Ask the experts, April 2008

The score is 56-49*, and you're dealt A-A-4-6-6-K. What do you keep?

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Dan Barlow:

I keep A-A-6-6. Saving six points and giving up a pair amounts to saving four points, and the two pair is helped by more cuts than may at first appear (A, 2, 3, 6, 7, 8, 9). While A-A-4-K gives me a slightly better hand with a good cut, I have to subtract the two points I tossed, and account for the possibility I've given up a big crib.

John Chambers:

In this situation your goal is to get to at least hole 70. I would keep the A-A-4-K and discard the two 6s. True, you are giving your opponent two points but you need 14 points to get to 70. If a tenth card comes up and you peg a few holes, you are right around your goal. The only way your opponent can get into position is to get to hole 85. That is over a street in his two hands.

DeLynn Colvert:

You are -3, you must play offense. Keep A-A-4-K.

George Rasmussen:

It's tempting in this position to toss the 6-6, as a lucky cut for 12 points would put me well around the corner to deal. Sorry, can't do it. I will play ultra defensively, trying to deprive dealer of a crib score. At 49, I can give the dealer an average hand — I just can't give up the score of a crib. Goodbye 6-K!

What? Why not hold four points with A-A-6-6? Isn't 4-K reasonably safe with you holding A-A? What are the differences in 6-K and 4-K as possible scoring combinations to dealer crib? The 6-K is likely to score two points or less about 10% more frequently than 4-K. 6-K will score in those wee numbers 41.4% of the time. 6-K is also less likely to give up eight or more points. The 4-K will score eight or more points nearly 30% more frequently than 6-K.

Michael Schell:

To an inexperienced player it might seem that I'm winning, but an expert will see that on a good day I'll win maybe 40% of the time from this position. I start the deal -4 to dealer's +5, so my positional deficit is about the same as my opponent's positional surplus. I can play balanced, or go all out on either offense or defense, depending on my cards.

In the event, going for offense with A-A-4-K pretty much shuts down the defensive option, but I think it's still the best strategy because it stands an exceptionally good chance of getting me to, or close to, the next positional hole (70). An A, 4 or K gets me 12 points, any other ten-card gets me ten, and leading the 4 stands a pretty good chance of pegging at least three points by running the A pair later. I'm not sure I'm even 50-50% to reach hole 70 on this deal, but I'm still going to guess my odds are better than they would be holding A-A-6-6, which either requires that dealer lay an egg here, or else for something dramatic to happen on one of the next four deals (as it's unlikely the game will last much longer than that).

Phyllis Schmidt:

I'm going for defense here, keeping A-A-6-6 and tossing 4-K. I'll try to keep dealer's pegging to a minimum too.

Peter Setian:

I would keep A-A-4-K. With opponent dealing from a very good board position of 49*, I would attempt to get the 1012 point hand, trying to get as far on Third Street as possible for my next deal. In the pegging I leave the A-A last for maximum offense.

HALSCRIB:

The humans seems split about the offensive option, but I think the skeptics are right. The trouble with A-A-4-K is that dealer's far enough along that with average scoring, he'll count out as dealer four deals hence, before I get to count my hand as pone. In that scenario, it won't help that I've played aggressively enough to get within striking range.

Better to take a more defensive approach. A-A-6-6 rates a little higher than A-A-4-6 since it keeps the door open for a forward play (e.g., on an 8 cut followed by a 6 lead), and is only a little worse in the crib. But either is significantly better than A-A-4-K. Here are some numbers from my latest, greatest (version 2.1) vision thing:

Keep  Toss        Average 
hand:
  Opponent's
crib:
  Pegging      Adjusted %
Net (pone/dealer) Loss Win
A-A-4-6     6-K   5.43   4.06   -0.55 (1.93/2.48)   65.8 27.8
A-A-4-K     6-6   8.61   6.78   -0.64 (1.96/2.59)   74.1 23.0
A-A-6-6 4-K   6.35   4.03   -0.96 (1.57/2.43)   63.9 29.8

An explanation of exactly what the Loss/Win percentages represent, and why they don't total 100%, can be found in the Help screens of HALSCRIB CLX.


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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.

John Chambers was one of the original founding members of the ACC. He is a Grand Master, winner of seven major tournaments, and author of Cribbage: A New Concept, He also directs three annual tournaments: the Ocean State Cribbage Classic, New England Peer Championship and Charity Cribbage Challenge.

DeLynn Colvert is the world's highest rated tournament player. He is a four-time National Champion, author of Play Winning Cribbage, and the ACC's only Life Master - Six Stars. He directs the Montana Championship and Montana Open, both held annually in Missoula, and served for many years as President of the ACC and Editor of the monthly magazine Cribbage World.

George "Ras" Rasmussen is a Life Master - Two Stars, a four-time All-American, the national Grass Roots Division1 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 20 years, 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 eight tournaments per year, including the ACC Tournament of Champions and the annual Grand National. He enjoys participation in Grass Roots Club #72.

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.


 
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