As pone, trailing 33-42*, you're dealt A-2-3-5-6-9.
What do you keep? |
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Dan Barlow:
When all options are terrible, I keep my points and hope for the
best. So I keep A-2-3-9 and cut a 3.
Dealer tossed A-8, so I come out smelling like a rose
for a change.
John Chambers:
In this position, on average, I am behind by about 11 holes. This
means that on average, after my count, I would be close to where I
should be for my three counts on Second Street. My opponent is only
a couple of holes behind as he now deals. Before I do anything, I
realize I have two goals:
- To keep my opponent from pegging and balk his crib
- To get into position for my three counts on Second Street
My choice would be to discard the 6-9. If I
discard anything else I either will not have many points in my hand
or else will help my opponent more than the 6-9. The
6-9 discard needs a few specific cards to help my
opponent. I would keep the A-2-3-5.
DeLynn Colvert:
With first count? I keep for max here, although it's a risky
play. I hold A-2-3-9, for a 12 or 14 try (and a
better pegging hand). I could easily lose the game with a 4,
5 or 6 cut, but I am drawing to four
known cards, and opponent has to guess at my discard.
George Rasmussen:
This is a tough place to be, as I would like ten points out of
this hand and to limit crib size for dealer. I'll play
A-3-5-6 and discard 2-9. No way with the
cards retained that I can score those ten points although the cut of
an A, 3, 5 or 9
will give me six points, a 7 will give me seven
points, and the cut of a 4 or 6
provides eight points.
Michael Schell:
This is as exasperating a discarding decision as you're likely to
see. At the start I'm -1. Dealer is technically +24, but could "jump"
ahead to be in Third Street position by making up two points here
(the next two positional holes are at 44 and 70). So ideally I need
to find some extra offense while limiting dealer to average scoring
at best. Unfortunately I don't have a discarding choice that fits
that bill, as retaining either of my best hands requires tossing
5-6
or 6-9. Without running the numbers, I see no obvious
right answer. So let's run some numbers:
Keep |
Toss |
|
Average
hand |
|
Opponent's crib: |
|
Expected
average |
|
Pegging (Mueller): |
|
Totals: |
|
Static |
Delta |
Dynamic |
|
Net |
(pone/dealer) |
|
Net |
Offense |
Defense |
A-2-3-5 |
6-9 |
|
6.89 |
|
6.26 |
-0.03 |
6.23 |
|
0.66 |
|
-0.8 |
(2.0/2.8) |
|
-0.14 |
8.89 |
9.03 |
A-2-3-9 |
5-6 |
|
7.98 |
|
7.47 |
+0.09 |
7.56 |
|
0.42 |
|
-1.0 |
(1.7/2.7) |
|
-0.58 |
9.68 |
10.26 |
A-3-5-6 |
2-9 |
|
5.46 |
|
4.70 |
-0.05 |
4.65 |
|
0.81 |
|
-0.7 |
(2.1/2.8) |
|
0.11 |
7.56 |
7.45 |
A-3-5-9 |
2-6 |
|
4.76 |
|
4.97 |
-0.14 |
4.83 |
|
-0.07 |
|
-1.2 |
(1.6/2.8) |
|
-1.27 |
6.36 |
7.63 |
2-3-5-6 |
A-9 |
|
4.33 |
|
4.55 |
-0.10 |
4.45 |
|
-0.12 |
|
+0.3 |
(2.9/2.6) |
|
0.18 |
7.23 |
7.05 |
2-5-6-9 |
A-3 |
|
4.96 |
|
5.07 |
-0.27 |
4.80 |
|
0.16 |
|
-1.0 |
(1.9/2.9) |
|
-0.84 |
6.86 |
7.70 |
3-5-6-9 |
A-2 |
|
4.96 |
|
5.07 |
-0.23 |
4.84 |
|
0.08 |
|
-0.9 |
(1.9/2.8) |
|
-0.82 |
6.86 |
7.64 |
The fact that dealer is starting out two points behind the positional hole
suggests that we have a little slack to work with on the defensive side, so I
suspect that the edge goes to A-2-3-5, the choice I'd probably come up with over
the board. However it wouldn't surprise me that doing 100 or 200 playouts from
this position, that the most aggressive of all, A-2-3-9, comes away with the
most wins. I'm pretty sure that the more defensive options are inferior at this
score. Move pone ahead four points to 37, though, and the more balanced
A-3-5-6 or 2-3-5-6 look best.
Eventually the bots will give us conclusive evidence on this kind
of "play on, play off, or split the difference" question when both
players are in marginal position. For now, A-2-3-5 is my
low-confidence choice.
Phyllis Schmidt:
I'll keep A-3-5-6 for two points. I can't give the
crib any points or cards in sequence when trailing by nine and not
dealing.
Peter Setian:
I would keep A-3-5-6 to first try and somewhat
hold the opponent with the 2-9 toss. At the same
time, I'm keeping a little better hand than 2-3-5-6.
For the A-3-5-6 hand, any cut but an 8
or ten-card is six to eight points. (Oops! Okay, a 2
is five points). Still, not a bad average.
HALSCRIB:
Yes, dealer is a little short of optimal position, but that's to
go out in three counts in the end. Since I'm nine points behind, the
most likely scenario is that opponent pegs out as dealer at
the end of the game. For that reason, I do indeed need to play
defense to improve my chances of counting out in the last hand. My
way of tackling this situation mathematically (the only way I know)
is to subtract dealer's pegging and expected crib from my average
hand, ignoring offensive pegging. This gives me the following:
Keep |
Toss |
|
Average
hand |
|
Opp. crib |
|
Opp. Pegging |
Defense
Value |
A-2-3-5 |
6-9 |
|
6.89 |
|
-5.96 |
|
-2.78 |
-1.85 |
A-2-3-9 |
5-6 |
|
7.98 |
|
-7.53 |
|
-2.67 |
-2.22 |
A-3-5-6 |
2-9 |
|
5.46 |
|
-4.41 |
|
-2.80 |
-1.75 |
2-3-5-6 |
A-9 |
|
4.33 |
|
-4.33 |
|
-2.59 |
-2.59 |
The higher total (lowest negative number) is the best choice,
leading me to go for A-3-5-6, with A-2-3-5
a close second.
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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 (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, 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 longtime 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 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 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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