Online Blackjack Insurance Strategy Dissected
Added: March 8, 2018
Insurance is a move available in many variants of online blackjack games. The move comes into play when the dealer’s face up card is an ac. The player has the option of placing the insurance bet. The bet amount is fixed at half the amount of his regular wager. If the dealer has a ten value card as his hole card then he gets a blackjack then the insurance bet wins with a payout of 2 to 1.
Let us look at this bet with an example. The player has bet AU$10. The dealer’s face up card is an ace. The player opts for the insurance bet and wagers AU$5. If the dealer has a blackjack then the player wins AU$10 on the insurance bet. He will lose the AU$10 on the main bet (unless he also has a blackjack) and end up quits. If the dealer does not have a blackjack then the payer will immediately lose the AU$5 insurance bet and the result of the AU$10 regular bet will be decided as usual.
Whether or not the player should opt for the insurance bet will depend on the probability of the dealer getting a blackjack after he is dealt an ace as the face up card. The probability for a single deck game in which the player is not dealt any ten value card is calculated as follows. After the first three cards are dealt (two to the player and one to the dealer) there are 49 cards left, out of which 16 are ten value cards. Therefore the probability of the dealer getting blackjack and the insurance bet winning is 16/49 or 0.327. The probability will decrease marginally as the number of decks is increased. It will decrease by a fair amount if the player is dealt one or two ten value cards. Literature takes 0.31 as the average probability and we will work with that.
The insurance bet was for AU$5. The payout on winning will be AU$10. The probability of winning is 0.31. Hence the expected payout on winning is (10 x 0.31), which AU$3.10. The probability of the insurance bet losing is (1 – 0.31), which is 0.69. If the insurance bet loses then the damage is AU$5. Hence the expected payout on losing is (-5 x 0.69), which -$3.45. Hence net expectation is (AU$3.10 - AU$3.45), which is -AU$0.35. Since the net expectation is negative the player will lose money on this bet in the long run. Even if you carry out the calculations with the most favourable probability of 0.327, the net expectation will be negative.
So the optimum insurance bet strategy is never to place this bet.