Blackjack Probability Chart: Complete Reference Tables [2026]

Q: How do I use these probability charts?

These charts show the mathematical backbone of basic strategy. Use the dealer bust chart to understand why you stand against weak upcards. Use the player bust chart to see why hitting stiff hands is risky. Use the EV table to understand which hands are profitable and which are damage-control.

Q: Which chart is most important for strategy?

The dealer final hand distribution by upcard is the most strategically valuable. It tells you exactly what the dealer will end up with based on their visible card, which drives every hit/stand/double/split decision in basic strategy.

Q: Do these probabilities change with the number of decks?

Slightly. The probabilities shift by small fractions between 1-deck and 8-deck games, but the overall patterns remain identical. The charts on this page are based on 6-deck S17 rules, which is the most common game configuration.

Q: What is the card removal effect?

The card removal effect measures how much the house edge changes when a specific card is removed from the deck. Removing a 5 benefits the player most (+0.67% per card), while removing an Ace hurts most (-0.59%). This is the mathematical foundation of card counting.

How to Use These Charts

This page is a data reference — the mathematical backbone behind every basic strategy decision. You don't need to memorize these numbers. Instead, use them to understand why the strategy chart tells you to make specific plays.

All charts assume: 6-deck shoe, dealer stands on soft 17 (S17), 3:2 payout — the most common ruleset worldwide. Numbers shift slightly with different rules or deck counts, but the patterns remain consistent.

How I Use These

Whenever I'm studying a hand I played poorly, I come back to these tables. "Why does basic strategy say hit 12 vs dealer 3?" I look at the dealer bust rate for 3 (37.6%) — not high enough to justify standing with just 12. "Why double 11 vs everything except Ace?" The EV table shows doubling 11 has massive positive expected value against most upcards. The charts turn confusing strategy rules into simple, visible math.

Chart 1: Dealer Final Hand by Upcard

This is the most strategically valuable chart on the page. It shows the probability of the dealer ending on each final total (17 through 21, or bust), broken down by their visible upcard. All numbers assume the dealer has already checked for — and does not have — blackjack.

Dealer Final Hand Probability (%) 6-Deck · S17 · After checking for BJ
Upcard	17	18	19	20	21	Bust
2	14.0	13.2	13.0	12.4	12.2	35.3
3	13.3	13.0	12.4	12.1	11.6	37.6
4	13.1	12.2	11.7	11.5	11.2	40.3
5	12.2	12.3	11.7	10.8	10.2	42.9
6	16.5	10.6	10.7	10.2	9.9	42.1
7	36.9	13.8	7.9	7.9	7.4	26.2
8	12.9	35.9	12.9	6.9	6.9	24.4
9	12.0	12.0	35.4	12.1	5.2	23.3
10	11.2	11.2	11.3	33.5	11.5	21.4
A	13.1	13.1	13.2	13.2	35.8	11.7

How to Read This

When dealer shows 7, they end on 17 a whopping 36.9% of the time — because 7+10 = 17, stand. When dealer shows 5 or 6, they bust over 42% of the time. When dealer shows Ace, they make 21 35.8% of the time and bust only 11.7%. This is why the Ace is the most dangerous upcard — and why insurance exists (though it's still usually a bad bet).

Chart 2: Dealer Bust Probability by Upcard

Upcard	Bust %	Category	Player Advantage
2	35.3%	Weak	+9.8%
3	37.6%	Weak	+13.4%
4	40.3%	Very Weak	+18.0%
5	42.9%	Weakest	+23.2%
6	42.1%	Very Weak	+23.9%
7	26.2%	Neutral	+14.3%
8	24.4%	Strong	+5.4%
9	23.3%	Strong	−4.3%
10/Face	21.4%	Very Strong	−16.9%
Ace	11.7%	Strongest	−36.0%

The dividing line is clear: upcards 2–6 are "bust cards" (35–43% bust rate), and 7–A are "pat cards" (12–26% bust rate). This binary split is the foundation of all basic strategy: stand on stiff hands vs bust cards, hit vs pat cards.

