Blackjack Odds and Probabilities

Dealer Bust Probabilities

One of the most important probabilities to understand is the chance a dealer will bust based on their upcard. These probabilities directly influence whether you should hit, stand, or double.

Notice that dealers bust most frequently when showing 5 or 6. This is why basic strategy recommends doubling and splitting more aggressively against these cards. Conversely, when the dealer shows 10 or Ace, they bust less often, so you need stronger hands to stand.

House Edge and Expected Value

The house edge is the casino's mathematical advantage over time. When you play basic strategy perfectly, you reduce the house edge to approximately 0.5%. This means for every $100 you bet, you expect to lose about $0.50 on average.

Deviations from basic strategy increase the house edge significantly. For example:

• Never hitting 12 against dealer 3-6: +1.5% house edge
• Never doubling 11: +0.9% house edge
• Never splitting Aces: +1.4% house edge
• Always standing on 16 against dealer 7: +0.5% house edge

This is why following basic strategy is so critical. Every deviation costs you money over time.

Blackjack Probability Distribution

Understanding what hands you'll likely get helps you make better strategic decisions. Here are the key probabilities:

• Natural blackjack (21 on first two cards): 4.83%
• Bust probability when hitting 12: 31%
• Bust probability when hitting 13: 39%
• Bust probability when hitting 14: 46%
• Bust probability when hitting 15: 54%
• Bust probability when hitting 16: 62%
• Bust probability when hitting 17: 69%

These probabilities explain why the basic strategy chart recommends standing on hard 12 against dealer 4-6, but hitting against 7-Ace. Against weak dealer cards, you can afford to take the bust risk because the dealer is likely to bust anyway.

Variance and Bankroll Management

Even though basic strategy gives you the best odds, blackjack is still a game of chance. You can have losing streaks even when playing perfectly. This is called variance.

To survive variance and come out ahead, manage your bankroll carefully. A general rule is to have at least 20-25 times your average bet as a bankroll. This gives you the cushion to survive downswings while maintaining your edge through basic strategy.