Thursday, September 12, 2013

5s, 10s, and Face Cards

This week we're talking about the most common type of cribbage hand: one five with three 10s or face cards (like 5-10-J-K, or 5-Q-Q-K). These make up about 5.7% of all hands. In fact, 5-10-J-Q is the most commonly held hand in cribbage, followed closely by 5-J-Q-K.


Today we're going to go over the most profitable ways to play these hands. Most players have a good intuitive understanding of the proper way to play these hands, and you're probably doing pretty well with them. But we'll go over the data a little, and give some advice that we think will help the average cribber.


Note that all the advice we give is designed to maximize your net pegging points: your points pegged minus your opponent's points pegged. Usually this is the right approach, but if your board position demands offense or defense (for instance, if your opponent is about to peg out and win the game) then you won't necessarily want to follow this advice.

What to lead as pone

Pone’s strategy depends on the composition of her hand. Does she have a pair? Does she have three of a kind? We'll talk about each of those scenarios separately.

What to lead when you don't have a pair

Of course you don't want to lead the 5. So which of your other cards should you lead? The good news (or is it bad news?) is that it doesn't make a big difference which card you chose. But if you want to score every last point you should choose these leads:


Pone's Hand
Best Lead
5,10,J,Q
J
5,10,J,K
10
5,10,Q,K
10
5,J,Q,K
J


Choosing your lead from this table will score you an extra 1/20th of a point, on average. Why are those the best leads? I've got no clue, but that's what the data shows. In each of these cases we've got 10s of thousands of samples, so this appears to be reliable. Is it worth memorizing this table to score your extra 1/20th of a point? Maybe not, so let's get onto something more useful.

What to lead when you have a pair

Lead from your pair if you have one. If you're holding 5-J-Q-Q you should lead a queen.If you're holding 5-10-10-K you should lead a 10. No matter which hand you're holding we've seen that leading from your pair gives you more points, and cuts down on dealer's pegging. Altogether you'll average an additional 0.5 net points by leading from your pair.

What to lead when you have three-of-a-kind

If you've got a 5 and three 10s or three matching face cards (e.g., 5-10-10-10, or 5-Q-Q-Q) you've only got two choices: lead the 5, or lead from your three-of-a-kind. Don't lead the five. Lead from your three-of-a-kind: you'll almost always peg more, and dealer will almost always peg less.

How to respond as dealer

When you don't have a pair

If you don't have a pair, you can choose your response from this table:


Pone's lead
Best Response
A
J if you have one, otherwise the K
2
K if you have one, otherwise the 5
3 or 4
K if you have one, otherwise the 10
6
Q if you have one, otherwise the K
7
K if you have one, otherwise the Q
8
K if you have one, otherwise the 5
9
K if you have have 5-J-Q-K, otherwise the 5
10, J, Q, K
Play your 5


We don’t show any advice for the 5 lead since our sample size is too low (since players rarely lead a 5).  In every other case our suggestions are based on the results of thousands of hands.


These results are confounding: they don't show an obvious pattern (at least to me), but once again the results are consistent across a ton of data. Maybe in a future article we'll dig a little deeper to explain why these results are the way they are.

When you have a pair

You're holding a hand like 5-J-Q-Q or 5-10-10-K. How should you respond to pone's lead?


Pone's lead
Best Response
A, 3, 4, or 6
Play from your pair
2
Play your 5
7,8
Play your highest card, whether or not it's part of a pair
9
Play a queen or king if you have one, otherwise play your 5
10, J, Q, K
Play your 5


Once again our sample size was too small to make a suggestion about how to respond to a lead 5.

When you have three-of-a-kind

If you're holding a hand like 5-Q-Q-Q you don't have a lot of pegging options, but the rules for how to maximize your pegging points are interesting enough to deserve their own table:


Pone's lead
Best Response
A, 3, 4, 6, or 7
Play from your three-of-a-kind
2
Play your 5
8
Play from your three-of-a-kind unless you have three 10s, in which case play your 5
9
Play from your three-of-a-kind unless you have three 10s or three Jacks, in which case play your 5
10, J, Q, K
Pair the lead if you can, otherwise play your 5


Your two biggest mistakes, and how to fix them

If you're like most Cribbage Pro players you're probably playing these hands correctly most of the time. In fact, most Cribbage Pro players are playing this hand in the optimal way. But there are a few common situations that most dealers don't play quite right. Here are two pieces of advice you can follow to give your game a quick tune-up.

Don't pair pone's lead, even if you have a pair

You're holding 5-10-10-J and pone leads a 10. Most players assume it's safe to pair the lead in this situation, but on average the 5 scores better. Play the 5 and you'll average an additional 1.6 net points.

Don't play a jack on a lead 9

Pone leads a 9, you're holding 5-10-J-J. Most players play a Jack here in this situation. Maybe they're trying to save their 5 for later? You'll net an extra point if you dump your 5 instead of giving pone the opportunity to play a 10 for a run of 3.


Note that you shouldn't play your queen on a lead 9, either, unless you have three queens. When you're holding 5-10-J-Q you'll net an extra 0.4 points if you play your 5 on a lead 9, rather than playing the queen.

Hey peeps, ask us some questions

You've got cribbage questions, and we've got the cribbage data to answer those questions. Just leave a comment below and we'll see about answering it.


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).

3 comments:

  1. I'd like to see some data on leading with a five. If I have a 5 with three different face cards or 10's I'll often lead with 5. If opponent scores15 for2 I have a 75% chance of pairing him and 0% chance of opponent getting triple 5's.

    ReplyDelete
  2. Hi Justin. That's a great question, and it frequently comes up when talking with more advanced players. The 5 lead is generally a losing play but it could be useful if you need to play offense. On average, pone will peg an extra 0.1 points leading the 5 (which is kind of good), but her opponent will peg an extra 0.5 points (which is really bad).

    For example, from 5-10-J-Q if pone leads the 10, J, or Q she'll average 1.8 points pegged and her opponent will average 3.5 points. If pone leads the 5 she'll average 1.9 points and her opponent will average 4.0 points.

    Thanks for the question

    ReplyDelete
  3. If I have a pair I will wait for later to use. Advanced players will not pair the lead, unless the alternative is giving up a run of 3. My thought is to trap them, so they have 1 card, and have no choice to pair, than I get my 6.

    ReplyDelete