Chart 3: Player Bust Probability by Total

Hard Total	Bust % on Hit	Cards That Bust You
11 or less	0%	None — impossible to bust
12	31%	10, J, Q, K (4 ranks)
13	39%	9, 10, J, Q, K (5 ranks)
14	56%	8, 9, 10, J, Q, K (6 ranks)
15	58%	7, 8, 9, 10, J, Q, K (7 ranks)
16	62%	6, 7, 8, 9, 10, J, Q, K (8 ranks)
17	69%	5 through K (9 ranks)
18	77%	4 through K (10 ranks)
19	85%	3 through K (11 ranks)
20	92%	2 through K (12 ranks)

Notice the sharp jump between 13 (39%) and 14 (56%). This is why hitting 13 vs a strong dealer upcard is reasonable, but hitting 17+ is almost never correct — the bust probability just becomes too high.

The "Stiff Hand" Zone

Hands 12–16 are called "stiff" for a reason — you're stuck between a rock and a hard place. Hit and you bust more often than not (31–62%). Stand and you need the dealer to bust. There's no comfortable play. That's blackjack. The strategy chart doesn't make these hands fun — it just picks the less painful option based on the math above.

Chart 4: Two-Card Hand Distribution

This chart shows the probability of being dealt each type of starting hand:

Starting Hand Type	Frequency	Examples
Natural blackjack (A + 10)	4.83%	A♠K♥, A♦10♣
Hard 17–20 (standing hands)	30.0%	10+7, 10+9, 10+10
Hard 12–16 (decision hands)	38.7%	10+5, 9+4, 8+6
Hard 5–11 (no-bust hands)	26.5%	7+3, 6+2, 5+4
Any pair	14.5%	8+8, 5+5, A+A
Any soft hand (excl. BJ)	13.0%	A+6, A+3, A+7

The critical takeaway: decision hands (12–16) make up 38.7% of all hands dealt — the single largest category. This is where knowing the chart makes the biggest difference. The other 61.3% of hands are either automatic plays or naturals.

Chart 5: Card Removal Effect

This chart shows how the house edge changes when a single card of each rank is removed from a 6-deck shoe. This is the mathematical foundation of card counting.

Card Removed	Effect on House Edge	Direction	Counting Value (Hi-Lo)
2	+0.40%	Benefits player	+1
3	+0.43%	Benefits player	+1
4	+0.52%	Benefits player	+1
5	+0.67%	Most beneficial	+1
6	+0.45%	Benefits player	+1
7	+0.28%	Slight benefit	0
8	+0.00%	Neutral	0
9	−0.18%	Hurts player	0
10/Face	−0.51%	Hurts player	−1
Ace	−0.59%	Most harmful	−1

Removing a 5 from the deck benefits the player by 0.67% — the largest effect of any card. Removing an Ace hurts the player by 0.59%. This is why the 5 is the most "important" card in card counting: when 5s are gone, the deck is significantly better for the player.

Why Hi-Lo Works

The Hi-Lo counting system assigns +1 to cards 2–6 and −1 to 10s and Aces. This chart shows why: those are the cards that move the house edge the most. Cards 7–9 have minimal impact, so Hi-Lo counts them as 0. The system isn't arbitrary — it's built directly from this card removal data.

Chart 6: Player Outcome by Final Total

This chart shows your approximate win, loss, and push percentage based on your final hand total (assuming basic strategy):

Your Final Total	Win %	Lose %	Push %
Bust	0%	100%	0%
17	26%	60%	14%
18	40%	46%	14%
19	56%	30%	14%
20	70%	18%	12%
21 (non-natural)	85%	7%	8%
Natural BJ	95%	0%	5%

Even with a total of 18 — which feels strong — you only win 40% of the time. A final total of 17 wins just 26%. This is why basic strategy rarely recommends standing on a soft 17 or 18 when the dealer shows a strong card — those totals just aren't winning enough.

