Firstly, this forum is becoming smaller. I’ve tried to raise a point of discussion but nobody wanted to say anything.


Secondly, I'll get a “no” helpful on whatever I say. There are only a few posters here, so it is easy to tell who input these. This often leads to negativity on this forum. I strongly recommend you remove the “no” option to the question “do you find this post helpful.”

[Norm]

The problem is that you post nonsense. Seriously. If you have a question, fine. But, stop making up math.

[21forme]

Norm - He had 30 days to think about what he's been doing wrong, ignoring your warnings, and nothing has changed. Maybe more time off will help (though I doubt it).

[aceside]

Do not focus on me. I am just a beginner AP posting to social. I have no interest of fighting anybody here.

[DSchles]

Then here's a suggestion: Ask a question and wait for expert answers. Don't make up your own answers. Or, write something along the lines of: In trying to determine the answer, this is how I would go about it. Can someone verify if my math is correct?

Don

[Norm]

Excellent suggestion.

[aceside]

How come putting more money(insurance wager) on the table decrease the variance? I can't figure out the logic.
I think it is an illusion that insurance wager is related to the original wager. Whether taking insurance or not won't affect the EV of the original bet.

For example:
I bet $100, dealer's upcard is an Ace.
There are exactly 50 tens and 100 non-tens remaining unseen.
The original wager of $100 is either lost(dealer has a ten underneath), or played out, regardless of the insurance bet.
Here comes the opportunity to place an insurance wager of $50, which literally means if the dealer has a ten, I win $100, and if the dealer doesn't have a ten, I lose $50.

In this situation, the insurance bet is simply a 2 to 1 payout bet, with 33.3% win rate, and zero EV.
How come adding such a wager decrease the variance?
A 1 to 1 payout bet with 50% win rate has a smaller variance than 2 to 1 payout bet with 33.3% win rate;
A 2 to 1 payout bet with 33.3% win rate has a smaller variance than the lottery ticket (huge payout, tiny win rate).
Flipping coin(1 to 1 payout, 50% win rate) definitely has a smaller variance than lottery ticket.

I agree with what the OP said here. In some later posts, people discussed the covariance between the main game blackjack and the side bet insurance. I believe the covariance here is zero.

Of course, nothing is absolute. In some rare deck situations, we might see otherwise. Right? This notion of reducing variance by taking insurance has been discussed here earlier, and I participated in this discussion too. It’s actually not very meaningful to compare different variance values, because EV and variance come up in pairs and they need to be compared as a whole pair too. We mostly care about positive EVs.

[aceside]

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
Don

I just thought about this again. What you said here makes sense, meaning there is a non-zero covariance between the main bet and the insurance bet. How to calculate this covariance? I’d like to learn this part.

[Gronbog]

Don asked me if I could run a simulation, collecting data on the situation where the EV of taking insurance is exactly zero. That is, when the number of unseen tens remaining is 1/3 of the number of unseen cards at the time of the insurance decision. He wanted to confirm his intuition that, even though more money is being put into play, the variance would still be lower when taking insurance than when not taking it.

I had to write a bit of code to gather the information for this rather specific situation, but that's one benefit of having one's own software. In the interest of a quick implementation, I used a direct brute force approach in which a "normal" simulation would be run and the software would detect the situation described above and collect separate data when it occurs. In this way, data for the situation is collected as it naturally arises with no attempt to create representative deck compositions and penetrations.

Because the OP asked about a 6 deck game, I chose 5/6 S17 DAS SPL3 as the rule set. The simulation was 10 billion rounds which resulted in 13,017,078 samples for the situation where the EV of taking insurance is exactly zero. That means that this situation only occurs about 0.13% of the time. This is rare enough to render this a theoretical issue as opposed to a practical one.

For not taking insurance, the initial bet advantage (IBA) was -37.48% with variance of 0.8189.

For taking insurance in this situation, the IBA was again -37.48% (as expected since the EV of the insurance decision is zero) and the variance was 0.737.

Don can sleep tonight knowing that his intuition was correct.