Taking Insurance in Blackjack
Insurance in blackjack is a side bet that the dealer has a 2-card total of 21. It seems like a no-lose proposition. You only put up half of your initial bet, and if the dealer has a blackjack, you win 2 to 1 on the insurance bet. This “cancels out” the loss on your initial bet. Mathematically, though, the right way to look at insurance is as a completely separate bet and decides whether it’s a positive expectation bet or not. You only get to take insurance when the dealer’s face-up card is an ace. This means the insurance bet pays off if the dealer’s face-down card is a 10.
What’s the probability of winning the bet, then? You have 52 cards in the deck, and those, 16 are worth 10 points. This makes the probability of the dealer having a 10 as her face card 16/52, or 30.77%. We will round that up to 31% for purposes of examining whether the bet is a positive expectation bet or not. Now assume you make this bet 100 times for $100 each, and you get mathematically perfect results.
You will win $200 on 31 of those bets, for total winnings of $6200. You will lose $100 on 69 of those bets, for total losses of $6900. This result in a net loss of $700 over 100 hands, or an average loss of $7 for every $100 you bet. That’s a house edge of 7% for this bet. In a game where the house edge overall is less than 1%, placing a bet where the house has an edge of 7% is foolhardy at best. Taking insurance is always a mistake unless you are counting cards and the deck is rich in 10s. Even then it’s a mistake, because it’s a tip-off to the casino that you are counting cards.