Insurance Is a Poor Bet at Blackjack, but not Uniformly So

8 February 2005

By Alan Krigman

Anyone who's ever sidled up to a casino blackjack table knows "the book says you're not supposed to take insurance." If not before, a neophyte will surely hear it from the veterans when the opportunity to make the bet first arises. Some of the veterans, of course, will be rationalizing why they're doing it anyway.

Insurance is a side bet, which can equal up to half of a player's original wager. Available when a dealer has an ace-up, insurance pays 2-to-1 if the dealer has a blackjack and loses otherwise.

Say you bet $10 and take $5 insurance. If the dealer flips a 10 you lose the $10 main bet to the resulting blackjack but win $10 on insurance; it's a wash. On other than 10 in the hole, you lose the $5 and the round proceeds. There's a twist when you have a blackjack yourself. Without insurance, you push if the dealer also gets lucky, or else win $15. With insurance, you win $10 either way; this is why insuring a blackjack is sometimes called "taking even money."

The gurus tend to be dogmatic in telling solid citizens to shun insurance. This, because of its large house advantage. Nominally, four out of every 13 cards in a deck are 10-valued. The chance that a dealer with ace-up has a 10 in the hole is therefore 4/13 or 30.8 percent; the chance of a non-10 is the other 9/13 or 69.2 percent. Since $1 of insurance either pays $2 or loses, edge is $2 x (4/13) - $1 x (9/13) or -7.7 percent. By contrast, edge in the main game, following basic strategy, is about -0.5 percent.

The nominal figures for insurance can be deceptive, however. The actual edge can be better or worse than -7.7 percent.

Here's the scoop. Pretend you're in an eight-deck game, at a table with seven spots in action. The cards are dealt for a round. The dealer has an ace-up and every player has a pair of 10s. Chances are good that some, or all, of your tablemates will take insurance to protect what they consider promising hands. But, do a little arithmetic starting with the assumption that you know nothing about cards withdrawn from the shoe in prior rounds.

A full eight-deck shoe has 52 x 8 or 416 cards. You see 15 of them on the table ?? the dealer's upcard and two each to seven player spots. This leaves 416 - 15 or 401 "unknowns," one of which will be the dealer's downcard. You also know that the full shoe has 16 x 8 or 128 10-values. In this hypothetical round, however, 14 of the 10s are withdrawn so 128 - 14 or 114 remain. In case you mislaid your inkpen, here's the arithmetic for the edge in this example. The probability that the dealer has a 10 in the hole is 114/401 or 28.4 percent, and does not have this downcard is (401 - 114)/401 which is 287/401 or 71.6 percent. The edge on insurance is therefore $2 x (114/401) - $1 x (287/401) or -14.7 percent. Nearly twice the nominal value of -7.7 percent.

When does insurance, based only on cards exposed at the start of a round, have the lowest house advantage? This condition occurs when all seven spots are in action and no 10s are exposed. Here, working out the figures yields an edge of only -4.2 percent, down from the nominal value by almost half. The irony is that a round like this might find everyone sitting with underdogs and nobody tempted to take insurance because they think they have nothing to protect, yet this is when the bet is least theoretically taxing.

As a point of reference, the range of edge on insurance narrows when fewer spots are in action. Playing alone, on one hand in an eight-deck game, the burden is lightest at -7.0 percent when you have no 10s, and heaviest at -8.5 when you have two of them.

You may want to take insurance under some or all circumstances. Fine, if that's your personal preference. But realize it's a separate bet that the downcard is a 10, not a sensible way to protect what you think is a strong hand. But who says the edicts gamblers get, give, or choose to believe are or even ought to be sensible? Certainly not the immortal Sumner A Ingmark, who noted:

Those who reason most illogically,
State their views most demagogically.