Insurance – By the Numbers

I was playing blackjack with a friend of mine, Phil.  My bet was $100 and his was $150.  I was dealt a 20 and he had a 19.

The dealer’s upcard was an Ace and we were offered insurance.  I shook my head "no" and Phil accepted the bet.  He looked at me funny and said, “I want to talk to you about this later.”

Later we took a break in the casino lounge.  Phil mentioned the insurance bet.

“I thought that you would want to insure a $100 bet, Martin.  At least that is my understanding of the purpose of insurance.”

“No, I didn’t want to insure my bet.  Insurance is only a good bet if you count cards and the deck favors the bet. Since I don’t count cards any more, I never take insurance.”

“But, as I recall, you had a 19 or a 20.  Doesn’t it make sense to insure a good hand?  And, when you consider that you had a large bet out with a good hand, it seems to me that insurance is the way to go.”

He was very adamant.  Before I tell you how I responded, let me tell you a little bit about the insurance bet in blackjack.

Insurance is a side bet offered by most casinos.  As with all side bets, it is a bet that heavily favors the house. 

It’s strictly a bet for novices and the faint of heart. 

And, for a few card counters, it occasionally makes sense.

Experienced players know not to take insurance.  I turned the tables on Phil and asked him why he took it.

“I just think it makes sense to insure a large bet.  And, it especially makes sense to insure a good hand like a 19 or 20.  I still don’t understand why you don’t take insurance.”

Here’s what I explained to Phil -

Insurance is simply a side bet on whether the dealer has a 10 as a hole card when she is showing an Ace up.  If she does, the bet pays 2 to 1.  It is only offered when the dealer shows an ace.

Here’s how it works.  The casino allows you to bet up to one half of your original wager.  To insure a $100 bet, for instance, you would make a wager up to $50 as the insurance bet.  If the dealer has a 10, and therefore a blackjack, you win the insurance bet, but lose your regular bet.  The net is a break-even.  It is called “insurance” because most players think of it as a way of insuring that you don’t lose money on a good hand or when your bet is large.  I have commonly heard players say, “I only insure a 19 or 20.”

As with much blackjack wisdom, this is totally wrong. Whether insurance is a good bet or a bad bet has nothing to do with the value of your hand or the size of your bet.  It makes just as much sense to insure a 14 as it does a 20. 

Whether you win or lose depends on the dealer’s hole card.  It has nothing to do with your hand.

Think about how the game goes when you take insurance.  If the dealer doesn’t have a 10, you lose the bet and the game goes on, just the same as if you hadn’t taken insurance.  If
she has a 10, she turns over her hole card, revealing her blackjack, and pays your insurance bet.  In either case, your taking or not taking insurance has zero influence on the basic game.  Your hand pays out the same whether or not you took insurance.

Phil was starting to nod.  But I could see that I hadn’t convinced him. 

“I still don’t see why, even if insurance is a side bet, that it doesn’t make sense to insure a good hand.  Please explain.”

I continued.  It helps to think of the insurance bet like homeowners insurance.  Having homeowners 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 beneficiary if the worst happens).  We know from strictly a statistical perspective that insurance is a bad bet.  If it wasn’t, then insurance companies couldn’t build all those skyscrapers in Connecticut and Omaha and buy all those politicians in Washington D.C. 

With most insurance we pay an affordable premium to avoid an unaffordable loss.  This is where blackjack differs from other insurance.  If your initial bet is an unaffordable loss, you have a bigger problem than worrying about taking insurance.

There is a psychological factor to consider.  It feels worse to have a good hand beaten by a dealer’s blackjack than a poor hand.  But this is strictly psychological.  It really makes no difference to your net winnings.  In fact, taking insurance will reduce your net winnings.  And, I would argue that net winnings or net profits are the main consideration in every blackjack decision.

Phil was frowning at me  “That’s all fine, Martin, but you still haven’t told me why taking insurance is a bad bet.  It seems to me that if I want to insure my good hands, that it should be up to me.”

“Okay Phil,” I responded.  “Let’s do some numbers.”

Let’s start with the fact that the insurance bet is nothing more than a side bet that the dealer has a 10 in the hole. 

With a full deck of cards, four out of every 13 cards are 10-valued cards, cards which could make the dealer’s blackjack when an Ace is up.

Let’s say you bet $10 on insurance every time she showed an Ace.  If you did this 13 times, on the average you would win four of the bets and lose the other nine wagers.  Your nine
losing bets would cost you $90.  Your four winning bets, paying 2 to 1, would bring in $80 for a net loss of $10. 

This is a net gain for the house of $10, or 7.7 percent.  

Now let’s consider what this might do to your hourly winnings.  The opportunity to make an insurance bet occurs on the average once every 13 hands.  At 80 hands an hour, this happens about six times an hour.  Taking a $10 insurance bet every time it is offered will cost about $4.60 an hour.  The player who only insures 19s and 20s will make about one insurance bet an hour.  This gets the cost down to 77 cents per hour. 

“Is that warm and fuzzy feeling you get insuring your 19 or 20 worth 77 cents an hour to you?” I asked Phil.

He stared at me and said, “I’ll have to think about it.  But what about insuring a blackjack?  Don’t you agree that this is a good move?”

In shared my thoughts with Phil.  Insuring a blackjack is the same as taking even money for a blackjack.  The same analysis applies to this bet that applied to insuring other hands.  In all cases, it is a bad bet.

Phil lamely countered.  “But card counters sometimes take insurance.  Don’t they know what they are doing?”

I explained that sometimes, when the number of 10s remaining to be dealt is heavy, it may tilt the insurance bet in the player’s favor.

Here’s an example.  Suppose the card counter’s count shows the deck is heavy in 10s.  Furthermore, suppose that the calculation of tens remaining showed there were five tens
out of every 13 cards remaining to be dealt.  In this case, if I took a $10 insurance bet at every opportunity, I would lose eight of my 13 bets for a loss of $80.   However, I would win, on the average, five of the bets, which paid at 2 to 1 would pay me $100 for a net gain of $20.

Of course, you will first have to learn to count cards to benefit from this information, and then you will have to learn how to make lightning fast mental calculations to know when to take insurance  Then you will have to find a situation where card counting can give you an edge.  Sadly, with multiple decks that are only dealt part way (the rule in most casinos) and the use of continuous shuffling machines, card counting opportunities are very limited.  Also, with online blackjack games, which are continuously shuffled, there are virtually no opportunities to count cards and ever profit from taking the insurance bet.

Phil kind of scrunched down in his chair.  “You are basically telling me that insurance is a sucker’s bet, aren’t you.”

“You got it Phil.  Now let me buy the next round.  Then let’s go play some more blackjack without taking insurance.”

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