Blackjack Probability of Winning – Odds for Each Hand

Thinking Man on Right With a Closeup of a Blackjack Table on Right

Blackjack strategy is heavily context-dependent. That means the right play depends on every variable in the game. Each player hand has a different optimal strategy which itself depends on the dealer’s up card and in some cases a running count.

The odd of winning a game of blackjack can be quantified, and players’ ideal moves have long been codified as optimal blackjack strategy.

In this post, I’ll talk about the probability of winning hands in blackjack, covering odds for each hand, hoping to explain and justify some of the actions required by following basic game strategy.

Overall Blackjack Probability of Winning

Let’s start by talking about how often players win, tie, and lose when playing blackjack for real money.

Assuming you’re playing a standard blackjack game in a casino and you’re following basic strategy, you have a 42.22% chance of winning on each hand, along with an 8.48% chance of a push, and a 49.10% chance of losing. Over an hour of play at a busy table, you’re likely to win 26 hands, lose 29 hands, and tie 5 times. If you’re betting $10 a hand, that hour of play will cost you an average of $30.

What about multiple wins or losses in a row? You can come up with a basic probability for the odds of winning or losing x number of times with some simple multiplication. Let’s say you want to know the odds of winning three times in a row – raise your overall odds of winning (42.22%) to the third power (for 3 wins in a row), and you get 7.5%. Winning three times in a row should happen about once every 12 or 13 sessions.

What about the odds of losing five hands in a row? Raise your odds of losing (49.10%) to the fifth power (for 5 losses in a row), and you get 2.8%. That’s about 1 in every 30 blackjack sessions.

I want to show an extreme example of consecutive losses to prove a point. Your odds of losing 12 hands in a row in blackjack are surprisingly high. Just take your odds of losing on each hand (49.1%) and raise it to the 12th power. That gives you a 0.019% chance of losing a dozen hands in a row. That means one in every 5,000 blackjack sessions could produce a string of 12 consecutive losses.

Variance is part of the game, and you’re more likely to see long streaks of wins and losses the more you play.

Blackjack Odds vs. Dealer Up Card

Here’s a chart showing the advantage held by a player following basic strategy against the dealer, based on the up card showing in the dealer’s hand:

  • Dealer 2 – dealer busts 35.3% of the time – player advantage is 9.8%
  • Dealer 3 – dealer busts 37.56% of the time – player advantage is 13.4%
  • Dealer 4 – dealer busts 40.28% of the time – player advantage is 18%
  • Dealer 5 – dealer busts 42.89% of the time – player advantage is 23.2%
  • Dealer 6 – dealer busts 42.08% of the time – player advantage is 23.9%
  • Dealer 7 – dealer busts 25.99% of the time – player advantage is 14.3%
  • Dealer 8 – dealer busts 23.86% of the time – player advantage is 5.4%
  • Dealer 9 – dealer busts 23.34% of the time – casino advantage is 4.3%
  • Dealer 10 – dealer busts 21.43% of the time – casino advantage is 16.9%
  • Dealer J – dealer busts 21.43% of the time – casino advantage is 16.9%
  • Dealer Q – dealer busts 21.43% of the time – casino advantage is 16.9%
  • Dealer K – dealer busts 21.43% of the time – casino advantage is 16.9%
  • Dealer A – dealer busts 11.65% of the time – casino advantage is 16%

Notice that the house gains a big edge when the dealer shows a 10-point card or an Ace. Also notice that an optimal strategy player has their biggest edge against a dealer 6, which is also the second-most likely total for the dealer to bust on.

You should also consider average player profits per $1 bet against a dealer’s hands. For example, the notorious 10-10 hand, which people argue about in terms of to split or not to split, performs differently depending on the dealer’s up card.

Dealt Blackjack Table

The below chart shows your profit expectations against different dealer up cards when standing with 10-10:

  • against a dealer Ace – $0.60 per dollar
  • against a dealer 10 – $0.56 per dollar
  • against a dealer 9 – $0.76 per dollar
  • against a dealer 8 – $0.79 per dollar
  • against a dealer 7 – $0.77 per dollar
  • against a dealer 6 – $0.68 per dollar
  • against a dealer 5 – $0.67 per dollar
  • against a dealer 4 – $0.65 per dollar
  • against a dealer 3 – $0.64 per dollar
  • against a dealer 2 – $0.63 per dollar

It may help to zoom in and analyze other blackjack scenarios in this manner to analyze the odds of each hand winning or to confirm what optimal strategy is instructing you how to play the hand that is dealt on the table.

