Blackjacked!

5 March 2023

By John Grochowski

QUESTION: Blackjack offers insurance only when the dealer has an Ace face up, and it pays off when the dealer has a blackjack. Why not when the dealer has a 10-value face up? Regardless of whether the dealer has Ace up and 10 down or 10 up and Ace down, it's still a blackjack.

ANSWER: The odds of the dealer having a blackjack are far different with a 10 up than with an Ace up.

In a single-deck game, if the dealer has an Ace up, 16 of the other 51 cards in the deck are 10 values that would complete a blackjack. That's 31.4 percent of the remaining deck.

If the dealer has a 10 value up, only four of the other 51 cards, or 7.8 percent, are Aces.

Make it a common six-deck game instead, and if the dealer starts with an Ace, 96 of 311 cards, or 30.9 percent, are 10 values. If the dealer starts with 10, 24 of 311 are Aces, or 7.7 percent.

That makes the odds against the dealer completing a blackjack when starting with an Ace about 2.18-1 with one deck or 2.24-1 with six decks.

Winners are paid at 2-1, and that just wouldn't do if insurance came with a dealer 10 up. In that circumstance, odds against a dealer blackjack are 11.82-1 with one deck or 11.99-1 with six.

The 2-1 payoffs on insurance make a nice neat package. Insurance bets are half the size of your blackjack wager, so if you lose a blackjack bet and win an insurance bet, you break even. The math also works out so that if you insure a blackjack, a win on insurance and a push on your hand would result in a payoff of even money on your blackjack bet. That's why players who want to insure blackjacks can just call "even money," take their payoffs and finish their hands.

There would be no such neat package for insurance bets with dealer 10s. Payoffs would need to be 11-1 or so, while still leaving an edge to the house.

As it is, the gap between odds of winning and payoffs is large enough that most players should never take insurance. Odds do constantly change as cards are dealt and removed from play, so card counters who know at more than a third of remaining cards are 10 values are in profitable territory to take insurance.

The math would change on an insurance bet on 10s. We don't know for sure what payoffs would be until someone tries it, but you could count on a large house edge.


QUESTION: I play 8-5 Double Double Bonus Poker on a nickel Triple Play/Five Play machine. I like the five-hand game.

A situation comes up a lot. I'm dealt something like a pair of 7s and a high card. Do I hold the 7s or the high card? Does it change if the high card is an Ace?

ANSWER: Regardless of whether an Ace is involved, a low pair is a much stronger starting position than a high card. You'll have a higher percentage of winning hands with the high card but more hands that bring payoffs larger than your bet if you hold the low pair.

Dealt 7-7-5-9-Jack of mixed suits in 8-5 DDB, your average return is 3.62 coins per five wagered if you hold 7-7, and only 2.17 if you keep the Jack and trash the rest. Change the Jack to an Ace, and averages are 3.62 on 7-7 and 2.35 on the Ace. Keep the low pair and hope for the best.