Why insurance is a bad bet

Insurance is a side bet that the dealer’s hidden card is a ten. It pays 2 to 1, so it only breaks even if more than a third of the unseen cards are tens. In a fresh six-deck shoe, 96 of the 311 cards you can’t see are tens — 30.9%. That gap costs you 7.4% of every insurance bet. Don’t take it, and don’t take even money either.

• Insurance is offered only when the dealer’s up card is an ace. You have 8 seconds to choose “Insure” or “No insurance”.
• It costs half your bet: with 1,000 on the box, insurance is 500.
• Then the dealer peeks. With blackjack, insurance pays 2 to 1 — your 500 comes back as 1,500 — and the main bet loses, unless you have blackjack too. Without blackjack, the 500 is gone and the round goes on.
• If you hold a blackjack yourself, the offer becomes “1 to 1 right now”: even money on your bet instead of the 3 to 2 you get when the dealer doesn’t have blackjack.

With a ten-value card showing, our dealer peeks for blackjack as well, but insurance isn’t offered.

Say you put 100 on insurance. Of the 311 cards you can’t see, 96 are tens. Over all 311 equally likely hole cards, you win 200 on 96 of them and lose 100 on the other 215:

96 × 200 − 215 × 100 = 19,200 − 21,500 = −2,300. Divide by 311 and you get −7.40 per 100 insured, on average, every time.

Your own cards move this slightly. Every ten in your hand is a ten that can’t be under the dealer’s ace, so tens in your hand make insurance worse:

Even the best case for insurance, with no tens in your hand, loses 6.8 per 100.

The usual advice is to insure a 20 because you “protect a winner”. It is the worst moment to buy it. Your two tens leave only 94 tens for the dealer, and insurance loses 8.7 per 100.

Insurance doesn’t protect anything. It is a separate bet on one card, settled before your hand is played, and your 20 keeps exactly the same chances whether you insure it or not.

With blackjack against the dealer’s ace, “1 to 1 right now” sounds safe: a sure win instead of a gamble. Compare the two on a 100 bet. Take even money and you get +100, always. Decline, and the dealer has blackjack in 95 cases out of 309 (a push, 0) and no blackjack in the other 214 (you get +150). On average: 150 × 214 ÷ 309 = +103.9.

Declining is worth 3.9 more per 100 — exactly what insuring a blackjack would cost: half the bet times the 7.8% that insurance loses with one ten in your hand. Even money is insurance under a friendlier name.

Insurance only has a positive result when more than a third of the unseen cards are tens. That happens when many small cards have already left the shoe — late in a shoe after a run of 2s to 6s. Card counters track exactly this, and insurance is one of the first decisions they change.

We measured how often it happens at our table. In 50 million simulated rounds the dealer showed an ace in 7.7% of rounds, and at 11% of those moments more than a third of the unseen cards were tens. Without tracking every card since the shuffle you can’t tell which 11% they are — and on the other 89% the bet loses. Averaged over every ace the simulator saw, insurance lost 7.5 per 100.

The dealer shows an ace about once in thirteen rounds, so the habit adds up slowly but surely. A player who follows basic strategy and always takes insurance and even money gives the house about 0.3% more of everything they bet: 0.28% by the exact calculation, and in the simulation the edge went from 0.43% to 0.74%. At 100 debens a hand, that is roughly 30 extra debens every 100 hands.

The residents marked AI at our tables never insure. They play basic strategy, and so should you: when the question pops up, press “No insurance” and keep the debens for a double.