|You're dealer with 5* points. Pone has 23. You deal yourself A-A-A-4-5-7.
Do you keep A-A-A-4 or A-A-A-7?
Though I'd rather put 4-5 in my crib than 5-7,
I would keep A-A-A-4. I'm already way behind, and A-A-A-7
will leave me with only six points on the cut of a 2, 3,
9, 10, J, Q
or K. Four of the five cuts that don't help if I save A-A-A-4
are a 3, 5, 6 or 7 —
but those cuts will all help my crib if I've tossed 5-7,
easing the pain.
Early in game and in deep doo-doo. Hold for max: A-A-A-4.
21 cards give you twelve points.
In this case, retain A-A-A-4 and discard 5-7
to crib. Your discard in this case assures two points minimum in crib
(as does the discard of the 4-5 with a hand retention of A-A-A-7).
There are many more cards which will benefit the retention of the A-A-A-4:
A, 4-4-4, 8-8-8-8, 9-9-9-9,
10-10-10-10, J-J-J-J, Q-Q-Q-Q
and K-K-K-K. That's a total of 28 cards which will
increase the value of that hand. Retaining the A-A-A-7,
the hand is benefited by the cut of A, 5-5-5-5,
6-6-6-6, 7-7-7 and 8-8-8-8.
That's a total of only 16 cards, making it much less likely that the cut
will add value.
The only times to retain A-A-A-7 in preference to A-A-A-4
are those game situations in which pegging potential is important. On a
ten-point lead, drop the 7. Opponent will generally push
the count to 27 rather than dispose of a 5 if holding
those cards. The As are scored consecutively for a pair
(two points) and pairs royal (six points) plus the go. That's
nine unanswered pegs, and it only works for the dealer. The other
situation in which you would retain A-A-A-7 in preference
to A-A-A-4 is when you absolutely must have 20 points or
better to win the game, and it appears getting close will not be to your
benefit. That is not the case here as the game has just begun.
A-A-A-4 will obviously score the most points between
hand and crib. But the idea of keeping A-A-A-7, going for
the killer peg, is alluring:
K 7 J A A (29-2)
With A-A-A-4, I'd be able to pull off the pegging
triple if pone is holding x-x-x-x, but not if he's
holding the more common 5-x-x-x. In that case, I'd only
get the triple if I keep A-A-A-7. Is it worth breaking up
the magic fives to do this?
Over the board, I'd just chicken out and keep the
"foolproof" A-4-4-4. But at home, I have the
luxury of doing a little analysis. Running the numbers indicates that A-4-4-4
returns about a one point higher expected average than A-A-A-7:
Does A-A-A-7 peg well enough to make up for this?
Well, Schempp's numbers have it pegging +3.5 (1.9/5.4), compared to +2.5
(1.7/4.2) for A-A-A-4. This makes the choice look like a
wash. But HALSCRIB 4.00 only shows A-A-A-7 pegging
.48 more on offense than A-A-A-4 — not enough to
make up the difference. Since HALSCRIB's numbers look more realistic to
me, I think A-A-A-4 is probably the better keep.
I would keep A-A-A-4. More ten-cards and possibly a 9.
7-5 to the crib.
I would keep A-A-A-4. The hands certainly average more
points. A 3 or 6 cut still helps the 5-7
discard. Seems too early in the game to go for an "all or
nothing" 6 cut. I might reconsider if the pone had a
whopping 33 points after the first deal instead of 23 points.
At 5*-23 I'm looking to score maximum points. The humans have been
awfully quick to dismiss A-A-A-7, but it's worth
considering since it pegs big against 4-x-x-x, 5-x-x-x,
9-10-J-Q, x-x-x-x and a few other hands
which manage to escape against A-A-A-4. Nevertheless, my
calculations indicate that this advantage only translates into a
˝ point better offensive pegging average. Since A-A-A-7
only improves to 12+ points on an A, 6 or 7
cut, while A-A-A-4 improves on an A, 9
or any ten-card, and since having three As in the can
means that a 4-5 in my crib will only get about
.2 points more than 5-7, I reckon A-A-A-4
is the better overall keep by just under a point.
Note that if I'd dealt myself an 8 instead of a 7,
it would be a dead heat between holding A-A-A-4 and A-A-A-8.
Dan Barlow won the 1980 National Open Cribbage
Tournament, and made the 1985 All American Cribbage Team. His cribbage
strategy articles appeared in Cribbage World for many years, and
can be seen on the ACC
Web site. He also provides strategy tips at MSN
Gaming Zone. He has written seven books on cribbage, two of which have been glowingly reviewed in Games Magazine. All, including his latest book Winning Cribbage Tips, are available at The
DeLynn Colvert (1931–2019) is the highest rated tournament player in the history of organized cribbage. He was a five-time National Champion, author of Play
Winning Cribbage, longtime editor of the monthly magazine Cribbage World,
and the ACC's only Life Master - Seven Stars. He also directed two annual tournaments in Missoula, MT, served as the ACC's President, and was one of the game's most affable emissaries. It's scarcely an exaggeration to say that Colvert's career defines modern cribbage.
George "Ras" Rasmussen is a Life Master - Two Stars, a four-time All-American, the national Grass Roots Division 1 champion in 2009, a former state champion in Virginia, Montana and Washington, and holds a Gold Award and a President's Award. He also directs the Washington State Championship,
held each year in Centralia, WA. His articles on cribbage are available
on the ACC Web site.
Michael Schell is a pioneer of modern cribbage theory, which synthesizes traditional concepts of expert play with new computer-informed insights and analysis. He has published Cribbage Forum since 2000. Schell holds a Bronze Award, is a Washington State Champion (2001), and was one of the principal architects of ACC Internet Cribbage.
Phyllis Schmidt is a charter member of the ACC, and has been
playing cribbage for about 40 years. She is a Life Master - One Star,
a Senior Judge, a National Champion (1992) and winner of the ACC Tournament of Champions (2005). She attends about 30
tournaments a year.
Peter Setian has played cribbage for over three decades, and has
been a member of the ACC for about 14 years. During that time, he has won
seven major tournaments and earned his Life Master rating. He plays
in about 12-16 tournaments per year, including the ACC Tournament of
Champions and the annual Grand National.
HALSCRIB is widely regarded as the world's strongest computer
cribbage player. Its opinion was solicited using a special analysis
version of the program. Since HALSCRIB only speaks binary, its thoughts
have been translated into English by Michael Schell and its creator, Hal Mueller, a retired mathematics professor and eight-time ACC tournament winner. For more information, see the HALSCRIB