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Dan Barlow:

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.

DeLynn Colvert:

Early in game and in deep doo-doo. Hold for max: A-A-A-4. 21 cards give you twelve points.

George Rasmussen:

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.

Michael Schell:

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)  A (30-7)}

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:

Keep:	Toss:		Average  hand:		Average crib:			Expected average:
					Hessel	Colvert	Ras	Hessel	Colvert	Ras
A-A-A-4	5-7		9.04		6.04	6.0	6.00	15.08	15.04	15.04
A-A-A-7	4-5		7.48		6.54	6.4	6.53	14.02	13.88	14.01

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.

Phyllis Schmidt:

I would keep A-A-A-4. More ten-cards and possibly a 9. 7-5 to the crib.

Peter Setian:

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.

HALSCRIB:

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 ½ 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.

Panelists

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 Cribbage Bookstore.

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 home page.