Easy Insurance Question in Blackjack

[DCWildcat]

I'm generally pretty bad at this kind of thing, so I've probably made some ugly mistakes. If anyone could check my reasoning and math on this, it'd be great.

This is trying to show why taking insurance when you have blackjack is not optimal. For those of you who don't play blackjack, insurance is essentially a side bet offered every time the dealer has an A as an upcard. If you take insurance, you get paid 2 to 1 every time the dealer ends up with blackjack, and you lose the bet when they don't. You can only insure up to half your original bet.

This assumes a 6 card deck, heads up, first hand of the deck.

First, your EV of not taking insurance: With 3 cards exposed, there are (6)(52)- 3 = 309 cards in the denominator. Of those, there are (6)(16)-1 = 95 cards left that can make the dealer blackjack. Thus, your EV for a 1 unit bet is

EVno insurance = (1.5)(214/309) (95/309)(0)
EVno insurance ~ 1.039

If you take insurance for the full amount (.5 units), you'll make 1 unit regardless of what you do:
1) If the dealer has blackjack, you push (no profit) on your original bet, but win 2 to 1 on your insurance half-bet, therefore winning 1 unit profit. This will happen with the same probability it happened above, 95/309 = .307443.
2) If the dealer does not have blackjack, you win 1.5 units for your blackjack but lose your insurance half bet, for a total of 1 unit profit. This will happen the majority of the time, or 214/309 = .692557

Therefore, since not taking insurance results in a better EV, insurance should not be taken, and the cost is ~.039 units of profit every time it is taken.

[TomTom]

Sklansky Talks Blackjack covers this (of course!)

Basically, your hand is completely irrlevant to an insurance bet. Insurance is a total misnomer.

You're simply betting the dealer's downcard is a 10. If it pays 2:1 then you need a better then 2:1 chance he has such for the bet to be +EV.

Unless you're counting you'll never have those odds.

[Gridder406]

This is only true if one is not card counting. Using the basic high-low system, the EV becomes positive to take insurance when the true count becomes +3. However, this blows your cover if you win too many insurance bets but that is a different beast all together. The CCCafe (card counting cafe) on Yahoo's groups has tons of info for card counting and other advantage play.

[Shroomy]

There is even a "perfect" insurance count that only counts 10's vs non 10's its worthwile if you are team playing.