Why You Can't Score 19 in Cribbage: Impossible Scores Explained
Learn why 19, 25, 26, and 27 are impossible scores in cribbage, and why a zero-point hand is called a 'nineteen.' Complete mathematical explanation.
Why You Can’t Score 19 in Cribbage
“I got a 19.”
If you’ve played cribbage, you’ve heard this — and you know it means the speaker scored zero points. But why 19? And what makes it impossible?
Welcome to the strange mathematics of cribbage scoring.
The Impossible Scores
In cribbage, there are four scores you can never achieve with a 5-card hand:
| Score | Status |
|---|---|
| 19 | Impossible |
| 25 | Impossible |
| 26 | Impossible |
| 27 | Impossible |
Every other score from 0 to 29 is achievable with the right combination of cards.
Why 19 Is Impossible
Let’s break down cribbage scoring:
The Building Blocks
| Combination | Points |
|---|---|
| Fifteen | 2 |
| Pair | 2 |
| Pair Royal (trips) | 6 |
| Double Pair Royal | 12 |
| Run of 3 | 3 |
| Run of 4 | 4 |
| Run of 5 | 5 |
| Four-card flush | 4 |
| Five-card flush | 5 |
| Nobs | 1 |
The Math
To get exactly 19 points, you’d need a combination of these values that adds to 19.
Possible without any fifteens:
- Pure runs don’t help (3, 4, 5)
- Pairs (2, 6, 12) don’t help
- Flushes (4, 5) don’t help
- No combination of these equals 19
With fifteens (multiples of 2):
- Fifteens contribute 2, 4, 6, 8, 10, 12, 14, or 16 points
- Adding pairs (2, 6, 12) and runs (3, 4, 5) and flush (4, 5) and nobs (1)
- No combination totals exactly 19
The problem: 19 is odd, and the only odd contributions are:
- Runs (3, 4, 5)
- Five-card flush (5)
- Nobs (1)
To get to 19 (odd), you need an odd total from the non-fifteen elements. But the hands that produce high fifteens also tend to include pairs (even), creating combinations that skip 19.
The Mathematical Proof
This has been verified by brute-force computer analysis of all possible 5-card hands.
There are C(52,4) × 48 = 778,320 possible hand+starter combinations.
None of them produce exactly 19, 25, 26, or 27 points.
Near Misses
| Score | Example Hand | What’s Missing |
|---|---|---|
| 18 | 6-6-7-8-8 | +1 would need nobs, but no Jack |
| 20 | 5-5-5-10-J | Has fifteens, pairs, nobs — skips 19 |
Why 25, 26, and 27 Are Impossible
These high scores fall in the gap between achievable totals.
Achievable High Scores
| Score | Example Hand |
|---|---|
| 24 | 5-5-5-J with 10 starter |
| 24 | 4-5-6-6 with 5 starter |
| 28 | 5-5-5-J with J starter (wrong suit) |
| 29 | 5-5-5-J with 5 starter (matching J suit) |
The Gap at 25-27
To score above 24 but below 28, you’d need a very specific combination that doesn’t exist. The hands that produce 28+ require four 5s and a Jack (or similar), which creates such strong scoring that it jumps over 25-27.
Why “19 Hand” Means Zero
The term emerged because:
- You can’t actually score 19
- Saying “I scored 19” is obviously a joke
- It’s less embarrassing than saying “zero”
- The humor is self-deprecating
It’s been cribbage slang for generations. When you hear someone announce “19,” you know they got skunked on that hand.
How Often Does Zero Happen?
Zero-point hands (actual 19s) occur with specific conditions:
- No fifteens (hardest to avoid)
- No pairs
- No runs
- No flush
- No nobs
Example 19 hands:
- A♠ 4♥ 6♣ 9♦ with K♠ starter — no scoring combination
- 2♠ 5♣ 7♥ 9♦ with K♣ starter — the 5 and K don’t pair, no flush, no fifteens, no runs
Frequency: Approximately 1.5-2% of hands score zero — about once every 50-70 hands.
All Achievable Scores
For completeness, here’s evidence that everything else is possible:
| Score | Example Hand |
|---|---|
| 0 | A-4-6-9-K (no combos) |
| 1 | Nobs only (rare) |
| 2 | Single fifteen or pair |
| 3 | Run of 3 only |
| 4 | Two fifteens OR flush |
| … | … |
| 18 | Various combinations |
| 20 | 6-7-7-8-8 with 9 |
| … | … |
| 24 | Multiple hands |
| 28 | 5-5-5-J-J |
| 29 | 5-5-5-J with matching 5 |
Trivia: Impossible vs. Improbable
| Situation | Status | Odds |
|---|---|---|
| Scoring exactly 19 | Impossible | Never |
| Scoring exactly 29 | Possible | 1 in 216,580 |
| Scoring exactly 0 | Possible | ~1 in 60 |
| Scoring exactly 1 | Possible but rare | ~1 in 500+ |
What This Tells Us
The existence of impossible scores reveals that cribbage’s scoring system, while elegant, has mathematical constraints. The designers (17th-century card players) almost certainly didn’t know about these gaps — they emerged naturally from the scoring rules.
It’s one of those delightful quirks that makes cribbage mathematically interesting centuries after its invention.
Next Time You Score Zero
Remember: you didn’t score zero — you scored 19.
And that’s the cribbage way.