When the dealer's up card is an ace, you are offered insurance: a side bet of up to half your stake that the dealer's hole card is a ten-value card. It pays 2:1. Almost every guide says not to take it and stops there, which is advice without a price attached.
The price is arithmetic. The bet wins if one of the unseen cards is a ten, a jack, a queen or a king, and there are sixteen of those per deck. With a six-deck shoe, the dealer's ace and your own two cards are already visible, so 309 cards are unseen and 96 of them pay. The bet returns 2:1 on those and loses on the other 213:
96/309 × 2 − 213/309 = −21/309 = −7/103 = −6.7961%
Losing 6.80 units per hundred staked makes insurance roughly thirteen times worse than the game you are already playing, which costs about 0.52% under a standard rule set.
What it costs by shoe size
| Decks | Unseen cards | Ten-value cards | Exact value | House edge |
|---|---|---|---|---|
| 1 | 49 | 16 | −1/49 | 2.04% |
| 2 | 101 | 32 | −5/101 | 4.95% |
| 6 | 309 | 96 | −7/103 | 6.80% |
| 8 | 413 | 128 | −29/413 | 7.02% |
Two things fall out of that table. The bet gets worse as the shoe gets bigger, because your own two non-ten cards remove a larger share of the ten density from a small deck than from a large one. And even at its best, in a single deck, it is four times the cost of the hand you are playing.
The figures assume you hold no ten-value card yourself. If you do, the bet is worse again, which is the opposite of the common table belief that a good hand is a reason to protect it. "Even money" on a blackjack against an ace is the same bet wearing a different name.
The one situation where insurance is not a losing bet is a counted shoe rich in tens, which is a different activity with different consequences. At a table you are playing normally, it never is.
Where the numbers come from
Related terms in odds & money
- House edge, The average share of each bet the casino expects to keep over the long run.
- Expected value, The average result of a bet if it could be repeated indefinitely.
- True odds, The payout that would make a bet exactly fair, with no advantage to either side.
- Natural, A hand that wins immediately on the first cards dealt.
Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.