Blackjack Insurance: Should you make this bet?

From: Casino Player

by Stephen W. Custer, PhD
The count was high and I had two $90 bets out. I was dealt 20 on the first hand, 14 on the second and the dealer showed an ace.

She started to check her hole card.

“Wait a minute. I want insurance,” I said.

“I didn’t think you took insurance,” she said.

“Only when I have a big bet.” She nodded as if this made sense. I pushed the two stacks of chips, one green and four red, in front of my original bets.

“Insuring the fourteen too?”

“Yep, both of them.”

Insurance is a side bet offered by most casinos. As with all side bets, it’s a house bet. It’s strictly a bet for novices and the faint of heart. Experienced players know not to take it. That’s why the dealer was surprised when I asked for it. The opportunity had presented itself several times earlier and I had turned it down.

It is simply a side bet on whether the dealer has a 10 in the hole. If she does, the bet pays 2-to-1. It is only offered when the dealer shows an ace.

The casino allows you to bet up to half your original bet. That way, if the dealer has a 10, the insurance pays 2-to-1, but you lose your original bet. The net is break-even. It is called “insurance” because most players think of it as a way of insuring that they don’t lose money on a good hand. It is common to hear a player say, “I only insure nineteen or twenty.”

As with much blackjack wisdom, this is wrongheaded. Whether insurance is a good or a bad bet has nothing to do with the value of your hand. It makes just as much, or just as little, sense to insure a 14 as it does a 20. Whether you win or lose depends on what the dealer has in the hole; it has nothing to do with your hand.

Think about what happens when you take insurance. If the dealer doesn’t have a 10, you lose the bet and the games go on just the same as if you hadn’t taken insurance. If she has a 10, she pays your insurance bet, and the game goes on just the same as if you hadn’t taken insurance. In either case, winning or losing the insurance bet has nothing to do with your cards. Your hand plays out the same whether or not you took insurance.

You could argue that all insurance works this way. Homeowner’s insurance doesn’t keep your house from burning down, any more than health insurance keeps you healthy or life insurance keeps you alive; it just pays you (or your beneficiaries) if the worst does happen. We know that from a strictly statistical point of view, insurance is a bad bet. If it wasn’t, insurance companies couldn’t build all those big buildings in Connecticut and buy all those politicians in Washington. That is, it’s a bad bet if we use a linear model for money. But for most of us the value of money is only linear up to a point. Twenty dollars may be twice as much as $10, but in terms of what it means to our life, $20 million isn’t twice as much as $10 million. With most insurance we pay an affordable premium to avoid an unaffordable loss. This is where the blackjack insurance differs from other types of insurance. If your initial bet is an unaffordable loss, you have bigger problems than worrying about insuring it.

There is the psychological factor that it feels worse to have a good hand beaten by a dealer’s blackjack than a poor hand. But this is strictly psychological; it makes no difference to your bank account. A beat’s a beat.

Let’s do the numbers to see why insurance is normally a bad bet, and why I chose to take it on this hand. Remember, it’s nothing more or less than a side bet on whether the dealer has a 10 in the hole. With a full deck, four of every 13 cards are 10s. Let’s say you place a $10 insurance bet. If you did this 13 times, on average you would win four of the bets and lose the other nine. The nine you lose cost $90. And, since the side bet pays 2-to-1, the four times you win pays $80. A net gain for the house of $10, or 7.7 percent.

The opportunity to place an insurance bet on average occurs once in 13 hands; at 80 hands per hour, about six times an hour. Taking a $10 insurance bet every time it is offered will cost about $4.60 per hour. The player who insures only 19s and 20s will place about one insurance bet per hour. This gets the cost down to 77 cents per hour. Is the warm feeling from not letting the dealer’s blackjack beat you worth it? That’s up to you.

By the way, taking even money on a blackjack is exactly the same as taking insurance, and the same calculations apply.

Now why did I take this bad bet? Remember, the count was high, which meant the deck was 10-heavy. Suppose in the above calculation there were five instead of four 10s for each 13 cards remaining in the shoe. Now I would lose eight of my 13 bets for a loss of $80. But I would win five, for $100, a net gain of $20.

The decision comes down to this: If the remaining percentage of 10s in the shoe is less than 33.3 percent, then pass up insurance. But if the percentage is greater than 33.3 percent, it’s an advantage bet. Most of the time the percentage of 10s is less than 33.3 percent, so the noncounting player is better off not taking insurance.

The above is just a first-order calculation. I used the ratio of 10s in a full deck, 16/52 = 30.77 percent. In fact, we are not playing with a full deck. Maybe I should rephrase that. We know several cards are removed from the deck, the ace the dealer is showing and the two cards we have. If we do not have a 10, the ratio of 10s in the remaining deck is 16/49 = 32.65 percent if we are playing single deck, 32/101 = 31.68 percent in double deck and 96/309 = 31.07 percent with six decks. This makes insurance a little less of a bad bet, but still not up to the 33.3 percent we need. Ironically, this second-order calculation shows that the conventional wisdom of insuring good hands (19 or 20), but not poor hands, is worse than no wisdom. If you have 19 or 20, you have one or two of the 10s, making insurance an even worse bet than insuring a poor hand with no 10s.

The dealer checked her hole card, put the corner of her up-card under it and flipped the 10.

“Nice call,” she said, as she pushed my bets back to me.

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