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Originally Posted by Aaron W.
CE? Cash equity? I'm not sure what you mean here.
Certainty Equivalent. Let's say there's a pool of 1,000,000 people. 999,999 will be healthy and 1 will be inflicted with a rare medical issue that will cost $1,000,000.
The EV of the pool is -$1, but depending on the ability of each individual to absorb $1,000,000, it is almost always "worth it" for everyone to pay a little more than $1 into a pool and let the insurance company take a small cut in order to reduce the uncertainty for everyone.
If you're the sole earner in a family with a lot of dependents and nobody else who has your earning potential, the loss of your life (however improbable) ends up being devastating for your family, and you can rationally pay more than your EV for the certainty.
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Why would you take blackjack insurance when it's -EV?
Same reason.
Let's start with a simple example, heads you win 10c, tails you lose 5c, or you can take 1c in certain winnings. EV = 2.5c, so you flip the coin and everyone who takes the certain money is stupid, right?
Not so fast - multiply the stakes by 100,000x and see what happens. Heads you win $10,000, tails you lose $5,000, or you can take $1,000. Depending on your ability to eat a few tails flips, you may rationally take the $1,000 even though it leaves over half of your expected value on the table.
Blackjack insurance is the same. It's EV+ a tiny fraction of the time, but even when it's EV-, it's possible that the amount of money you have at risk - say a large bet at TC +3.5 (insurance becomes positive at +4, IIRC) - is worth locking up rather than gambling for a little more.
The math is complicated. And it depends on your bankroll and risk tolerance and a bunch of other assumptions. And sometimes the answer is take insurance and other times the answe is don't take it, but what is definitely true is that if you always or never take insurance, there's a near certain chance you don't know as much as you think.
And of course, I say "near certain" instead of certain because I can think of one example where you'd always take insurance - by Wonging in and out at TC +4, often as the gorilla - and one example where you'd never take it, as the spotter for the gorilla. In that case, both players are playing optimally even while doing the opposite thing.
I'm just pointing out that the self-made analysts are often grossly overestimating their ability to analyze things past some superficial level, and that often the easiest way to arrive at the best answer is to ask someone who knows (despite all the pitfalls of that).