How Should You Respond to Pone’s Lead?

Today we’re going to talk about how dealer should respond to pone’s initial lead. As usual, all our figures are based on our database of millions of hands of actual cribbage play. None of this is guesswork on our part -- it’s all based on real games played by real players.

All our numbers are based on average dealer points pegged minus pone points pegged. So if dealer pegs 5 and pone pegs 3 we’ll consider that a net advantage of 2 points for the dealer. When we say something like “playing the 6 gives you an extra 1.3 advantage over playing the 3”, we mean “the difference between your score and your opponents will be, on average, 1.3 points larger if you play the 6 than if you play the 3”.

All the situations we describe below are relatively common. You won’t run into them every game, but you’ll see them often enough that playing them right will make a difference in your win rate.

These statistics don’t take into account situations where you want to play offensively or defensively. We’ll talk about offensive and defensive play in a future article, but for now you can use our recommendations as general guidelines for your play.

A few points makes a big difference

Before we get to the meat of the article, let’s talk about how big a difference a few points can make. Our data shows that 3.4% of games end up being decided by a single point. An average player winning 50% of her games will find herself stuck in the stink hole 50% * 3.4% = 1.7% of the time. If our average player fine tunes her strategy to squeeze out one more point per game she’d win those 1.7%.

Another 3.7% are decided by exactly two points -- the loser is stuck in peg 119 when the winner pegs out. That means you’re probably losing 50% * 3.7% ˜ 1.8% of your games by exactly two points.  If you could manage to score an extra 2 points per game you’d be winning about 1.7% + 1.8% = 3.5% more often. An extra 3.5% win margin is the difference between being good and being a great player.

Here’s a chart breaking down the difference between the winner’s final score (121), and the loser’s final score. These numbers only take into account games between two “A” level players.

In this article we’ll show common mistakes players make that cost them a few points per game. If you use them to flesh out your strategy you should see yourself scoring an extra point or two, and making a noticeable difference in your win rate.

Dealer holds 7-8-9-9, pone leads a 3

The right play here is a 9, but for some reason dealer’s are only playing it 46% of the time. On average when the dealer plays the 9 she ends up pegging 0.8 more points than pone. When dealer players the 8 she ends up scoring 0.2 points less than pone. And when she plays the 7 it’s even worse -- she pegs 0.4 points less than pone.

Why is the 9 the right play? Couldn’t pone have another 3 and make 15 for 2 points? Well, she could but that only happens 35% of the time. It’s almost as likely that she has a 4 (33%), so you’re not saving much there.

Why are so many people playing the 8 here? One theory is that they like to take the count to 11.  Pone will be nervous about playing a ten/face card to make the count 21, and might make a mistake. It’s not a bad idea, but the data shows you can score more by playing differently.

It’s more likely that she’s got a 2 and two face cards. When that happens you’re likely to score 31 for 2:

Pone	Dealer	Points
3
	9
10/J/Q/K
	9	+2 for dealer (31 for 2)
—
2
	7
10/J/Q/K
	6	+1 for dealer (go)

If dealer leads the 8 she’ll end up with two "GOs" for a total of 2 points, rather than a 31 and a go for a total of 3 points. So play your 9 on pone’s 3, and on average you’ll pick up an extra point. That’s a 1.7% increase in your likelihood of winning.

2-3-3-4, pone leads the 7

The 3 is the right play here, but most players are playing the 4 or the 2. Are they hoping to save their 3s for a pair later on? Are they playing the 4 to take the count to 11? Are they trying to avoid taking the count to 10 in case pone has a 5?  No matter what the reason, playing the 2 or the 4 doesn’t work.  On average the dealer pegs 2.6 more points than pone when she plays the 3. She only scores 1.3 more than pone when she plays the 4, and only 0.9 more when she plays the 2.

Go for the run if dealer plays a 5 for 15-2 on top of your 3.  In 32% of the cases where dealer plays the run she scores big:

Pone	Dealer	Points
7
	3
5		+2 for pone (15 for 2)
	4	+3 for dealer (run of three)
6		+5 for pone (run of five)
	2	+6 for dealer (run of six)
	3	+7 for dealer (run of six, and a go)
—
?		+1 for pone (go)

Dealer scores 3+6+7=16 points, to pone’s 2+5+1=8, for a net gain of 8 points.

Executive summary, play the 3 instead of the 4 and you’ll gain 2.6 points on your opponent instead of just 1.3.

