The Importance of Naturals in Blackjack

What’s a “natural” in blackjack?

And why is it so important?

A natural is a two-card hand that totals 21. There’s only one way for this to happen—you must get an ace as one of your initial two cards, and the other card must be worth 10 points.

And a natural is also called a blackjack, but since the name of the game is blackjack, it’s often easier to write about the hand as a “natural” to avoid confusion.

But the importance of this specific hand can’t be understated, and in this post, I look at why naturals are so important in blackjack.

The main reason a natural is so important is because it results in a 3:2 payout instead of an even money payout. In other words, if you bet $200 on a hand and get a natural, you get a $300 payout instead of a $200 payout.

This changes everything, and you’ll find out why below.

The Concept of Expectation in Blackjack

It’s a good idea to understand what the odds of getting a blackjack are. It’s a happy event, but there’s nothing you can do, decision-wise, to improve the probability of getting a blackjack. You either get two cards that total 21 or you get some other total.

You only make decisions when you have another total. When you have a blackjack, you just collect your winnings and celebrate.

One of the things we’re concerned with when talking about casino games is the player’s expectation on a bet. It’s usually expressed as a percentage. If it’s an expectation of 100%, the game is a breakeven proposition.

Of course, in a casino, the expectation is always lower than 100%. The difference between the player’s expectation and 100% is the house edge.

Every possible payout contributes to the expectation; you multiply the potential payoff by the probability of getting it to get that situation’s return. When you add up all the returns, you get the total expectation for the game.

A Simplified Explanation of Expectation in Blackjack

In blackjack, a simplified view of the expectation looks at the probability of the following events:

• Losing
• Winning
• Getting a natural
• Push

When you lose, you lose whatever bet you place. Bet $200 on a hand of blackjack and bust, for example, and the casino dealer takes your $200.

When you win, you get even money, except in the case of a natural. In other words, if you bet $200, you get to keep your $200 and you get $200 in winnings.

When you get a natural, you get a 3:2 payout—that’s the same as getting $300 on a $200 bet.

In the case of a tie, you’re said to “push.” In that case, you don’t lose your bet, but you don’t get any winnings either.

A simplified view of your expectation, assuming a totally fair game, might look like this:

• 45% chance of losing $200 (That’s -$90.)
• 45% chance of winning $200 (That’s +$90.)
• 5% chance of winning $300 (That’s +$15.)
• 5% chance of winning/losing $0. (That’s $0.)

In such a game, your edge would be huge.

But the dealer makes you play your hand first, and if you bust, the dealer wins, even if the dealer busts later in the hand. This changes the percentages in such a way that the bonus payout for a natural still isn’t enough to give you an edge over the casino.

All the examples I’ve given so far offered fictional numbers for the sake of making it easy to understand something like calculating odds. You don’t really have a 45% chance of winning or losing; your probability of winning is actually lower than that. Even the 5% probability of getting a blackjack is just an estimate.

The Probability of Being Dealt a Natural in Blackjack

What’s the actual probability of being dealt a natural?

It’s not a complicated formula, actually.

First, you look at the probability of getting an ace as your first card. Since you have 4 aces in a deck of 52 cards, the probability is 4/52, or 1/13.

To get a blackjack, you also need to get a card worth 10 as your next card. You have 16 cards in the deck that are worth 10, so the probability of that is 16/51. (Notice that the denominator changed because one of the aces is already accounted for.)

But you might also get a 10 as your first card, in which case, you need to get an ace as your next card. The same formula applies, but in reverse, and you add the two probabilities together to get 2 in 41.44, which is the same as 1 in 20.72.

You can convert that into a percentage and see that your probability of getting a natural is 4.83%.

As you can see, my 5% estimate in the previous section wasn’t that far from accurate.

Dealers Get Blackjacks Too

But we also need to consider how often the dealer gets a blackjack.


That formula isn’t complicated, either, although we now have to adjust for the cards that have already been dealt.

For the dealer to get an ace as her first card, the probability is 3/50. You only have 50 cards left in the deck, and only three of them are aces.

For the dealer to get a 10 as her next card, the probability is 15/49.


3/50 X 15/49 = 45/2450, which is the same as 1 in 54.44 or 1.84%.

Double that to account for the possibility of getting a 10 as your first card and an ace as your second card, and it’s easy to see that the probability of a push when you and the dealer both get a natural is 3.68%. That’s about the same as 1 in 27.22.

This means that out of every 27 or so blackjack that you’re dealt, the dealer will also get a blackjack and the hand will result in a push.

How Does It Affect the Odds?

The house gets an edge because the dealer plays her hand after the player. If the player busts, his bet is taken as a loss before the dealer even has to play her hand. This gives the house a big edge. After all, how often do you bust in blackjack?

And if you play your hand so conservatively that you never bust, you’ll lose even more money.

The common wisdom is that the house edge for blackjack is between 0.5% and 1% if you play with perfect basic strategy.

What would happen if you removed the bonus payout for the blackjack and just paid even money for that hand?

It would increase the house edge by 2.32%.

That doesn’t sound like much; it’s not even 3%. But let’s look at what effect that has on the grind.

An average blackjack player might get in 80 hands per hour at a table, and he might be betting $10 per hand. This means he’s putting $800 into action per hour.

On average, he expects to lose 0.5% of that at a blackjack table, which is about $4 per hour.

This is what makes blackjack such cheap entertainment.

Add 2.32% to the house edge, and now the edge is 2.8%, which means that same player is now losing an average of $22.40 per hour.

The losses per hour increase by a factor of 5, almost 6.

It’s still better than slot machines, but the point isn’t to compare blackjack with worse casino games.

It’s to realize how big a deal the payout on a blackjack is.

Lowered Payouts for Naturals

You will indeed find blackjack variations in casinos with a lowered payout for a natural. The casino will usually offer other perks in exchange for the lowered payout, but these more favorable rules are never favorable enough to compensate for the change in the house edge.

In fact, the casino almost always has a higher edge in these games than in a standard blackjack game.

You can also find casinos offering 6:5 payouts for a blackjack. I think it’s especially insidious because the casinos try to make it sound like you’re getting a good deal even though you’re not. They figure that the mathematically illiterate customers will think that 6 is bigger than 3, and so they’re getting a better deal.

I skip any blackjack game with a payout for a natural of less than 3:2.

Higher Payouts for Naturals

On the other hand, some casinos have special promotions where they’ll offer higher than usual payouts for a blackjack. They might offer a 2:1 payout instead of 3:2.

Any time you can take advantage of such a special, you should. Often, this change alone is enough to turn blackjack into a positive expectation bet, albeit a game with a small edge for the player.

How to Find Blackjack Promotions

The best way to find blackjack promotions like this at a casino is to join the players club. You’ll get plenty of advertising about the casino’s promotions for all their games, blackjack included.

You’ll also get rebates as a percentage of the amount of action you’re bringing to the casino.

But be cautious.

Casinos don’t run rebate programs because they lose money on them. They run these programs because they profit from them.

In other words, most gamblers spend more time and money at the casino after joining the players club than they did before.

And the casinos offer bigger perks based on which tier you fall into in the players club. I have a friend who was in the top of three tiers at the casino, but he was visiting the casino at least once a week to try to keep his membership level.

Conclusion

As I said in the introduction to this post, it’s hard to understand the importance of a natural in a blackjack game. The big payout for the natural is the reason the house edge is so low in the game. After looking at the math behind this, it should be obvious why.