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Is Insurance a Good Bet?

Wednesday 23rd June 2010

When you play blackjack you have a number of options or decisions to make based on the run of cards, one such decision is whether or not to take insurance.

The name "insurance" is misleading, because you are not insuring anything. You are making a side-bet on whether or not the Dealer has a ten value card as his face down card. The Dealer must make the insurance offer before looking at his down card, so he has no idea what is there when he takes the insurance bets.

You make an insurance bet in an amount up to one half of your initial wager in the betting square. Insurance pays off 2 to 1. For example, if you originally bet $10, and the Dealer has shown an Ace up, you could bet up to $5 in the insurance semicircle. If the Dealers card turned out to be a 10, you would lose your original $10 bet, but your insurance bet of $5 would win the $10 back. If the dealer does not have a ten as the face down card, you lose your $5 and play on; the hand continues in the normal fashion.

Insurance is a sucker bet for the average player. Some so called "smart bettors" insist that you always insure if you hold a natural 21 against a Dealers Ace up. They reason that if the Dealer also has a natural, you can't lose. For example, if you have bet $2 you can insure for $1. If the Dealer has a natural, your normal $2 bet is lost, but the $1 insurance wager pays off 2 to 1, winning the original $2 back. But if the Dealer does not have a natural, you lose your $1 insurance bet. The question is: does the Dealer have ten under his Ace often enough to risk justifying another dollar? The answer is no!

If you ignore any cards that have been played (which is the basic strategy assumption), the odds of the Dealer having a ten down card can be calculated exactly. There are fifty-two cards in the deck, sixteen of which have the value of ten, thirty-six cards are therefore non-10s. Three cards are visible to you, your Ace, the Dealers Ace, and your 10. So there are 49 unseen cards in the deck, fifteen of which are 10s and thirty-four of which are non-10s. Here are the long-term results of this situation:

15 hands dealer has 10 down x $2.00 payoff = $30.00 won

34 hands dealer has non-10 down x $1.00 bet lost = $34.00 lost

=$4.00 net loss

The problem is that in his situation, the payoff for an insurance bet is won fifteen times every forty-nine hands, while you are betting it will happen fifteen times every forty-five. This four-hand difference accounts for your net loss. The best possible insurance situation you can face without tracking the cards is still a loser.