This one was submitted by Hal Mueller. At 116*-108 you deal yourself 2 3 5 6 7 10. What do you keep from this hand? Suppose you kept 5-6-7-10 and the 8 was cut. What would you play on a J lead? Would you play the same card if the cut was the 8 instead?

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Dan Barlow:

I'd keep 2-3-7-10 and try to play one of the low cards early, leaving me with a nice assortment of cards that should help avoid getting trapped into letting him peg a lot.

With 5-6-7-10 on an 8 cut I'd drop the 6 on pone's J lead, hoping for a 31-2 with no pegging by pone. I'd play the same on an 8 cut. Hands that were worth twelve with the 8 are now worth thirteen, enough to go out, so I'd need to peg out to win. However, he may have eleven points (5-5-J-Q), in which case I still want to limit his pegging.

DeLynn Colvert:

Keep the 3-5-7-10 and play the 3 on a J lead. Stay away from pone at all costs, you do not need to peg. Dropping the 7 may play into a twelve-point hand and lose the game. A 3 may result a 15-2 or a pair for two, but pone will have an eight hand at best with that combo. The 7 and 5 are dangerous cards with an 8 cut and a J lead. Dump them at the first opportunity.

If I'm stuck holding 5-6-7-10, I would play the 6 on a face card lead, as I do not need to score. It doesn't matter whether the cut is a diamond or heart.

George Rasmussen:

The only sure thing revealed with an 8 starter with a J lead is that pone has gained one point on the cut of the heart starter. Your opponent is thirteen points out, the 8 cut does not go well in most hands in which the J is retained. Play defensively. It's not likely you can peg five points anyway, so force your opponent to get those thirteen from the score of the hand. Play the 6 on the J lead and you'll likely score 31-2 with the play of the 5. Ideal to close the count at 31 with that 5-spot. Don't pair a 5 if pone drops one unless it puts the count beyond 26. Play the 6 on the J lead regardless of the suit of the 8 starter.

Michael Schell:

The first question is whether to keep 5-6-7-10 in lieu of, say 3-5-6-10, 3-5-7-10 or 3-6-7-10. With pone thirteen out, my intention is to play off and hope my opponent falls short. But 5-6-7-10 gives me unusually good offensive prospects —  despite starting five holes out — in case the cut and pone's cause me to think my chances are better trying to peg out. Even for defense 5-6-7-10 looks pretty good, with a magic eleven, a 7 to respond safely to a 2, 3 or 4 lead, and the 10 as an out card on a 6 or 7 lead. The alternatives space the ranks out a little better, but probably not enough to offset the flexibility of 5-6-7-10.

Now to the choice of replies to the J lead. My first impulse is always offensive, so over the board I'd be wondering if there was any reason not to take the 15-2. After all, it gives me a shot at pegging out if I can find just one more two-point score (since I'm guaranteed a go or last card). The problem is that pone could have 5-5-x-x, 5-10-J-Q or 5-J-Q-K, and if these include the right J, or a pair (in the case of 5-5-x-x), then taking the 15-2 kills me. Note that among these hands, the losers playing my 5 on a 8 cut are limited to 5-5-J-J.

OK, so what about playing off with the 6, which general principle suggests is the the right thing to do at this score? This loses to 6-7-8-J (8 cut), and it eschews a chance to peg out against 13+ point hands like 6-7-8-J (8 cut), 7-8-9-J or 4 5 6 J. Note that against 7-7-8-J or 7-8-8-J I'll peg out playing either the 5 or the 6. I guess I'd have to say that the prospect of winning against the mid-card leads outweighs the likelihood of losing to 5-5-J-J if the starter doesn't match the lead, but it doesn't outweigh the likelihood of losing to the other 5/x hands if the starter does match the lead. So I'd play the 6 on a right J lead, but the 5 on a wrong J lead.

Phyllis Schmidt:

I'll keep 5-6-7-10 and play the 5 on pone's J lead, regardless of the starter suit. My opponent may have all face cards, and I still have a chance for 31 on the next card, and a final go.

