Insurance and even money maths

Key facts

Insurance pays 2:1 but, ignoring your own cards, the odds against a 10-value hole card are 35:16 (2.19:1) in a single deck and 215:96 (2.24:1) in six decks, so the bet loses money.
The house edge on insurance is 3/51 ≈ 5.9% of the insured amount in a single deck and 23/311 ≈ 7.4% in six decks, from exact arithmetic.
Insurance is a fair bet only when at least one third of the unseen cards are 10-value; it becomes profitable above that, which a card counter detects at a Hi-Lo true count of +3 or higher.
Taking even money on a blackjack against an ace is mathematically identical to insuring it; declining it is worth about 1.039 units in six decks against exactly 1.000 for even money.
Basic strategy never takes insurance or even money; Wikipedia and the Wizard of Odds both state the bet is never correct without a count.

Insurance is a side bet, offered when the dealer shows an ace, that the hole card is a 10-value card. It pays 2:1, but from a fresh shoe the true odds against a 10 in the hole are about 2.2:1, so the bet loses between 5.9% and 7.4% of the amount insured depending on the deck count. Even money on a blackjack is the same bet in different clothing, and basic strategy declines both.

How the bet works

When the dealer’s upcard is an ace, you may place up to half your original stake on insurance before the dealer checks the hole card. If the hole card is a 10, J, Q or K the dealer has a natural; insurance pays 2:1 and your main hand loses (or pushes, if you also have a natural). If the hole card is anything else, the insurance bet is lost and the hand continues. The Wizard of Odds describes the payout as 2 to 1 “if the dealer’s hole card is any 10-point card”; Wikipedia calls it “a side bet that the dealer has a blackjack”.

The main hand is irrelevant to the side bet’s value. Insurance wins or loses on one question: is the hole card a 10?

The true odds of a 10 in the hole

Ignoring your own two cards, every unseen card other than the dealer’s ace is equally likely to be the hole card.

Decks	Unseen cards	10-value cards	Non-10s	Odds against a 10	P(10 in hole)
1	51	16	35	35:16 = 2.19:1	31.4%
2	103	32	71	71:32 = 2.22:1	31.1%
6	311	96	215	215:96 = 2.24:1	30.9%
8	415	128	287	287:128 = 2.24:1	30.8%

The Wizard of Odds card-counting introduction quotes the six-deck figure the same way: the remaining cards are “about 30.87% tens”, and the bet only becomes good “if the probability gets above 33.33%”.

Why 2:1 is short

A bet paying 2:1 breaks even when the chance of winning is exactly one third: win 2 units one time in three, lose 1 unit two times in three, net zero. The fresh-shoe probability is about 31%, not 33.3%, so the payout is short of the true odds.

Expected value per unit insured is 2 × P(10) − 1 × (1 − P(10)). Showing the arithmetic:

Single deck: 2 × 16/51 − 35/51 = (32 − 35)/51 = −3/51 ≈ −0.0588, a 5.9% house edge.

Six decks: 2 × 96/311 − 215/311 = (192 − 215)/311 = −23/311 ≈ −0.0740, a 7.4% house edge.

Eight decks: (256 − 287)/415 = −31/415 ≈ −0.0747, a 7.5% house edge.

On a £10 main bet the maximum insurance stake is £5, and the expected loss on it in six decks is £5 × 0.074 ≈ 37p every time you take it. That is nearly a hundred times the expected cost of the main hand at a 0.4% house edge.

Your own cards shift these figures slightly. If you hold two 10s, only 94 of 309 unseen six-deck cards are 10s (30.4%) and insurance is worse; if you hold 5+6, 96 of 309 (31.1%) and it is fractionally less bad. No two-card hand moves the probability past one third in a shoe game.

Even money is insurance by another name

Suppose you hold a blackjack, the dealer shows an ace, and you insure for half your stake (0.5 units on a 1-unit bet):

Dealer has a natural. Your blackjack pushes (0). Insurance wins 2 × 0.5 = +1. Net +1 unit.
Dealer has no natural. Your blackjack wins 1.5. Insurance loses 0.5. Net +1 unit.