Dealer Final Hand Odds

What kind of hand do you need to form to beat the dealer? It helps that blackjack dealer’s in-game behavior is controlled by the rules of the game so that in most games the dealer stands on a soft total of 17.

Below is a chart showing the dealer’s odds of drawing each final hand:

  • Natural blackjack – 4.82%
  • 21 (multi-card hand) – 7.36%
  • 20 – 17.58%
  • 19 – 13.48%
  • 18 – 13.81%
  • 17 – 14.58%
  • Bust – 28.37%
The dealer is going to do no worse than a push when he gets a natural – that 4.82% comes straight out of your bankroll. Likewise, provided you’re following optimal strategy and don’t bust out yourself, 28.37% of dealer’s hands that bust are most likely going to be wins that go straight to your pocket.

The other 66.81% of dealers’ hands will require more finesse if you want to win more often than you lose. With a dealer total of 20 or 21, your most likely positive result is a push. If you do the math, you’ll see that those totals account for about 25% of all dealer’s hands.

Odds of Each Blackjack Two-Card Combo

Every round of blackjack starts with two cards dealt to each player. Your odds, and even your ideal strategy, depend heavily on this two-card draw.

Let’s start by looking at a chart of the frequency of each type of two-card combo to start the game:

  • Natural blackjack – 4.8%
  • Hard 17-20 – 30%
  • 2-16 – 38.7%
  • Any total less than 11 – 26.5%

What do we learn here? Those decision hands (totals of 2-16) make up more than 1/3 of all hands you play, while those hard standing totals of 17-20 make up less than 1/3. You won’t need to worry much about that 4.8% of hands that result in a natural – you’ll win most of those no matter what.

Closeup of Blackjack Table

This chart also tells us that we should probably only be hitting about 65% of the time, a little less than 2/3 of all hands. If you’re hitting more or less frequently than that, it may be time to brush up a little more on your strategy.

Odds of Busting on Each Blackjack Hand

Speaking of hitting strategy, how likely is each blackjack hand to bust when taking a hit?

  • 20 – 92%
  • 19 – 85%
  • 18 – 77%
  • 17 – 69%
  • 16 – 62%
  • 15 – 58%
  • 14 – 56%
  • 13 – 39%
  • 12 – 31%

It surprises some people to s6ee that a total of 14 will bust more often than not when you hit it. It seems like a relatively safe total to hit from since there are six cards you can draw that won’t cause you to bust. Such is the mathematics underpinning blackjack – hit a hand point total between 14 and 16, and you’ll bust out close to 60% of the time.

This chart also shows why 15 and 16 are such maddening totals. The dealer will beat your 16 more than 2/3 of the time (66.81%), but if you hit that 16, you’ll bust out at almost the same rate (62%).

Another important feature to point out – less than 1/3 of hit 12 hands will bust. Four cards (6 through 9) will put you in the best possible position to beat the dealer. This is the reason optimal strategy generally prefers hitting a hard total of 12.

Your odds of beating the dealer only conflict with your odds of busting out against a dealer’s upcard of 4, 5, or 6. Remember that the dealer is at the greatest risk of going bust with a total of 4-6.

In Conclusion

Beating the house at blackjack is a matter of luck and knowing how to quit when you’re ahead. Since you’re likely to lose a little more often than you win over the long-term, beating blackjack means getting ahead of the house and walking out with whatever profit you managed to scrape together.

The house doesn’t always win – I showed earlier how a string of five wins is relatively common, and the dealer busts on almost 1/3 of all their hands. But based on the rules of the game, the casino has an advantageous position, sometimes more or less depending on the in-game context.

Use the probabilities and odds information in this post to make smarter and more informed decisions when playing blackjack. You won’t necessarily win more money, but you might win more often and will have a better handle on the game’s ubiquitous strategy.

Posted in: StrategyTable Games

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