Peter Setian:

Leave it to Hal Mueller to ask three questions in one! First of all, I would have kept 3-5-7-10 and discarded 2-6. This gives you plenty of points and the most variety to stay away from pegging trouble. Now that I have 5-6-7-10, and see a J lead, this seems to be one of those close 50/50 plays which would take too long at the table to figure out. (Yes, too long.) My first impulse is to play the 6 for defense, but this is so close that even the right J shown may change my first decision. If we sit and analyze, a couple hands that the pone could have with the J where playing the 6 would be regretful include 6-7-7 and 6-7-8. Or flush hands like A 6 8 J, but these are very unusual. The hands where playing the 5 would be regretful include a rare 8-8-8 or a more likely 5-5-J remaining, where you may or may not peg out, depending on the pone's tough end play. Again there are also unusual flush hands like A 5 9 J or A 5 7 J also.

I suppose with all possibilities considered, the chances of the pone holding 6-7-7 or 6-7-8 may be slightly higher, but holding a J would probably mean pone had to discard two more face cards, figuring most other low cards would have been held with the hand. Ask the computer (see below)! Of course there are hands where the pone could have 13-16 points without pegging, and either play won't matter.

HALSCRIB:

My first priority is to make sure I'll go out if pone doesn't win first. Since I'm certain to peg at least one point, all I need is four points between hand and crib. Fully eleven of the fifteen possible keeps guarantees me at least four combined points after the starter, so I'll start by ruling out the three that don't (2-3-5-6, 2-5-6-10, 2-5-7-10 and 3-6-7-10). My next step is to estimate how many points each of the remaining hands can be expected to give up in the pegging. The fewer, the better. Here are my numbers:

Keep	Toss		Average opponent's pegging
2-3-5-7	6-10		1.04
2-3-5-10	6-7		1.20
2-3-6-7	5-10		1.33
2-3-6-10	5-7		1.43
2-3-7-10	5-6		1.20
2-5-6-7	3-10		1.20
2-6-7-10	3-5		1.26
3-5-6-7	2-10		1.24
3-5-6-10	2-7		1.28
3-5-7-10	2-6		1.11
5-6-7-10	2-3		1.26

Of the eleven candidates, I think 2-3-5-7 will give up the fewest pegs on average, so that's my choice.

When pegging as dealer on Fourth Street I consider the frequency of pone's possible hands given pone's starting score (since these frequencies can vary quite a bit depending on how far pone has to go). I then calculate my possible plays against pone's possible holdings, weighting the results based on the likelihood of pone holding each particular hand. These calculations are used to estimate my opponent's total winning chances (Lose %), which I obviously want to minimize. I also get a "free" estimate of my chances of pegging out before pone gets to count his hand (Win %), though my concern here is just to win the game regardless of whether that's by pegging or by holding pone short. Assuming I've held 5-6-7-10 and tossed 2-3, here are my numbers based on pone's lead of the J:

My Play		8 starter:			8 starter:
		Lose %	Win %		Lose %	Win %
5		0.7	45.8		8.0	45.8
6		6.1	6.4		9.6	7.0
7		4.2	4.1		16.0	4.1
10		28.7	6.0		30.4	14.5

As you can see I'd play the 5 with either an 8 or 8 starter. Granted, if the cut matches the suit of pone's J lead, then this raises the possibility of pone having a ten-point hand like 5-10-J-Q, and pegging enough to go out as follows:

^J  _5 (15-2)  ^5 (20-2)  _7! (27-1)    ^Q  ₆  ^10 (26-1)    _10 (10-1)

But by taking the points, I'll peg out nearly half the time regardless of what pone has. If pone has a flush, she'll have an extra two points on the heart starter (counting the right J), and by pegging out I'll deny her victory in those cases where she already has enough to go out. Taking the 15-2 also snatches a win against 5-5-5-J or 5-5-J-right J. By playing the 7 on pone's 5, I win immediately on a 10 lead. The risk of giving up a go or 31 to a 2, 3 or 4 doesn't amount to much, since a stray low card will probably leave pone short of home even with a few pegs.

Putting it all together, I think the benefits barely outweigh the risks, so I'll take the points rather than play off with the 6. What are the humans afraid of?

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.