This situation happened to me awhile back but it's an interesting puzzle. I'd also appreciate any commentary or advice on handling similar situations.

Dealer has an Ace up, then fumbles the hole card so that the table can see that he has an 8, 9, or 10. I didn't take insurance. What kinds of hands must I have? The puzzle's not that difficult but it's intriguing.

I didn't really know what other kinds of hands would also decline insurance, but would appreciate any thoughts, as well as what to do if let's say the dealer has a 9 or 10, or 50% chance of blackjack.