Taking Insurance without Card Counting

Blackjack School

Many people think that only card counters have a chance at winning some serious money playing blackjack. They believe that only when you count cards can you assess when you have an advantage over the casino, but that is not the case.

Take for example the insurance bet that you are able to make against the dealer having a natural blackjack when the dealer’s up-card is an ace. The insurance bet pays 2-to-1 if the dealer’s hole card is a 10 value card and loses if it is any other card (which means the dealer did not get a blackjack).

This wager is considered a bad move by anyone playing basic blackjack strategy and many even refer to it as a “sucker’s bet”. The word insurance is misleading as you are not actually insuring anything, you are simply making a side bet that offers you crappy odds.

Professional blackjack players will tell you that there are situations when making the insurance bet is worthwhile and that is when the shoe is loaded with 10-value cards. Such a situation makes it more likely that the dealer’s hole card is a 10-value card and makes the insurance bet favor the player instead of the casino.

The Odds

Imagine you are playing single deck blackjack and in the first hand dealt you get a pair of 10’s and the dealer is showing an ace and offers you insurance. You know that there are 14 ten-value cards left in the deck and 33 'ace to 9 cards'. This means that the dealer’s chance of having a 10 that will give him the winning blackjack hand is 33-to-14 or 2.357-to-1.

As you can see the odds offered are worse than the payout of 2-to-1 that is offered for winning the insurance bet. This means the casino has the edge and you should not make the insurance bet. Only when the ratio of ‘ace to nine cards’ to 10-value cards left in play is lower than 2-to-1, does the insurance bet makes mathematical sense.

No Card Counting Required

There is a way for a non-counter who is proficient in basic blackjack strategy to assess whether the deck is loaded with 10-value cards and therefore is favorable towards the dealer hole card being a 10, a situation that would warrant an insurance bet being made.

Let us imagine you are playing an 8 decks blackjack with a total of 6 players playing. The game has been going on for a while and taking a look at the discarded cards rack, you estimate that there are already about 5 decks out of play and 3 decks that are still in play.

Another round of play commences and you see the 12 cards that were dealt to you and the other five players and you see the dealer’s up card. None of the 13 cards on show are 10-value cards. The dealer is showing an ace and offers players insurance.

Working on the basis of 3 remaining decks in play the shoe now contains 156 cards. Without card counting in previous rounds of play you can guess that on average there are 4x4x3=48 cards that are 10-value cards.

After the deal when no 10-value cards are showing you can subtract the 13 cards on show from the total cards in 3 decks 156-13=143 unseen cards. Since no 10-value cards are showing you can deduct the 48 10-value cards from the total of unseen cards 143-48=95 non-10-value cards left.

Under these conditions the chances of a dealer have a 10 in the hole are 95 to 48 or 1.98 to 1. Since insurance pays at 2-to-1 the odds of 1.98-to-1 are more favorable to you and give you an edge of 0.7 cents for every $1 bet.

In games where the shuffle point is deep and play continues when there are 2 decks only still in play, there would be 104 cards left in play. 6 players are dealt and no one is showing a 10-value card. Dealer shows an ace. Now the count will be 104-13=91 cards left in play.

On average such a shoe will consist, before any cards are dealt, 32 10-value cards and 91-32=59 non-10s in the game. The odds of the dealer’s hole card being a 10-value card, are 59-to-32 or 1.84-to-1. Since the odds are lower than 2-to-1 the insurance bet is favorable by giving you an edge of almost 5.5 cents to every $1 bet.

In addition when 2 decks remain in the shoe you are at an advantage even if there is one 10-value card showing after the deal. Your edge will be almost 2.2 cents for every $1 bet.

Some Words of Caution

Do not confuse positive expectation, when the odds are in your favor, with thinking you have a guaranteed win.

It is rare to have ideal conditions for taking insurance. In most blackjack games shoe penetration is never deep enough and a reshuffle takes place when the shoe reaches 3 decks.

Take into account the fact that if you underestimate or overestimate the number of decks remaining in the shoe, you can easily miss assess your odds.

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