The Question of Insurance

2 April 2023

By John Grochowski

QUESTION: I've read insurance in blackjack is a bad bet. It's even supposed to be bad to take even money on blackjacks, but the temptation is really strong to take that sure payoff.

How bad is it? How much am I losing if I insure blackjacks.

ANSWER: Let's use a six-deck game as an example, since that's the most common condition in modern casinos. Assume average deck composition, as if you're starting with a fresh shuffle. It's different for card counters who have an idea of the proportion of high and low cards remaining to be dealt, but for basic strategy players, average composition is the default assumption.

There are 312 cards in six decks. If you start with an Ace and a 10 value for a blackjack and the dealer has an Ace face up, there are 308 other cards. Ninety-five of those are 10-value cards.

Dividing 308 by 95 tells us there is a 1 in 3.24 chance of the dealer completing a blackjack. The house edge in this situation is a whopping 7.4 percent.

Insurance pays 2-1, so it's an even break for the player only if there is a 1 in 3 chance of a dealer blackjack. Card counters take insurance if there is a 1 in 3 chance or better of the dealer having a 10 face down.

Imagine you bet $10 on each of 308 hands in which you have a blackjack. If you don't insure, you win 213 times and push on the 95 dealer blackjacks. With 3-2 payoffs bring a profit of $15 per win for a total of $3,195.

Now imagine you insure those 308 blackjacks, which you can do by calling "even money." You win every hand, but each payoff is equal to your bet. That reduces your profit to $3,080.

You win more often by insuring your blackjacks, but you win more money by just playing out the hands.

I'd rather have the extra $115 on my side of the table, so I decline insurance and accept that sometimes, a dealer blackjack will push mine.

QUESTION: My sister, my mom and I were playing slots. Mom went for a machine, and sister said, "You don't want to play that one!" Mom asked why not, and sister said, "Someone just cashed out for more than $900. It's already paid out."

Mom told her, "Those are the machines I look for. I want the hot game."

They got into a whole big thing over looking for a zero cashout on the meter because the wins are coming or a big cashout because it's a winning machine.

When I said I never even looked to see payoffs to the last player, they both looked at me like I was from Mars.

Does it make a difference.

ANSWER: Previous player cash outs make no difference at all to your chances of winning.

The random number generator that determines slot results doesn't know how much the game has played. It doesn't know where its numbers are mapped, what symbols or reel positions correspond to which numbers, or how much combinations of those symbols pay. Those functions are done by different applications.

All the RNG does is generate numbers, and it generates numbers randomly from the same set regardless of whether the previous player has cashed out $2,000 or 2 cents.

Variations on this question are the most common emails I get from readers. It's an issue I address from time to time because there always are players new to the concept that past results have no effect on future outcomes.