Thursday, September 20, 2012

What Card Should I Lead? Lightning Round Edition


One of the great things about our huge database of cribbage games is that we can identify hands that are frequently misplayed. Today we're going to give a high level overview of a few of those hands. Keep in mind that these results aren't our opinions -- they're the actual results across a sample of millions of cribbage hands. Some of these results are just as surprising to us as they are to you.

A-4-X-X

About 4.8% of pone (non-dealer) hands will hold an ace, a 4, and two 10s/face cards. (From now on we'll use "X" as a shorthand for "a 10 or a face card"). Most players lead the 4 from this hand, but around 7% lead the ace. The players that lead the ace, on average, have a 0.55 point pegging advantage: they peg 0.18 points more, and their opponents peg 0.37 points fewer.

Why is the ace a better lead? There are pros and cons to either lead, but our data shows that by far the biggest factor is that dealers are less likely to pair an initial ace. Of the tens of thousands of A-4-X-X hands that we've analyzed we've seen that the dealer pairs a lead 4 at 19.93% of the time, but only pairs a lead ace 12.84% of the time. An interesting and common case is when both players have A-4-X-X hands. Here's how the pegging plays out in that scenario when dealer is willing to pair a 4 but not an ace:

Pone leads a 4


Pone
Dealer
Points
4
4
+2 for dealer (pair for 2)
X
X
A
A
+3 for dealer (pair for 2 and a go)
X
X
+1 for dealer (go)


Pone leads an Ace


Pone
Dealer
Points
A
X
4
+2 for pone (15 for 2)
4
+2 for dealer (pair for 2)
X
A
+1 for dealer (go)
X
X
+1 for dealer (go)

Leading the 4 gives dealer 6 points to pone's 0 for a net disadvantage of 6. Leading the ace gives dealer 5 points to pone's 1 for a net disadvantage of 4. Executive summary: lead the ace from A-4-X-X.

A-7-8-9

Most players lead the 8, but leading the ace gives a 0.78 point advantage (pone pegs 0.38 points more, and dealer pegs 0.40 points fewer). The data shows dealers making a couple mistakes when pone leads the ace:

  • Dealers holding 5-X-X-X see the ace and expect pone to have a 4. Dealer plays her 5 to avoid giving pone a a 15-2. Pone plays a 9 on dealer's 5 and pegs 15 for 2 points.
  • Dealers holding middle cards (6s through 9s) end up trading runs back and forth with pone, and usually lose in this situation

Executive summary: lead the ace.

A-A-5-9, and A-6-8-9

At the risk of seeming predictable, we're going to suggest leading the ace for these two hands. A-A-5-9 is one of the few hands that most players are playing properly: 50.3% of Cribbage Pro players lead the ace from this hand.

Leading the ace from A-A-5-9 averages a 0.50 point advantage over leading the 9. Leading the ace from A-6-8-9 averages a 0.57 point advantage over the 8 (the most popular lead, and the second best choice).

Executive summary: lead the ace.

5-5-6-7

The last hand we'll look at today is 5-5-6-7. Most players correctly lead the 7, but about a third lead the 6. Leading the 7 gives a 0.57 point advantage over the 6.

The big story here is that pone comes out better if dealer plays an 8 on pone's 7 than if dealer plays a 9 on pone's 6. When dealer plays an 8 on pone's 7, dealer averages 7.59 points of pegging to pone's 3.68 (for a net -3.91 loss for pone). When dealer plays a 9 on pone's six, dealer averages 5.99 pegs to pone's 0.88 (net -5.11 point loss for pone).

That's it for today

Disagree with these results? Want to see the results for another hand? Leave us a comment below and we'll get back to you.

Editor's Note: This is a guest post by Aaron Harsh continuing the series on cribbage strategy and tips. Aaron lives in Portland, Oregon with his wife Stacy and daughter Audrey. He spends his evenings analyzing cribbage strategy for Fuller Systems, and his days analyzing television viewership for Rentrak Corporation's Advanced Media & Information group. You can play him on Cribbage Pro Online as user "aaronhars", or in person at American Cribbage Congress grassroots club #28 (Oregon's Finest).

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