SHOULD YOU ALWAYS INSURE A BLACKJACK?

SHOULD YOU ALWAYS INSURE A BLACKJACK?
By Charles Jay

Were you ever wondering about this?

There is perhaps no bigger argument at a blackjack table than that which involves the player insuring a two-card natural (commonly known as a blackjack). The insurance rule says that when the dealer turns an Ace as the upcard, he will ask the players if they’d like to “insure” their hands. The player puts up one-half of his original bet, and if the insurance wager wins (if the dealer has blackjack), it pays off at two-to-one odds.

When the player is dealt, for example, a Jack and an Ace, which constitutes the aforementioned blackjack, and the dealer has an Ace showing, there is a great propensity on the part of the player to “protect” that hand by buying insurance. After all, the logic goes, the blackjack is a bonus hand, which pays off at three-to-two odds. The player doesn’t get a blackjack that often, so players feel they had better get something out of that situation. If they have a blackjack and the dealer also has one, it’s a push (a tie) and the player gets nothing.

Many supposed blackjack “experts” recommend strongly that their students always insure their blackjack in that situation. The rationale is that whatever happens, the player will always end up with a profit. And you know something? They’re right! The player will come out with a profit every time, if they insure a blackjack. But I’m telling you that insuring the blackjack is not the percentage play.

Let’s illustrate.

Take a 52-card deck. In this deck, there are 16 ten-value cards, and 36 non-tens, a ratio of 2.25-to-one. When we are faced with the situation in which we have a two-card blackjack and the dealer has an Ace showing, there are now 15 tens and 24 non-tens remaining. That’s a ratio of 2.27-to-one. Remember that insurance pays only two-to-one, so you’re sort of getting “the worst of it.”

But let’s get back to the illustration. Imagine that you’re laying out $10 bets in each of these situations. There are four different scenarios that can take place:

1) YOU TAKE INSURANCE AND THE DEALER HAS BLACKJACK;

2) YOU TAKE INSURANCE AND THE DEALER DOES NOT HAVE BLACKJACK;

3) YOU DO NOT TAKE INSURANCE AND THE DEALER HAS BLACKJACK;

OR

4) YOU DO NOT TAKE INSURANCE AND THE DEALER DOES NOT HAVE BLACKJACK.

In scenario one and two – which we do not recommend for any player – the yield is $10 each for the player. If the player bets $10 and insures for $5, he’ll push the primary bet and win $10 on the insurance bet. If the dealer doesn’t have blackjack, the player wins $15 from the primary bet, but loses the $5 insurance bet, leaving a $10 profit.

In scenario three, we have not wagered on insurance, and tied the dealer on our blackjack. We retain our $10 bet, giving us a net gain of zero. In scenario four, we beat the dealer with our blackjack, giving us a gain of $15 on the hand.

As you can see, when you take insurance, you are guaranteed a return on investment, while in one of our scenarios you gain nothing.

Let’s take a look at probability for a moment: remember, we have 15 tens and 34 non-tens left, making a theoretical total of 49 cards remaining. Since the dealer has to have a ten in the hole to complete a two-card blackjack, let’s calculate the chance of that happening. Just divide 15 by 49, and you come up with a 30.6 percent chance of the dealer having blackjack. That leaves us with a 34/49, or 69.4 percent chance of the dealer not having blackjack. Clearly scenarios two and four are going to happen much more often than the first and the third, even in an online casino.

Now let’s look at what our expected gain is per 100 situations for each of our scenarios:

1) TAKE INSURANCE + DEALER BLACKJACK = $10 (30.6%)

2) TAKE INSURANCE + NO DEALER BLACKJACK = $10 (69.4%)

3) NO INSURANCE + DEALER BLACKJACK = $0 (30.6%)

4) NO INSURANCE + NO DEALER BLACKJACK = $15 (69.4%)

Just multiply it out.

Scenario #1 gives you an expected return of $306 for every 100 situations;

Scenario #2 yields $694 for that same duration. That’s a total of $1000 even.

Scenario #3, in which there is no insurance, offers an expected return of $0, since there was no protection for the blackjack. But in scenario #4, where the dealer doesn’t turn over a natural, we win $15 per play, or $1041 over the course of 100 situations ($15 x .694 x 100).

The difference, or gain, between the results when you TAKE insurance (Scenarios #1 and #2 added) and DON’T TAKE insurance (Scenarios #3 and #4 added) is $41 for every 100 situations, or $1000 wagered.

Our most profitable scenario, therefore, is the one that occurs the vast majority of the time. As this example illustrates, we are gaining 4.1 percent for every $1000 wagered by NOT insuring. The truth is, as we’ve stated before, it is not mathematically sound to exercise the insurance option if you’re a Basic Strategy player.

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