Cribbage has a perfect hand, a handful of scores that cannot exist, and some odds long enough to be worth framing. Here is the arithmetic behind the game's strangest corners.
Twenty-nine is the highest score possible in a cribbage hand, and there is exactly one shape that produces it:
In hand: 5♥ 5♦ 5♣ J♠
Starter: 5♠
Three 5s and a Jack, with the fourth 5 — matching the Jack's suit — cut as the starter.
Total: 29 points.
Note what makes it perfect rather than merely excellent: the Jack has to be in your hand, and the 5 of that same suit has to be the starter. Swap them — Jack as the starter, 5 in hand — and you lose the nobs point. The dealer would peg 2 for his heels instead, but the hand itself counts 28.
Consider all possible combinations of a four-card hand plus a starter. There are C(52,4) = 270,725 four-card hands, and 48 remaining cards to cut for each, giving 12,994,800 distinct hand-plus-starter combinations.
Exactly four of them score 29 — one for each suit the Jack might be. That makes the chance of a random four cards plus a random starter coming to 29 about 1 in 3,248,700.
In a real two-handed game you are dealt six cards and keep four, which gives you C(6,4) = 15 chances at it from a single deal. That brings the figure to the one usually quoted:
Roughly 1 in 216,580 deals. A regular player who deals a few thousand hands a year might reasonably expect to see one in a lifetime — or never. Plenty of lifelong players have never had one.
This is why cribbage clubs make a fuss about it. The American Cribbage Congress recognises 29 hands scored in sanctioned play, and a great many boards hanging on walls commemorate a single deal.
Twenty-eight is the second-highest possible score, and unlike 29 it can arise from two different shapes:
The second case is the cruel one. You are holding a 29 in everything but suit, and a single point of luck decides which story you tell afterwards.
Twenty-four is the highest score you have a realistic chance of holding, and it turns up often enough that most regular players see several a year. Two common shapes:
7 7 8 8 with starter 6
24 points.
4 4 5 6 with starter 5
24 points.
The pattern is the same in both: a double double run, where two ranks are duplicated, producing four separate runs of three and two pairs, with the fifteens stacking on top.
Every whole number from 0 to 29 is a possible cribbage hand score except 19, 25, 26 and 27. This is not a rule — nobody legislated it — but a consequence of how the scoring combinations fit together, confirmed by working through all 12,994,800 possible hands.
The gap at the top has a clear explanation. Once you are past 24, the only structures that can get you there involve four 5s or three 5s plus a Jack, and those land exactly on 28 or 29. There is no arrangement of cards that produces a total of 25, 26 or 27 — the scoring simply jumps.
The gap at 19 is more arbitrary. Hands scoring 18 and 20 both exist in quantity; 19 just happens to be unreachable given the way fifteens (always even), pairs (always even), runs, flushes and the single nobs point can combine.
If you ever count a hand to 19, 25, 26 or 27, you have made a mistake. Count it again. It is the only arithmetic self-check the game gives you, and it works.
Because 19 is impossible, cribbage players adopted it as the standing joke for a hand worth nothing at all. Turn over four cards that score zero and the traditional announcement is "nineteen" — delivered deadpan, and understood by everyone at the table.
Zero-point hands are far from rare. Four ten-cards with no pair, no run and no flush will do it, as will plenty of scattered low hands. It is the sort of thing that happens two or three times an evening, which is exactly why the joke needed a name.
Hands get the attention, but the play has its own extremes. The largest number of points a single card can score during pegging is 14, and it comes from combining a double pair royal with a 31.
Cards are played in this order: 3 → 7 → 7 → 7 → 7
The running count goes 3, 10, 17, 24, 31.
14 points, on one card.
The same thing works at the other end of the count — A, 2, 3, 3, 3, 3 reaches fifteen on the fourth 3, for 12 plus 2. Either way, if you are ever on the receiving end of one of these, the correct response is to say nothing and move your peg.
After all the extremes, some perspective. Across all deals:
| Quantity | Approximate value |
|---|---|
| An average four-card hand plus starter | ~8 points |
| An average crib | ~4.5–5 points |
| Dealer's pegging per deal | ~3–4 points |
| Non-dealer's pegging per deal | ~2–3 points |
| Total points per deal, both players | ~26 |
That last figure is the useful one for endgame planning: roughly 26 points move across the board every deal, split unevenly in the dealer's favour. If you are 30 behind with the deal, you need two good hands and some luck. If you are 30 behind without it, you need to start gambling on your discards now rather than later.
And if a 29 shows up while you are doing the arithmetic, take a photograph. You have earned it, statistically speaking, about once.
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