Every branch nets exactly one unit, so casinos skip the paperwork and offer “even money”: a guaranteed 1:1 payout on the natural before the hole card is checked. Wikipedia describes the trade as giving up “the usual 3:2 payout for 1:1”.

The alternative is to decline and take your chances. With your ace and 10 and the dealer’s ace removed from a six-deck shoe, 309 cards remain with 95 10s, so the dealer has a natural with probability 95/309 ≈ 30.7%:

EV(decline) = 1.5 × (214/309) + 0 × (95/309) = 1.5 × 0.6925 ≈ 1.039 units.

EV(even money) = 1.000 unit.

In a single deck: 49 unseen cards, 15 10s, EV(decline) = 1.5 × 34/49 ≈ 1.041. Declining is worth roughly 4% of the stake more than taking even money in either game. On a £10 blackjack, even money hands you £10 profit now; declining averages £10.39, with a 30.7% chance of a push. The Wizard’s basic-strategy pages state the assumption outright: the strategy “assumes you never take insurance or even money”.

When counters take it

Insurance is the one side bet with a clean mathematical switch: it is profitable exactly when the unseen cards are more than one third 10-value. Card counters track that ratio. In the Hi-Lo system the Wizard of Odds and blackjackinfo.com both give the insurance index as +3: take insurance when the true count is +3 or higher, decline below. Insurance is the first entry in the Illustrious 18 because it is worth more than any playing deviation; a counter who does nothing else with the count except insure correctly still captures a meaningful slice of the available gain.

The reason it is so valuable is the leverage. The main-hand index plays swing EV by a few hundredths of a unit. Insurance at a high count swings a bet of half a unit from −7% to positive several percent, and it does so on every ace the dealer shows. The Illustrious 18 article covers the rest of the list and the Hi-Lo tutorial explains how to reach a true count.

At a fresh shoe the Hi-Lo running count is zero and the ratio of 10s is 30.9%. A +3 true count in a six-deck shoe means roughly three extra high cards per remaining deck, enough to push the 10 fraction past one third. Without a count you have no information beyond the fresh-shoe average, and the fresh-shoe average says no.

Training rules: six decks · dealer stands on soft 17 · no surrender

This is a separate educational profile. Rules can differ between app tables and other games.

Six decks. Dealer stands on all 17s, including soft 17.
US hole card and peek: decisions assume the dealer has checked and does not have blackjack.
Double any first two cards, including after splitting. Doubling ends the hand after one extra card.
Split equal card values into at most four hands. Split aces receive one card each; no resplitting aces.
No surrender. A natural blackjack pays 3:2; 21 after splitting is not a natural.
Total-dependent strategy. No card counting or expected-value estimates.

Profile six-deck-s17-das · rules 1.0.0 · strategy 1.0.0. The trainer asks for one decision per hand; it does not simulate wagers or settlement.

Frequently asked

Is insurance ever a good bet?

Only when more than a third of the unseen cards are 10-value. From a fresh shoe about 31% are, so the 2:1 payout is short of the roughly 2.2:1 true odds. Card counters take it at a Hi-Lo true count of +3 or more.

What is the house edge on insurance?

About 5.9% in a single deck and 7.4% in six decks, ignoring your own cards. Exactly: (2 × 16 − 35)/51 = −3/51 for one deck and (2 × 96 − 215)/311 = −23/311 for six.

Should I take even money with a blackjack against an ace?

No, unless you are counting and the count is high. Declining returns 1.5 units when the dealer has no natural, which is about 69% of the time in six decks, for an average of 1.039 units against the certain 1.000 of even money.

Why is even money the same as insurance?

If you insure a blackjack for half your stake, every outcome nets exactly one unit: a dealer natural pushes your hand and pays the insurance 2:1; no natural wins 1.5 units and loses the 0.5-unit insurance. Casinos simply pay the one unit up front.

Sources & editorial notes

By Blackjack World Tour · Updated 2026-10-12 · Owner review pending. Sources were checked on the update date.

Where this guide states a strategy decision without naming rules, it assumes the site profile: six decks, dealer stands on soft 17, double after split, no surrender. Basic strategy cannot guarantee a winning hand.

From theory to the table

Practise the decision.

Ten hands under the stated profile, with the reasoning after every answer.

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