What is the mathematical probability of busting (going over 21) when hitting with a hand total of 16?

Okay, let's talk about a classic scenario in Blackjack.

In short: Hitting on 16 has a bust probability of approximately 61.5%

This is a considerably high risk. Below, I'll break down exactly why this number is what it is.

Why this number?

Let's do some simple math, assuming we're using a freshly shuffled, complete 52-card deck.

1. First, identify which cards will make you bust

You have 16 points. In Blackjack, exceeding 21 points is called a "bust". So, 16 + ? > 21. Simple calculation tells us that if your next card's value is greater than 5, you will bust.

These "dangerous cards" are:

• 6
• 7
• 8
• 9
• 10, J, Q, K (these cards all count as 10 points)

2. Count how many of these "dangerous cards" are in the entire deck

• 6, 7, 8, 9: There are 4 cards of each of these four ranks (Spades, Hearts, Clubs, Diamonds). So, 4 x 4 = 16 cards.
• 10, J, Q, K: These four cards also count as 10 points, and there are 4 of each. So, 4 x 4 = 16 cards.

Adding them up: 16 + 16 = 32 cards. Out of a 52-card deck, there are 32 cards that will cause you to bust immediately when you have 16.

3. Calculate the probability

Probability is the number of cards that cause you to bust divided by the total number of cards in the deck. So, the theoretical probability is:

32 / 52 = 8 / 13 ≈ 61.54%

The Gap Between Theory and Reality: Why "Approximately"?

The 61.5% mentioned above is an idealized theoretical value. At an actual blackjack table, the situation is slightly more complex because:

• Your own hand: The cards that make up your 16 points are no longer in the deck. For example, if you have 10+6, then there's one less 10 and one less 6 in the deck. If you have 9+7, there's one less 9 and one less 7. This slightly alters the distribution of the remaining cards, thus affecting the probability.
• Dealer's upcard and other players' cards: All cards already revealed on the table will not reappear in the deck. If many small cards (e.g., 2, 3, 4) have already appeared on the table, then the probability of large cards remaining in the deck increases, and your bust risk also increases. The opposite is also true. This is the basic principle of "card counting".

Game Strategy Tips

Precisely because the bust risk of hitting on 16 is so high (over 60%), it becomes a very critical decision point in Blackjack strategy.

• When the dealer's upcard is 2, 3, 4, 5, or 6: The strategy usually advises you to Stand. Because the dealer also has a high risk of busting, you don't need to take that risk yourself; leave the pressure on them.
• When the dealer's upcard is 7, 8, 9, 10, or A: The strategy then advises you to Hit. Although the bust risk is high, you have to gamble. Because the dealer has a high probability of getting 17 or more, you're almost guaranteed to lose with 16 points, so you have to grit your teeth and draw a card, hoping for that less than 40% chance of good luck.

Hope this explanation helps you! At the table, understanding these basic probabilities is the first step to making correct decisions.