Insurance and even money

The ace creates a second question

You have twenty. The dealer shows an ace. Before resolving the hand, the dealer offers insurance. The name suggests protection for your strong hand, but the offer asks a narrower question: is the dealer’s hidden card worth ten? Your twenty does not participate in that bet.

In the usual US hole-card game, insurance is offered against an ace before the dealer checks for blackjack. You may wager up to half your original stake; successful insurance pays 2:1. These are separate settlement rules from the main hand. See the Wizard of Odds rules reference and our guide to blackjack rules.

With a £20 main bet, full insurance costs £10. If the dealer has blackjack, that insurance earns £20 profit and returns its £10 stake. Without your own natural, the main wager loses £20, so the combined result is zero. If the dealer lacks blackjack, insurance loses £10 and the main hand continues. You might eventually win, lose or push that hand.

A strong hand does not improve the price

Suppose the hidden card has probability p of being ten-valued. For every £1 of insurance, the profit is £2 when it wins and a £1 loss otherwise. Its expected profit is therefore:

2p − (1 − p) = 3p − 1.

At p = one third, this is zero. Above one third, insurance has positive expectation; below one third, it has negative expectation. This threshold follows directly from the 2:1 payout. It is not a judgment about whether your original hand deserves saving.

There are sixteen ten-valued cards in a standard deck: four tens and twelve picture cards. An infinite-deck approximation uses p = 4/13, producing an insurance expectation of −1/13, about −7.69% of the insurance stake. As a finite-shoe comparison, if the only known card in six fresh decks is the dealer’s ace, 96 of the other 311 cards are ten-valued. That gives about −7.40%. Actual information includes your cards and any other exposed cards, so this is an illustrative baseline, not the exact price of every offer. Michael Shackleford’s insurance lesson explains the finite-shoe calculation and the basic-strategy recommendation to decline.

Even money puts a price on certainty

Now give yourself a natural blackjack: ace–king, with the same £20 stake. At a 3:2 table, you earn £30 if the dealer lacks blackjack and push if the dealer also has a natural. An offer of “even money” exchanges those possible outcomes for a guaranteed £20 profit.

Full insurance creates exactly that result:

Declining produces expected profit of £30 × (1 − p). Using the simple 4/13 approximation, this is about £20.77. Taking even money yields £20. The difference is roughly 77p on this offer, not £10: the £10 insurance stake and the expected cost of buying certainty are different quantities.

For a more specific fresh-six-deck example, after seeing only your ace–king and the dealer ace, 95 of the 309 unseen cards are ten-valued. Declining even money then has expected profit £30 × 214/309, about £20.78. This independently calculated example illustrates why removing a ten-valued card in your own blackjack matters. The Wizard’s even-money explanation reaches the same basic-strategy conclusion.

The payout is part of the argument

The equivalence above requires a 3:2 natural. At 6:5, a £20 blackjack wins £24. Adding £10 insurance would produce £20 profit against dealer blackjack but only £14 otherwise. Those outcomes are not an even-money guarantee. Check the actual offer and payout rather than transferring the 3:2 arithmetic unchanged. Choosing a table begins with precisely this kind of rule difference.

Buying insurance because your last three good hands lost confuses emotion with information. Buying it because an observed shoe has enough ten-valued cards remaining is a different mathematical proposition. Card counting explains that distinction; a favorable-looking hand alone supplies no such conclusion.

Our trainer teaches total-dependent basic strategy. It does not offer insurance, even-money decisions or shoe-counting advice. Practice the main-hand decision there, and use this calculation to understand the separate offer. The useful habit is to ask what the wager pays, what event wins it, and whether its probability clears the price.