You're dealing at 32*-36. You tossed yourself
Q-K. Pone cut a J. What do you
do:
- Holding 2-3-4-4 on a 2
lead, and
- Holding 8-9-10-10 on an
8 lead?
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hide answers
Dan Barlow:
It's too early in the game to be basing my decision on the board
position. I pair in both cases. In the long run, pairing everything
(unless you can score 15-2) pays off.
John Chambers:
In this situation you should be at least at hole 44*. So you're
about 12 holes short of where you need to be. On a 2
lead I would play a 4 from 2-3-4-4. If
your opponent plays a 3 you may be able to gain
multiple points if your opponent is trapped. True, your opponent may
peg but you have to make up 12 holes. It's a chance you have to
take. Or if your opponent pairs your 4 you can get a
pairs royal for six points. You could pair the deuce but being 12
points behind your position, two points won't mean much, and your
opponent may get better position with a pairs royal.
On an 8 lead I would pair it holding
8-9-10-10. You're probably saying "but you just said not
to pair"! Because of the cards this is a different situation.
Let's face it, if your opponent leads an 8 and you
play a 10, you've set up your opponent for a three
card run and a go with no recourse. That's four points. If you pair
and he does get have the other 8, of course he gets
seven points. But I feel there is a good chance he might not have
the third because you each have an 8. That means that
in eight cards (yours and opponent's) there are three 8s
and in the other 40 cards there is only one 8. I'll
take the chance. If it does work you have a good chance to hold your
opponent from pegging and gain a little on your position.
DeLynn Colvert:
Holding 2-3-4-4 on a 2 lead, I'd play
the 4. If paired you score six. If a 3
is played, pair the 3.
Holding 8-9-10-10 on an 8 lead?
Play the 10, and if not paired, it is a safer lead
back in the second sequence. Only the three 9s can
beat this (or the two 10s). This is a "board" play.
If playing all-out offense, pair the 8, but defense
says play the 10.
George Rasmussen:
On a 2 lead, I would play a 4 from
2-3-4-4. I have it backed up, and I cannot afford to
give pone a triple here for six points. If I give up six points here
by pairing that deuce, my opponent is likely to be in great shape
for the next deal.
On an 8 lead I would play a ten-spot from
8-9-10-10 for the same reasons. An 8 lead is
generally an indication of other middle cards (6-7-9).
I am holding a 9, which makes the play of the
10 safer than other choices. I can't afford six points on a
triple. That Second Street zone is too close to take that chance.
With a real cagey player the 8 lead might also mean
that pone is holding 2-3-4 or 3-4-5
along with that eight-spot. In that case, when they make count 22
with the play of the 4, close the count with the
9 for 31. In the latter case, they will likely make
the count 23 with the play of the 5. Close the count
with the 8 for 31-2.
Michael Schell:
This is a classic situation. You have a double run (or a four-card run)
and face a lead against an undoubled edge card. You must choose between
pairing (thus risking a triple), or playing one of your end cards.
I start by checking the board. At 32*-36 I'm -12 to pone's +2. The
J cut makes me -10, and the ten-point hand (worth two
more than average) makes me effectively -8. Defense is probably still in
order, but if I have a promising crib (maybe I dropped a pair of
5s!) an exchange of pegs could actually get me into position by
the end of the deal.
For offensive or balanced play, pairing the lead is always a
no-brainer in these cases. You get two immediate points, and though
you'll occasionally be tripled, mathematically you'll come out ahead in
the long run, despite the tendency of most players to favor leading from
a pair where possible. For many years, the conventional wisdom held that
you should also pair when playing defensively, on the grounds that you
were "trapped" and would do better to minimize the number of losing
cards. HALSCRIB, though, has taught me that there a bit more to it.
Specifically, I would pair the 2 in the first case, but
would refuse with a 10 in the second case.
The difference is that if you refuse the 8, you risk a
pair and a run, whereas if you refuse the 2, you risk a
pair, a run, and a 15-2. This is what's missed by most analysts
who tell you to always pair away. Compare the objective risk here:
Scenario: |
Objective risk: |
|
Pair |
Refuse |
2-3-4-4
against a 2
lead |
(2 cards ∙ 6 points) =
12
|
(4 cards ∙ 2 points)
+
(2 cards ∙ 2 points) +
(3 cards ∙ 3 points) =
21
|
8-9-10-10
against an 8
lead |
(2 cards ∙ 6 points) =
12 |
(2 cards ∙ 2 points) +
(3 cards ∙ 3 points) =
13 |
Pairing the 2 is clearly superior than refusing with a
4, even allowing for pone's likely bias in favor of
leading from a pair. In the case of the 8 lead, the
objective risk is about the same, but factoring in pone's leading bias,
I agree with HALSCRIB that a 10 will give up about
¾ pegs less in the long run.
Remember this idea: when holding a double run and facing a lead against
your undoubled edge card, pair the lead unless you're playing off
and won't risk a 15-2 by refusing the pair.
As you can see below, the bot decided to go
ahead and pair the 8 anyway at this board position —
not out of any tactical disagreement, but because it
decided that more offense was called for.
Phyllis Schmidt:
In the first scenario, I'll play a 4. I don't want to
give away six points if I play a 2 and the opponent has a
2 and I couldn't get away from further runs. If he does
get the run I would play along and take what ever run was available to
me.
In the second scenario I would match the 8. There's
not much room for movement there. Playing any card is risky, so I'll
take the two points.
Peter Setian:
Almost without a choice, I would definitely play aggressively in
both pegging situations, which would mean pairing the 8
lead with 8-9-10-10 and probably pairing the 2
lead with 2-3-4-4, even though playing a 4
might produce more pegging points as play continues (an eight
point crib seems almost certain given my toss and the cut,
especially if pone trips the pair).
HALSCRIB:
In both scenarios, my projected endgame scores will be 115* with
me dealing and pone at 114 with first count. On average, pone will
peg and then count her hand for a win with three holes to spare.
Considered in this light, both scenarios are identical and pose the
same question: should I pair or not. The humans will probably couch
their replies based on knowledge of whether the opponent habitually
leads from a pair. Unfortunately, I won't have this capability until
version 7. So my current answer lies in the expected average pegging
gain for each player based on hand frequencies and board position
which suggests that opponent would lead from a pair if available.
Here are my calculations holding 2-3-4-4 facing a
2 lead:
|
Average pegging: |
Net |
(pone/dealer) |
2 |
+2.04 |
(2.73/4.77) |
3 |
-0.34 |
(3.34/3.00) |
4 |
+0.91 |
(3.04/3.95) |
Note that my average pegging paring the 2 includes
two point for the pair. Now for 8-9-10-10 versus an
8 lead:
|
Average pegging: |
Net |
(pone/dealer) |
8 |
+1.76 |
(2.76/4.52) |
9 |
-1.49 |
(3.97/2.48) |
10 |
+0.51 |
(2.02/2.53) |
Based on these numbers, I will pair in either case so that on the
last deal I increase my chances of pegging out. If my opponent
triples me, the game is still far from totally lost.
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, longtime editor of the monthly magazine Cribbage World,
and the ACC's only Life Master - Seven Stars. He also directed two annual tournaments in Missoula, MT, served as the ACC's President, and was one of the game's most affable emissaries. It's scarcely an exaggeration to say that Colvert's career defines modern cribbage. 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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