Understanding Blackjack Insurance Strategy

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Insurance is a move available to the player in many variants of online blackjack games. The move functions in this manner. If the dealer’s face up card is an ace then the player can take insurance if he wants to. If the player exercises this option then he places one half the amount of his wager in the area marked as insurance. If the dealer has a ten value card as his hole card and thus gets a blackjack then the player receives a payout of 2 to 1 on his insurance bet. Since he then loses his original wager he ends quits. If the dealer does not have a blackjack then the player loses the insurance bet and the play continues.

All blackjack guides state that the insurance bet is a losing proposition. For most blackjack players this piece of advice is the end of the matter. When asked during the game if they would like to take insurance they say no and get on with the game. However there are blackjack players, especially the mathematically minded ones, who have a desire for understanding why the insurance bet is a bad bet. This article explains the working using a few simple examples.

Consider a one deck game. 3 cards out of the 52 are revealed at the time the insurance move is to be made. The dealer’s face up card is an ace, and 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. Therefore the probability of the insurance bet winning is 16/49 or 0.327. If the insurance bet was for $1 the payout on winning will be $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. If the insurance bet loses then the player loses his wager of $1. Hence the expected payout on losing is (-1 x 0.673), which -$0.673. Hence net expectation is ($0.654 - $0.673), which is -$0.019. Since the net expectation is negative the player will expect to lose money on this bet in the long run.

A similar calculation can be carried out to show that the situation worsens when the player is dealt 2 ten value cards. There are 49 cards left in the deck, out of which only 14 are ten value cards. Therefore the probability of the insurance bet winning is 14/49 or 0.286. If the insurance bet was for $1 the payout on winning will be $2. Hence the expected payout on winning is (2 x 0.286), which $0.572. Out of the 49 cards 35 do not have a value of ten. Therefore the probability of the insurance bet losing is 35/49 or 0.714. If the insurance bet loses then the player loses his wager of $1. Hence the expected payout on losing is (-1 x 0.714), which -$0.714. Hence net expectation is -$0.142, which is considerably worse than in the previous case.

Similar calculations can be done for multi deck games and the outcome will be the same.

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