Understanding Blackjack Insurance Bet

• Published: November 23, 2018
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Insurance is an option offered to players in many online blackjack variants. The move becomes available when the dealer’s face up card is an ace. It preys on the fear of the novice player that now the dealer will reveal a 10 value hole card and win. Therefore the careless blackjack player will go for the insurance bet. He will have to place one half the amount of his regular wager as the insurance bet. If the dealer ultimately ends up with a blackjack then the player receives a payout of 2 to 1 on his insurance bet. If the dealer does not have a blackjack then the insurance bet loses.

This fear of the player is unfounded. The standard and unconditional optimum strategy in this regard is to ignore the insurance bet. When the dealer is dealt an ace face up and the prompt message asks if the player would like to take insurance, he should click No and get on with the game. The simple explanation is that the payout on the insurance bet is not sufficient to cover the probability that the dealer gets a blackjack. However, if you are a mathematically minded blackjack player, you may want a more detailed understanding of why the insurance bet is a bad bet. The number crunching for a simple example is given below.

Consider a one deck online blackjack game. 3 cards out of the 52 are revealed at the time the insurance bet is offered and the dealer’s face up card is an ace. The player stakes $1 as the insurance bet. For further simplicity, let us assume that there are no ten value cards dealt to the player. The insurance bet will win if the dealer’s hole card is a ten value card. There are 49 cards left, out of which 16 are ten value cards. The probability of the insurance bet winning is 16/49 or 0.327. The payout on a winning insurance bet is 2 to 1, so the player will win $2. Hence the expected payout on winning is (2 x 0.327), which $0.654. Out of the 49 cards 33 do not have a value of ten. Therefore the probability of the insurance bet losing is 33/49 or 0.673. In this event the loss is $1 and the expected payout is (-1 x 0.673), which is $0.673. Hence net expectation is negative and the player will lose money on the insurance bet in the long run.