To expand a little on Gronbog's response, I'll provide some numerical examples that may help to clarify the point.
1. Suppose you bet $10 on your hand, and you receive anything but a natural. The dealer's upcard is an ace. You take insurance for half of your bet, or $5. Now, there are two possibilities: 1. The dealer doesn't have blackjack. In that case, you immediately lose your $5 insurance bet and the hand continues, the same as if nothing had happened. (Of course, you lost your $5.) 2. The dealer does have a blackjack. In that case, you lose your original $10 bet, but your $5 insurance bet is paid at 2 to 1, so you win $10 there. Net result? You break even, hence the somewhat erroneous concept that you have "insured" your hand and prevented a loss.
2. Now, suppose that your hand IS a natural, and the dealer shows an ace. If you insure, again, there are two possibilities, but interestingly, whether the dealer has a natural himself or not, the result is the same: you win even money, or, in this case $10. Why? Again, you have two cases. 1. The dealer doesn't have blackjack. In that case, you immediately lose your $5 insurance bet but you also immediately get paid 3 to 2, or $15, for your natural. Net result? You win $10. 2. The dealer does have a blackjack. In that case, you push your original $10 bet, but your $5 insurance bet is paid at 2 to 1, so you win $10 there. Net result? You win $10 again. Since your original wager was $10 and, by insuring, you guarantee a $10 win no matter what, you can simply state, "Even money" and get paid that certain $10 without actually going through the motions of placing the insurance bet. (Note that, although I haven't been there in a while, in A.C., it used to be that you couldn't just voice "even money" in that manner; stupidly, you actually had to physically put the insurance wager on the table.
Clear?
Don
