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Last Updated: November 9, 2018

Insurance in Blackjack - Just Say No!

Michael Shackleford: Hi guys, this is Mike and the purpose of today's Wizard of Odds Academy lesson will be to explain why you should never take insurance in Blackjack. What insurance is, is a side bet that the dealer has a 10 point card in the hole.

It is offered when the dealer already has an ace up, so it wins in the event that the dealer gets a blackjack. The insurance bet can be made for up to half of the player's original bet and it pays two to one if it wins.

I'm going to

…put a two for the pace if the dealer has a 10 point card in the hole and a negative one if the dealer has an ace and a nine which represents that the player lost his insurance bet.

Let's assume six packs of cards, shall we?

Assuming no other information other than the ace up the dealer already has, there are 96 winning cards for the insurance bet, 16 times 6 out of 311 left. There's 311 because a full six-deck shoe is 312 cards and we take one out because of the dealer's ace, and there are 215 cards that will cause the insurance bet to lose.

Insurance in blackjack

Let's take the product of the win and the probability.

2 times 96 over 311 is 61.74% and 215 divided by 311 times -1 is -69.13%. In other words, the player can expect to win 61.74% of his bet and lose 69.13% of his bet. We take the sum which is -7.40%. That means that for every dollar the player bets on insurance, he can expect to lose 7.4 cents or 7.4% of whatever his insurance bet is.

7.4% is a pretty high house advantage and consequently, I recommend that you say no to insurance every time. Before someone says in the comments, "Mike, what if the count is good? What if I'm counting cards?"

Yes. Then, of course, there are exceptions. If you've been counting cards and you know that the remaining cards are very 10 rich, but for the recreational player that's not counting, insurance is a terrible bet and, again, I recommend you decline it every time.

"What about even money?"

You might be asking me. Well, let me explain to you first of all, that the even money offer is the same thing as taking insurance. It's only offered when the player already has a blackjack and the dealer has an ace up.

Let's look

…at what would happen both ways if the player has a blackjack and takes insurance. If the dealer ends up getting that blackjack, the main bet will push, so it wins nothing, but the insurance but will win one unit because the player bets half a unit on insurance. The insurance but pays two to one on the winning blackjack. One-half times two equals one.

Next…

If the dealer does not get that blackjack, the player's main wager will pay one and a half but he will lose half a unit on the insurance. The combined when between the main wager and the insurance wager is one unit when the dealer does get a blackjack and one unit when the dealer does not get a blackjack.

It doesn't make any difference whether or not the dealer gets a blackjack. If the player has a blackjack and takes insurance, he wins one unit either way and what the dealer is essentially saying is, "Look, if you take insurance, you're going to win one to one regardless if I have a blackjack. I may as well just pay you now before I even check what I have.”

It sounds attractive but let's do some math and see if you should take it. Let's evaluate the situation where the player has a blackjack, the dealer has an ace up and the player declines insurance. If the dealer has a 10 in the hole, then the player will win nothing because it will be a blackjack against blackjack tiein other words, a push. If the dealer has anything else in the hole, the player will win his full three to two on his wager or 1.5.

Let's assume:

knowledge of no other cards in the shoe other than what's already on the table. There are 309 cards left out of the 312 card shoe, less than three cards already involved, the player's ace and 10 and the dealers ace.

Blackjack

The probability that the dealer has a 10 in the hole is 95 divided by 309. Like I just said, there's 309 cards left, the shoe started with 96 tens but the player has one of them. The chances that the dealer has an ace to 9 in the hole is 214 divided by 309.

Let's examine what the player can get back either way:

If the dealer does have that 10 in the hole, the player can expect to get back nothing because the probability of zero times anything is zero. If the dealer does not have a 10 in the hole, the player can expect to get back 1.5 with a probability of 214 divided by 309. The product of those two numbers is 103.88%. If we add them up, it's obvious you still get that same 103.88%.

What this means is

…if the player has a blackjack, the dealer has an ace up, the player can expect to win 1.0388 times his bet or about 104% of whatever he bet. The decision to whether or not to take even money is the decision; do you want to get back an average of 103.88% of your bet or just 100%? What's more? 100% or 103.88%? Well, 103.88% is more, therefore, if you're seeking the greater expected value, which you should be in any casino game, you should decline even money and go for that 103.88%.

Few caveats here:

Number one - again this is assuming the player is not counting cards, just a recreational player. Number two - this is assuming that a blackjack pays three to two.

Finally, this question has come up on every once in a while and a lot of people use the argument that yes, I make a good mathematical argument for declining an insurance even money but what about the psychological argument?

If you’re in this situation with a blackjack against the dealer ace, some people will say you have a 100% chance of being happy by taking the even money, locking in a sure win but only a 69.26% chance of being happy by declining the even money.

Those figures are right but

…in the casino as well as real life, you should be long-term minded. You should be thinking what is the expected average gain for any decision that you make? Do not always play conservatively and lock in the small win when the average win by taking a chance is greater.

Of course, there are exceptions for life-changing situations but if you’re playing Blackjack, it assumes that you like gambling, to begin with. You’re in the casino you’re gambling, gamble on winning that full one and half, don’t settle on the measly one unit. Furthermore, even if you do use this argument of I want a 100% chance of being happy right now, I’ll take the even money. That happiness is only going to last less than a minute until the next hand.

I think…

…you should be thinking what is going to be your happiness when you finally walk away from the table and you go home for your trip? The more money you win or the less money you lose from that sitting and the whole trip, the happier you’re going to be.

Furthermore, you’re going to get more, shall we say, action by taking that chance on winning with your blackjack. Like I said you’re gambling, to begin with, so gamble!

I can’t think of anything else to say on this topic. I hope that I’ve convinced you to always say no to insurance and even money.

Thanks, guys for listening and I’ll see you in the next video.

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