Insurance

When the dealer’s upcard is an ace, you are offered insurance: a side bet of up to half your original stake that the dealer has blackjack. It pays 2:1.

It sounds like protection. It is a separate bet with a bad price.

The arithmetic

For insurance to be fair at 2:1, the dealer would need blackjack one time in three, a ten-value card appearing 33.3% of the time.

In a full deck there are 16 ten-value cards out of 52. Accounting for the visible ace, the dealer’s hole card is a ten roughly 30.8% of the time.

Per £100 of insurance:

• Win (30.8%): +£200
• Lose (69.2%): −£100
• Expected: (0.308 × 200) − (0.692 × 100) = −£7.60

A 7.6% house edge. Worse than American roulette, worse than most slots, and dramatically worse than the 0.5% game you are sitting at.

“Even money” is the same bet

If you hold a blackjack and the dealer shows an ace, the dealer will offer “even money”: take a guaranteed 1:1 instead of the 3:2 you get if the dealer has no blackjack.

This is insurance under a different name, with identical mathematics. Declining it and taking 3:2 when the dealer does not have blackjack is worth about 4% more over time.

The offer is made verbally, warmly, and at speed, which is part of why so many people take it.

The one exception

Card counters take insurance when the count indicates the remaining deck is rich in tens. Once ten-value cards exceed about one third of the remaining shoe, insurance becomes positive expectation.

This is a genuine exception and it is the reason the bet exists in the form it does. For anyone not counting, the rule is simply: never take insurance, and never take even money.