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Blackjack Probability

Master the mathematics behind optimal Blackjack strategy

How to Play Blackjack (For Beginners)

Never played Blackjack before? No problem! It's one of the easiest card games to learn:

The Goal

Get your cards to add up to 21, or as close as possible without going over. If you go over 21, you "bust" and lose automatically. You're playing against the dealer, not other players.

How a Hand Works

  1. You get 2 cards face-up (you can see them)
  2. Dealer gets 2 cards - one face-up (you can see it), one face-down (hidden)
  3. You decide: Do you want more cards to get closer to 21?
  4. Dealer plays after you're done
  5. Whoever is closer to 21 wins!

Your Options

  • Hit: Take another card (trying to get closer to 21)
  • Stand: Keep your current cards (you're done)
  • Double: Double your bet, take exactly 1 more card, then stand
  • Split: If you have two of the same card (like two 8s), split them into two separate hands

Card Values

  • Number cards (2-10): Worth their face value (a 7 is worth 7 points)
  • Face cards (Jack, Queen, King): All worth 10 points
  • Aces: Worth either 1 or 11 points - you choose! (Usually 11 unless that would bust you)

Special Terms

  • Blackjack: An Ace + a 10-value card (like Ace + King = 21). This is the best hand!
  • Bust: Going over 21 - you lose immediately
  • Hard Hand: A hand without an Ace, or where the Ace counts as 1 (like 10 + 7 = 17)
  • Soft Hand: A hand with an Ace counting as 11 (like Ace + 6 = "soft 17")
  • Dealer's Upcard: The dealer's card you can see

Dealer Rules (Important!)

The dealer doesn't make choices - they follow fixed rules:

  • Must hit (take a card) if they have 16 or less
  • Must stand (stop) if they have 17 or more
Example Hand: You have Ace + 6 = 17 (soft 17). Dealer shows a 9. Should you hit or stand? You should HIT! Why? Because your Ace can count as 1 if needed, so you can't bust on the next card. If you get a 4, you'd have Ace + 6 + 4 = 21!

Quick Rules Summary

  • Objective: Get closer to 21 than the dealer without going over
  • Blackjack (Ace + 10-value): Best hand, usually pays 3:2
  • Bust (over 21): You lose immediately
  • Dealer must hit on 16 or less, stand on 17+

Basic Strategy

Basic strategy is the mathematically optimal way to play every hand based on your cards and the dealer's upcard.

Hard Hands (No Ace or Ace counted as 1)

  • 5-8: Always hit
  • 9: Double if dealer shows 3-6, otherwise hit
  • 10: Double if dealer shows 2-9, otherwise hit
  • 11: Always double
  • 12: Hit if dealer shows 2-3 or 7+, stand on 4-6
  • 13-16: Stand if dealer shows 2-6, hit on 7+
  • 17+: Always stand

Soft Hands (Ace counted as 11)

  • Soft 13-15: Hit if dealer shows 5-6, otherwise hit
  • Soft 16-17: Double if dealer shows 4-6, otherwise hit
  • Soft 18: Double if dealer shows 3-6, stand on 2,7,8, hit on 9+
  • Soft 19+: Always stand

Pairs

  • Aces and 8s: Always split
  • 10s: Never split
  • 9s: Split if dealer shows 2-6 or 8-9
  • 7s: Split if dealer shows 2-7
  • 6s: Split if dealer shows 2-6
  • 2s and 3s: Split if dealer shows 2-7

Key Probabilities

Dealer Bust Probability by Upcard

Dealer Upcard Bust Probability
235.30%
337.56%
440.28%
542.89%
642.08%
725.99%
823.86%
923.34%
1021.43%
Ace11.65%

Player Bust Probability by Hand Value

Hand Value Bust Probability if Hit
1231%
1339%
1456%
1558%
1662%
1769%
1877%
1985%
2092%
Key Insight: The dealer's 6 is the worst upcard for them (42% bust rate), which is why basic strategy tells you to stand on weaker hands when the dealer shows 4-6.

House Edge

  • Perfect Basic Strategy: ~0.5% house edge
  • Average Player: 2-3% house edge
  • Poor Strategy: 4-5% house edge
Important: Following basic strategy reduces the house edge to its minimum. Every deviation from basic strategy increases the house advantage.

Strategy Tips

  • Never take insurance (increases house edge)
  • Always split Aces and 8s
  • Never split 10s or 5s
  • Double down on 11 when possible
  • Stand on hard 17 or higher
  • Hit soft 17 or lower
  • Learn basic strategy perfectly before attempting card counting

Interactive Blackjack Trainer

Practice making optimal decisions with real-time feedback!

A♥
7♣
Your Hand: 18
Dealer showing: 6♦
What's your move?
Correct
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Total
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Accuracy
0%