True Insurance Odds—Worth the Wager? Part II

Earlier today I explained how the odds of an insurance bet in blackjack are not equivalent to the payout, making it an unfair blackjack wager.

Yes, fair wagers do exist. Take that single number roulette wager. It carries 36-1 odds and has a 36-1 payout. That makes it a fair wager.

We already determined this morning that if in the first round of blackjack that the dealer had an Ace showing and neither of your cards were worth 10 that the odds were 2.0625-1, which does not equal the 2-1 payout that the house offers.

But that is an unlikely scenario. So let’s look at a more realistic one.

Let’s say that that the dealer still has the Ace showing and you do have a 10 in your hand. That means that there are only 15 10 value cards left in the deck (remember, we are using a single deck in these examples to make the math easier to show), and 34 non 10 value cards left. So the odds are now 34-15 that the dealer has a 10 for a hole card; those odds reduce to 2.26-1. So the equivalent payout here would be \$22.60 on a \$10 insurance bet. But we already know that we would only get \$20.

Now we are going to say that two rounds have passed and that we are on the third. There are 40 cards left now, and with 3 10 value cards taken out of play already, that leaves 13 left in play. The third round begins and the dealer is dealt an Ace up while you are dealt a 10 and a non 10 value card.

So now there 12 10 value cards left in play and 16 non 10 value cards left. That means the odds are 38-12, reducing to 3.167. That means that if the dealer were to have a 10 for a hole card, you should be paid \$31.67 on a \$10 bet. And that is definitely not the \$20 you would be paid for an insurance wager.

So you can see why insurance is not a good bet in blackjack. The odds do not match the payout. And because the payout is lower than what the odds say it should be it means that the house as the advantage on this odds-wise because it is an opportunity that you are losing money on. And you will remember that if it is an opportunity in which you are set up to lose money the odds favor the house and not you.