7410sb said:
Is it ever a good idea to take even money when you have a BJ and the dealer is showing an ace?
Sometimes.
(1) Taking even money is the same as taking insurance. If dealer has BJ (4/13 of the time), you push your main bet (0) but win the insurance bet (+1). If dealer doesn't have BJ (9/13 of the time), you win your main bet (+1.5) but lose your insurance bet (-0.5).
(2) Taking insurance is generally a sucker's bet. (4/13*1-9/13*0.5)/0.5 = -0.076, or 7.6% house edge.
(3) That being said, taking even money is often useful for reducing variance. If you don't take even money, you will get paid 9/13*1.5-4/13*0 = +1.04, or 4% more than even money, in the long run. However, sometimes you will get paid 0. If you have a large bet (relative to your bankroll) out and you get a blackjack, you might want to give up a little in order to be sure of a win.