Insurance, even money and surrender at blackjack

Three decisions at a blackjack table are not about the cards you were dealt. The dealer offers them, each sounds protective, and two of them are worse than doing nothing. We have worked all three out from the composition of the deck rather than repeating the chart, because the arithmetic is short enough to follow.

Insurance: the price is 2 to 1 and the deck pays 32.65 per cent

The dealer shows an ace and offers insurance at 2 to 1 for half your stake. The bet wins if the hole card is a ten, jack, queen or king. A bet paying 2 to 1 breaks even at one chance in three, or 33.33 per cent, so the only question is how often the hole card is a ten-value card.

Count the cards you can see. From a single deck you hold two and the dealer’s ace is face up, so 49 cards are unseen and 16 of them are ten-value. Sixteen over 49 is 32.65 per cent, against the 33.33 the price demands. Per pound insured, the return is 16 times 2 minus 33, all over 49 — that is minus one over 49, or −2.04 per cent.

It gets worse in the case where players most want it. Hold a blackjack and one of your two cards is a ten, so only 15 ten-value cards remain in 49, and the insurance return falls to minus four over 49, or −8.16 per cent. The hand that feels most worth protecting is the hand where the protection is priced worst.

The one condition that reverses it is a count: if you know the remaining cards are richer in tens than one in three, the bet turns positive, which is why insurance is the first deviation any counting system teaches. What that actually requires of a player is the subject of our page on card counting myths against the reality of the online game, and the short answer is that against a continuously shuffled online shoe the condition never arrives.

Even money: the same bet wearing a different coat

You have a blackjack, the dealer shows an ace, and you are offered even money — one unit, settled immediately, no push risk. Decline and two things can happen: the dealer has blackjack and the hand pushes, or he does not and you are paid 3 to 2.

With a blackjack in your hand, 15 of the 49 unseen cards make the dealer’s hand, so you are paid 1.5 units 34 times in 49 and nothing happens 15 times in 49. That is 1.5 times 34 over 49, or 1.0408 units. Even money hands you 1.0000. Taking it costs 4.08 per cent of your stake — which is the same −8.16 per cent as insurance, applied to half a stake. It is insurance, offered under a name that sounds like certainty rather than like a bet.

Surrender: the one worth taking

Late surrender gives back half your stake and ends the hand. It is therefore correct whenever the hand in front of you expects to lose more than half — and a handful of hands do.

The figures below assume an infinite shoe, a dealer who stands on all 17s and has already checked for blackjack, and a player who takes one card and then stands. Under that model the dealer’s ten busts 22.98 per cent of the time and makes 20 in 37.07 per cent of hands, which is what makes these two hands so grim.

Your hand	Stand	Take a card	Surrender
hard 15 against a ten	−0.5404	−0.5045	−0.5000
hard 16 against a ten	−0.5404	−0.5398	−0.5000

Both lose. Surrendering loses least, by three and a half and four hundredths of a stake respectively — small per hand, and the only free improvement on the table. Note how close hitting and standing are on 16: the long argument about which one to pick is an argument about four ten-thousandths of a bet, while the option nobody takes is worth forty times more.

Two cautions. Surrender must be late — offered after the dealer has checked for blackjack; early surrender is a different and much more generous rule that almost no game still offers. And it is not available at every table, online or live, so it belongs on the list of rules to read before sitting down, alongside whether the dealer hits soft 17 and what blackjack pays. Our page on blackjack strategy and the rules of the game sets out the rest of that list.

The pattern across all three

Each of the three is sold as a way to reduce risk, and in each case the question is only whether the price matches the chance. Two of them are priced a fraction over the odds and are therefore declines. One of them is priced under, and almost nobody uses it. The same test applies to every optional bet in the building — our table of edges converted into returns runs it across eight of them, and the side bets that ring the modern blackjack layout all fail it by a wider margin than insurance does.