If the dealer's starting card is an ace, he will offer to play it safe. As noted in the Standard Blackjack chapter, insurance is nothing more than a side bet where you bet on the dealer's blackjack.
Whatever the "experts" tell you, this is a side bet and nothing more. And if so, insurance has nothing to do with the general line of play and the basic strategy described above is final.
But how do you respond to the dealer's offer?
If we follow the hypothesis of uniformity, the answer should be negative - insurance is not profitable. The dealer will receive blackjack if he receives a ten, i.e. with a probability of 4/13. By insuring, you will lose your insurance in 9 cases out of 13. In the remaining 4 cases, your winnings will be double your insurance. The odds are obviously against you: on average, you will lose 1/13 of the insurance.
There are casinos where the croupier offers to hedge not only on the ace, but also on the ten. This proposal makes no sense at all: the dealer will have a blackjack if he gets an ace - only in one case out of 13. The average loss with such insurance will be 10/13 of the insurance.
Source: https://stargambling.net/games/blackjack/
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