Friday, September 7, 2012

What card should I lead? (Part 2)


Today's topic is on playing 4-5-6-6 as pone. This is going to be short and sweet, because the wrong way to play this is just so wrong! This is one of the first hands cribbage players study when they begin to take the game seriously, and playing it correctly is a great way to start improving your game.

Lead the 6 and trap the dealer's 5

It would be foolhardy to lead the 5, and the data shows that Cribbage Pro players rarely do that. But 32% of players are leading the 4 from this hand, and that's just plain wrong. Here's why (keeping in mind that the two most common hands for dealer to have are 5-10-J-Q and 5-J-Q-K):


PoneDealerPoints
6
K
6
5
4+5 for pone (run for 3 and 31 for 2)
Q
5+2 for pone (15 for 2)
J+1 for dealer (go)


This play is commonly referred to as the "non-dealer 5 trap." The dealer is trapped after pone plays her second 6: the count is 22, and the 5 is the only card she can play without taking the count over 31. Pone ends up pegging 7 points to dealer's 1, leaving pone with a net 6 point advantage.

That's awesome! Let's talk about it some more!

One of the great things about this play is that the dealer has no escape route: he can't play his 5 on pone's initial 6 (he'd be out-pegged 9 to 1 if he did), so he has no hope but to sit back and watch pone peg away. Personally, my heart sinks a little when I've got 5-J-Q-K and pone leads a six.

Another great thing about this play is that it works fairly often. Pone scores her 7 points as long as dealer's hand is made up entirely of 10/face cards and 5s. Dealer has one of those hands about 9% of the time, which is pretty often in cribbage terms.

You can peg almost as many points without the 5. Any hand with a 4 and two 6s in it is a candidate for this five trap. You won't score that last 15 for 2, but you'll still get the run for 3 and the 31 for 2.

In a defensive situation? Lead the 6

Surprisingly the 6 is a better defensive lead than the 4. On average the dealer pegs 3.90 when pone leads the 6, vs. 4.05 when pone leads the 4. (These averages are based on several thousand 4-5-6-6 hands played on Cribbage Pro Online).

Even better, when pone leads the 6 dealer is limited to just one point 22% of the time, vs. 9% of the time when pone leads a 4. Here's a chart that shows the dealer pegging probabilities for the two leads:


There's a 22% chance that the 6 lead will hold the dealer to 1 point of pegging, but only a 9% chance that the 4 lead will do that. The 4 lead's only advantage is that it's slightly more likely to keep dealer's pegging under 8 points (8.82% chance of dealer pegging 8+ points if you lead the 4, vs. a 9.15% chance if you lead the 6).

Executive summary: there's no defensive advantage to leading the four.

Desperately need to peg a point? Lead the 6

Here's a similar chart, showing pone pegging probabilities.  Note that we swapped the “=”s out for “=”s in this chart -- the “=1” bar in this chart shows the chances that we’ll score at least one point, rather than at most one point.

The 6 lead wins across the board: you're more likely to peg at least one point when you lead the 6 (67% chance, vs. 56% when you lead the 4), and more likely to score at least two points (52% for the 6 vs. 40% for the 4). In fact, no matter how many points you need to peg, you're more likely to get those points if you lead the 6.

Executive summary: there's no offensive advantage to leading the four.

Moral of the story

The 6 lead is superior in ability to score a small number of points, ability to score a large number of points, and ability to keep dealer from pegging. You should always lead the 6.

Is there ever a situation where the 4 is the right lead? Leave us a comment and let us know what you think.

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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