Insurance pays 2.2 to 1

I received the following question from a reader:


There is a current policy involving Blackjack payouts and insurance at my casino. When a player has a natural 21 and betting a 50¢ piece they are paid $1 opposed to 75¢ due to not having 25¢ cheques. Also when a player has a bet of say $5.50 and they insure for $2.50 and win the insurance bet they are paid the 2-to-1 as well as keeping the 50¢ cheque of their initial blackjack bet since they, due to the lack of 25¢ cheques, cannot insure for full. The question I pose to you is with this policy how much does this cut into the house edge on Blackjack?

The first scenario the reader states refers to a 50 cent wager on blackjack, where the casino pays $1 instead of 75 cents on a player-blackjack. This is the same as blackjack paying 2-to-1. Excluding blackjack-blackjack ties, on a double-deck game a blackjack will occur once every 21.68 hands. Therefore the player will win an extra 25 cents once per 21.68 hands, for a net profit of 0.9032 cents per hand (less than a penny). The player’s net profit will be 90.32 cents per 100 hands because of this rule.

On a $5 game, if the player wagers $5.50 per hand and is paid $8 on a blackjack ($7.50 on the $5 wager and $1 on the 50 cent wager), then as I showed above, the player will win an extra 90.32 cents per 100 hands. Assume a house edge of 0.50% on the base game. Then the house edge on the main game will cost the basic strategy player who is wagering a flat $5.50 per hand (100)x($5.50)x(0.005) = $2.75 per 100 hands. By refunding 90.32 cents, the player will lose a net $1.85 per 100 hands. This effectively reduces the house edge to 0.33%. In other words, the house still has the edge.

As for your insurance question, in this case the player’s cards don’t matter. The player is simply considering a bet that the dealer has a ten-valued card in the hole when he shows an Ace up. In this case, according to your question, casino policy pays $5.50 on a $2.50 insurance bet. This is the same as insurance paying 2.2-to-1. In this case, the house still has an edge on the insurance bet of 0.583% in a double-deck game. Taking insurance gives no advantage to the player.

insurance pays 2.2 to 1
Neither of these situations allows the basic strategy player to gain an edge over the house and therefore would not be targeted by APs.