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).

Mid-August has arrived, bringing with it the Cribbage Pro dealer discard quiz. Same rules as last week: we show a common hand, and you (playing as dealer) guess which discard gives the best results.

Just like last week the crib is often the deciding factor, so you might want to take another look at the Cribbage Pro discard table before starting the quiz.

We rate each discard by its net effect on dealer’s points:

points pegged by dealer
  + points in dealer's hand
  + points in dealer's crib
  - points pegged by pone

We don’t take into account the points scored in pone's hand or the points scored due to heels (cutting a jack), since dealer’s discard doesn't affect those points.

A♠ 2♥ 3♦ 4♣ Q♠ K♥

Most players discard Q-K in this situation, probably to keep the A-2-3-4 run together. About 5% of players discard the 2-3 in this situation, probably because our discard table shows that the 2-3 discard gives particularly good cribs.

Here’s a breakdown of the average points scored for each of the two discards.

Discard	2♥ 3♦	Q♠ K♥
Dealer points pegged	2.99	3.95
Dealer points in hand	6.99	7.84
Dealer points in crib	7.02!!	3.49
Pone points pegged	1.56	2.45
Dealer's net points	15.43	12.83

Dealers who discard Q-K actually peg more and have higher scoring hands, but the 2-3 gives dealer a significantly larger crib and keeps pone from pegging as much. Executive summary: discard the 2-3 and on average you'll net an extra 2.6 points.

2♠ 3♥ 4♦ 5♣ 9♦ Q♥

This hand poses a similar dilemma. Keep the run of four, or give yourself a gift in the crib? Once again most players keep the run, and once again that doesn't work out very well for them. Our discard table shows why: Q-9 is the second worst discard (after K-10), and discarding Q-9 instead of Q-5 weakens dealer's crib by almost 4 points.

Discard	5♣ Q♥	9♦ Q♥
Dealer points pegged	4.00	4.59
Dealer points in hand	8.08	8.18
Dealer points in crib	6.56!!	2.81
Pone points pegged	1.80	2.69
Dealer's net points	16.83	12.90

2♠ 3♥ 4♦ 5♣ 7♠ 9♥

Have you figured out the pattern? Most players keep the 2-3-4-5, but about 10% keep 2-3-4-9. You would do well to emulate those 10%: discard the 5-7 and you’ll net an extra 2.1 points, primarily due to your superior crib.

Discard	5♣ 7♠	7♠ 9♥
Dealer points pegged	4.09	4.64
Dealer points in hand	8.01	8.28
Dealer points in crib	5.77	3.82
Pone points pegged	1.63	2.61
Dealer's net points	16.24	14.13

2♠ 3♥ 5♦ 7♣ 9♠ J♥

Hopefully by now we've convinced you to put good cards in your crib. Sometimes you've got a lot of good cards and you’re not sure which should go in your crib. When dealt this hand (2-3-5-7-9-J) we’ve seen some dealers discard 2-3, some discard 5-J, and some discard 7-9. Which one should you go with? Once again, the discard table comes to the rescue: 2-3 gives the best results of any of our possible discards, and gives dealer about 2 more net points than the 7-9 discard.

Most players discard 7-9 in this situation, probably to keep the 2-3 and the 5 together with the Jack. An interesting fact about cribbage is that your hand (or crib) is guaranteed at least two points if it has a combination of cards that add up to 5 (see the Wikipedia Cribbage Statistics page for an explanation why). So even though discarding the 2-3 means you lose your 15 for the 2-3-J combination you’re guaranteed to make it up with at least 2 points in your crib.