Chart 7: Expected Value by Starting Hand

This chart shows the player's expected value (EV) per dollar wagered for common starting hands against each dealer upcard. Positive = player favored, negative = dealer favored. All figures assume optimal basic strategy.

Player EV (cents per $1 bet) 6-Deck · S17 · Basic Strategy · Selected Hands
Hand	vs 2	vs 3	vs 4	vs 5	vs 6	vs 7	vs 8	vs 9	vs 10	vs A
Hard 8	+5	+7	+10	+15	+16	+7	−1	−7	−13	−14
Hard 11	+24	+27	+30	+34	+35	+22	+15	+7	+3	−3
Hard 12	−25	−23	−18	−13	−15	−21	−24	−26	−25	−29
Hard 16	−29	−25	−22	−17	−15	−41	−44	−48	−54	−51
Hard 20	+64	+65	+66	+67	+70	+77	+79	+76	+56	+60
Soft 18	+12	+15	+18	+22	+26	+40	+10	−9	−18	−10
A,A	+47	+51	+56	+62	+65	+51	+35	+14	−6	−11
8,8	−7	−4	+1	+8	+18	+3	−22	−38	−47	−38

Hard 11 is the best non-natural starting hand — positive EV against 9 out of 10 dealer upcards. Hard 16 is the worst — negative EV against everything, with the deepest losses against dealer 9, 10, and Ace. Pair of Aces (always split) has outstanding EV because each split Ace can catch a 10 for 21.

What the Numbers Tell You

Look at 8,8 vs dealer 10: the EV is −47 cents per dollar. That's brutal. But the alternative — playing hard 16 vs 10 — is also terrible (−54 cents). Splitting loses less. Basic strategy isn't about finding good options; it's about finding the least bad one. This table shows that in the most concrete way possible.

FAQ — Probability Charts

How do I use these probability charts?

Use them to understand why the strategy chart makes specific recommendations. The dealer bust table explains why you stand against weak upcards. The player bust table shows the risk of hitting stiff hands. The EV table reveals which hands are profitable and which are damage control.

Which chart is most important for strategy?

The dealer final hand distribution (Chart 1). It tells you exactly what the dealer will end up with based on their upcard, which drives every hit/stand/double/split decision.

Do these probabilities change with the number of decks?

Slightly — fractions of a percent between 1-deck and 8-deck games. The overall patterns are identical. These charts use 6-deck S17, the most common configuration. For exact numbers by deck count, see the Wizard of Odds dealer probability tables.

What is the card removal effect?

It measures how much the house edge shifts when a specific card is removed from the deck. Removing a 5 benefits the player most (+0.67%), removing an Ace hurts most (−0.59%). This is the mathematical basis of card counting.

Sources & References

Wizard of Odds — "Dealer Odds in Blackjack under U.S. Rules": Definitive dealer final hand probability tables for 1–8 decks, S17 and H17. wizardofodds.com
Wizard of Odds — "Blackjack Expected Values": Composition-dependent EV tables for every starting hand vs every dealer upcard. wizardofodds.com
BlackjackInfo — "Dealer Outcome Probabilities": Ken Smith's verified dealer final hand tables with peer-reviewed accuracy. blackjackinfo.com
BeatBlackjack.org — "Blackjack Dealer Probabilities" & "Player Probabilities": Full dealer and player final hand distributions under correct strategy. beatblackjack.org
Cache Creek Casino — "Blackjack Odds, Probabilities, and Payouts Explained": Player bust chart and dealer bust by upcard with rule-impact context. cachecreek.com
Riverwind Casino — "Blackjack Odds": Player outcome by final total and hand distribution frequencies. riverwind.com
BlackjackTactics — "Blackjack Probability Odds Charts": Card removal effect data and two-card frequency tables. blackjacktactics.com