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Dan Barlow:

I discard 6-10. This allows me to move at least four holes on any cut except a 6, J, Q or K, and four holes puts me in excellent position. The main concern is that dealer may have a good hand, so give him what's least likely to turn into a big crib.

DeLynn Colvert:

Discard the 6-10. Play defense here — you cannot afford a sixteen point crib (or worse)! Keeping the 3-3-8-10 gives you a shot at six points at least.

George Rasmussen:

This one is easy for me. I tend to play defensive in such situations. I can afford to allow my opponent to have an average hand and cannot afford the score of a large crib. I would discard 6-10. That's the most defensive discard in the hand. This choice is reinforced when I consider the most frequent discards made by dealer. Of the ten most frequent discards to dealer's own crib, five of those are middle card combinations as follow in order of frequency: 7-8, 6-9, 6-7, 6-8 and 8-9. If a middle card is cut in this situation a game that appears to have been won has turned into a stunning loss.

Michael Schell:

This is the sort of positional problem that is widely misunderstood, even among experts. A novice would, of course, keep the points and toss 6-8. Most tournament players wouldn't dream of doing this when they are already "in position", and will toss the safe 6-10 instead. It's certainly true that tossing 6-8 can get you killed, giving up as many as 24 points in the crib if it catches three other mid-cards. And it's easy to dwell on the times when a single disastrous discard like this costs you a game you thought you had won. But games can also be lost by being too conservative: sacrificing points for defense only to see your own cards falter on Fourth Street. You fall short by a few pegs, then your opponent goes out with her three counts. This kind of loss is unspectacular, it often gets blamed on bad luck rather than bad strategy, and it tends to make less of an impression on a player's memory. As a result there is a real tendency nowadays to underestimate its likelihood in situations like this.

Consider your positional standing at 94-86*. You are +8, and dealer is -10. Should you be favoring defense? No, you should play cautious offense, or maybe even play on a little! You are statistically more likely to lose because your cards falter on Fourth Street than because your opponent starts lighting up the board. This is all the more true in this case because you've been dealt a weak six-card hand. If you know your discard averages well, you'll recall that throwing your opponent 6-8 gives up about 1.6 points more than throwing 6-10. In exchange for this, you keep two points more in your hand. Over the board I would stop here and toss 6-8 on the principle that a "sure" two point gain in the hand is worth 1½ more points in the crib if you're not specifically playing off. Running the numbers at home, I can see that the actual gain in hand potential is 1.53 points (about the same as the cost in the crib), and that 3-3-8-10 may peg a little better than 3-3-10-10, which probably makes the choice a tossup at this score. The novice may not be absolutely right to keep 3-3-10-10, but he is not wrong by very much! Move my or dealer's score forward two pegs and keeping 3-3-8-10 is definitely right. Move either player back two pegs and keeping 3-3-10-10 is definitely right.

Keep  Toss    Average   hand Opponent's crib:    Expected    average   Static    Delta   Dynamic  3-3-8-10     6-10 4.04 4.31 -0.09 4.22 -0.18 3-3-10-10 6-8 5.57 5.86 +0.08 5.94 -0.37

Keep  Toss      Pegging (Schempp):     Pegging (Mueller): Net (pone/dealer) Net (pone/dealer) 3-3-8-10     6-10 -0.2 (2.6/2.8) -1.2 (1.3/2.5) 3-3-10-10 6-8 -0.6 (2.2/2.8) -1.9  (1.0/2.9)

If you're still skeptical about this, reflect for a moment on how precarious your own position really is. Say you keep 3-3-8-10 and cut a 6, J, Q or K — a 33% shot. Now you have a two-point hand, and there's a good chance you'll be shut out in the pegging. If your opponent gets average scoring (allowing for the fact that you've made an unusually safe toss), you'll find yourself dealing at about 96*-101. What do you think she will do as pone at that score? If she has a shot at a 16+ hand she'll take it, and will occasionally convert, winning straight out or getting close enough to peg out as dealer next hand. Otherwise she'll just make the stingiest possible discard, breaking up her hand if necessary, and try to hold down your pegging. At 96* you are only a slight favorite to go out on your three cuts anyway, and now you must do so against an opponent who will be throwing every possible obstacle in your path. It's safe to say you are an underdog at 96*-101 despite being in an ostensibly favorable position. Those two extra points you passed up are starting to look pretty big.

Phyllis Schmidt:

I would throw 6-10, holding back as pone and hoping to do better on my deal.

Peter Setian:

I would discard 6-10. Dealer is short of a good board position, but easily within striking distance if 6-8 materialized in the crib. By discarding 6-10, of the remaining cut cards will give the hand four or more points (without pegging) for good dealing position next hand.

HALSCRIB:

I estimate that I will win the game as non-dealer with six holes to spare and with opponent dealing from hole 112*. So I'll play defensively to maintain my position. Scoring does count for something though, so I will factor in hand value, but will examine pegging solely from a defensive perspective. Using the formula

expected average - opponent's pegging = defensive value

I evaluate the candidate hands as follows:

Keep	Toss		Defensive value	Average   hand	Opponent's  crib	Expected   average	Average pegging:     Net (Pone/Dealer)
3-3-8-10	6-10		-2.61	4.04	4.15	-0.11	-1.24 (1.26/2.50)
3-3-10-10	6-8		-2.89	5.57	5.53	0.04	-1.91 (1.02/2.93)
3-6-10-10	3-8		-3.57	3.39	4.63	-1.24	-1.24 (1.09/2.33)

3-3-8-10 returns 1.5 points less on average in the hand, but I more than make up for it in denying dealer a huge crib and in the pegging. It's my choice at this score. If board position were reversed (86-94*) I would choose 3-3-10-10 as the best chance for a large hand, though this may give up a potentially huge and devastating crib. 3-6-10-10 gives up the fewest pegging points and the smallest maximum crib (fourteen points) at a cost of points less in the hand and ½ point more on average in the crib. Although I have a comfortable lead, it's not comfortable enough to justify playing this safe.

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.