Discard	2♠ 3♥	7♠ 9♥
Dealer points pegged	4.51	3.72
Dealer points in hand	5.40	7.28
Dealer points in crib	7.02	3.78
Pone points pegged	2.22	2.02
Dealer's net points	14.70	12.76

A♥ 2♠ 3♠ 5♣ 6♠ 9♥

The best discard here is 5-6, with 2-3 a close second. But two thirds of Cribbage Pro players are sabotaging their cribs by discarding 6-9. Sure 6-9 gives a guaranteed 2 points in the crib, but we’ve already seen that a 2-3 or a 5 in our crib will guarantee us 2 points. Discarding 5-6 also leaves us with A-2-3-9 in our hand for a 15 and 2 points. You can bring your game up a notch by discarding 5-6 instead of 6-9 in this situation.

Discard	5♣ 6♠	6♠ 9♥
Dealer points pegged	3.67	4.67
Dealer points in hand	7.88	6.66
Dealer points in crib	6.40	4.77
Pone points pegged	1.82	2.67
Dealer’s net points	16.13	13.42

A♥ 5♠ 6♠ 7♣ 8♠ J♥

Half of the Cribbage Pro players toss the A-J; the other half toss the 5-J. Keeping the 5 in your hand helps a little with pegging (an extra 0.8 points on average), but tossing the 5-J raises your crib’s value by 3.3 points. The correct discard from this hand is 5-J.

2♠ 3♥ 4♠ 5♣ 6♠ 9♦

It’s tempting to discard the 2-9 (to keep the 3-4-5-6 run), or 6-9 (to put a 15 for 2 in your crib), but the best discard here is 2-3, which nets dealer an extra 3 points over the 2-9 or 6-9 discards..

2♣ 3♥ 5♠ 6♣ 9♦ J♠

Tossing 6-9 guarantees us at least 6 points (two points each for 2-3-J, 5-J, and 6-9). But our cribbage math also tells us that 2-3 guarantees us six points (5-J, 6-9, and at least two points in our crib, since 2-3 add to 5). Since you've read this far you've probably already guessed that we recommend discarding 2-3. The 2-3 discard gives you an extra 2 point net over the 6-9 discard.

2♥ 3♥ 4♣ 5♦ 10♠ K♠

The most popular discard from this hand is the 10-K, but our discard table shows us that a 10-K gives dealer a lower average crib than any other pair of cards. Discard the 5-10 instead and net an extra 3.1 points.

A♠ 2♦ 3♣ 6♣ 8♠ 9♥

Fewer than 10% of players get this right. Most players keep the run of three and discard the 6-8 or the 6-9, but let’s consider the 2-3 discard. Putting the 2-3 in your crib leaves you with A-6-8-9 in your hand, for a total of 4 points. We know that a 2-3 in the crib guarantees at least 2 points, guaranteeing us a total of at least 6 points. That’s better than the 5 point guarantee for either the 6-8 or 6-9 discard. The 2-3 discard scores best here.

A♠ 2♥ 3♠ 4♣ 5♠ 6♦

We've suggested discarding 2-3 so many times in this article. This has to be a trick question, right? Nope, once again the answer is to discard 2-3. Most players discard A-2 in this situation, but the 2-3 discard gains dealer an extra 1.9 net points.

A♥ 2♠ 4♥ 5♦ 8♣ 9♠

This one's a little puzzling to me, but the data shows a clear winner. Put A-4 in your crib and you’ll average 0.8 net points more than you would if you'd discarded 5-8, and 1.0 more than if you'd discarded 2-4.

3♠ 4♥ 5♦ 6♣ 10♠ Q♥

Don't be afraid to split up that run. Keeping 4-5-6-10 instead of 3-4-5-6 gives you an extra point in your hand (an average of 10.3 instead of 9.3), an extra half a point in your crib, and lowers pone's pegging by 0.7 points. Putting the 10-Q in your crib seems like it opens up the possibility of a straight, but our discard tables show that open-ended straight draws rarely pay off.

We want to look at your hands

Here’s your opportunity to improve your cribbage skills. Just leave us a comment below telling us about a hand that’s troubling you. We’ll comb through our database and let you know which play gets the best results.

Thursday, September 12, 2013