Change in blackjack odds

A recent blackjack rule change at a couple Vegas casinos, reported in Business Insider: a “natural” blackjack (that is, being dealt two cards that sum to 21) will now pay out at 6:5 odds instead of 3:2. For those not familiar with blackjack: in blackjack, an ace can count as 1 or 11, and 10, jack, queen, or king all count as 10. So to get 21 you have to be dealt one of the eight pairs

(A, 10), (A, J), (A, Q), (A, K), (10, A), (J, A), (Q, A), (K, A).

There are 169 possible pairs (I’m ignoring the issue of sampling with or without replacement, or alternatively working with a shoe with infinitely many decks), so the odds of being dealt a natural blackjack are 8 in 169. The payout on a bet of 1 goes from 1.5 to 1.2, so this raises the house edge by (0.3)(8/169) = 1.42%. Given the typically narrow house edge in blackjack, that’s quite a change – certainly more than I expected from hearing it until I did the math.

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