pair bonus?

This casino has pair bonus, if you get a pair in your first 2 cards it pay 10:1. However if dealer gets blackjack when you get a pair it pays 40:1. what is the house edge of this bet?

Consider an infinite deck game. The probability of a pair is 1/13; that of a blackjack is 8/169. Therefore, the probability of a dealer blackjack and a player pair is (1/13) x (8/169); that of a dealer non-blackjack and a player pair is (1/13) x (161/169).

Using these numbers, we get the house edge of 4.5%.