Some other popular hands

You’re holding 4-5-6-9 and pone leads the 7. A lot of players are playing the 4 here, but the 9 will, on average, give you an additional 1.6 points advantage over your opponent.

Dealer’s holding 5-10-J-K and opponent leads a king. We’ve seen that 48% of players will pair the king. The 5 is the better play, giving you an extra 2.2 point advantage over the king.

Dealer has 4-5-6-J and opponent leads a 6. Most players go for the pair, but they shouldn’t. Play your jack instead. The jack gives you a massive 2.4 points extra pegging advantage over the 6.  (And please don’t play the 4 or the 5 instead -- they do even worse than the 6).

Last one for today: dealer holds 6,6,7,8 and opponent leads a 10. Play the 6 instead of the 7 for a 1.6 point increase in your advantage over pone.

Let us know what you think

Want to see the results for another hand? Want more details on why these plays work so much better? 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).

Fun Flush Facts

Cribbage Pro player “sm15” sent me a message asking about the pegging advantage of playing a flush. That’s a great question, and got me thinking about flushes in general.

How likely is your opponent to have a flush?

About 3.0% of dealer’s hands are flushes. Pone’s hand holds a flush about 3.3% of the time.

Pone’s initial lead gives a clue as to whether or not they have a flush. A lead 5 is only 1.4% likely to be part of a flush. A lead 2 or 3 is 4.0% likely to be part of a flush. Basically if a lead card is more likely to be part of a trap (see the “Should you pair your opponent’s lead?”), it’s less likely to be part of a flush.

How likely are you to have a flush in your crib?

Remember that a flush in the crib only counts if the cut card is the same suit as the cards in the crib, so it’s significantly less common than a flush in the hand. Around 0.17% of cribs hold a flush (1 in 588). Even when dealer tosses two suited cards in her crib she still only ends up with a flush 0.81% of the time (1 in 123). When pone tosses suited cards in the crib she ends up giving dealer a flush 0.77% of time time (1 in 130).

Should you toss suited cards in the crib?

If it’s not going to make a difference to your hand, you might as well toss suited cards as dealer, and off-suit cards as pone. Usually all things are not equal, though, and pone might be faced with the choice of splitting up her hand to avoid giving dealer a flush. Changing your hand to avoid throwing suited cards is a pretty subtle play. When pone tosses suited cards into dealer’s crib she has a 0.77% chance of giving dealer 5 points, which works out to an average of 0.04 points.

Do situations exist where that 0.04 would make a difference? Sure. When pone discards 8-6 she gives dealer, on average, 0.01 points more than if she’d discarded 8-9. But if pone’s 8-9 is suited it might make sense for her to toss an off-suit 8-6 instead. That would offset the extra points from the 8-6, penalizing dealer an average of 0.03 points. Those three-one-hundredths-of-a-point could win you the game, but you've probably got more important cribbage-related things to worry about.

The Jack is a special case. Imagine you’re playing as pone and your hand holds: J♣, J♦, 6♦, 7♠, 8♠, 4♦. The right toss is probably the 4 and a Jack. But which Jack? If you toss dealer the J♦/4♦ you’ll give her a 10/46 (10 diamonds left in the deck after the Jack, 6, and 4, and 46 cards left in the deck) chance of scoring 1 for his knobs, plus a 0.77% chance of giving her 5 points for a flush. That works out to about 0.256 points.

If you toss the J♣/4♦ you’re giving her a 12/46 (12 clubs left in the deck / 46 cards left in the deck) chance of scoring 1 for his knobs, which works out to about 0.261 points. Throwing the off-suit Jack gives dealer an extra 0.005 points that you’d just as soon she not have! So if you’re going to toss a Jack into your opponent’s crib, consider tossing the suit that shows up most often in your hand, even if it might give dealer a flush.

How big is the pegging advantage?

To answer sm15's original question, the results depend on the hand being played, and who’s playing it (dealer or pone). For instance, we've seen that when dealers play a suited 6-7-8-9 they peg about 1% more points, while their opponents peg about 9% fewer points. A dealer holding suited A-4-Q-K will peg about 1% fewer points, while her opponent will peg about 7% fewer. And when pone holds A-4-Q-K she’ll peg the same number of points whether or not its suited, but dealer will peg 5% fewer points if pone’s A-4-Q-K is suited. (All of these statistics are based on several hundred examples of pone playing suited versions of those hands)

Taking into account every possible hand, dealer will peg about 1% fewer points if her cards are suited than if they’re not; and dealer’s opponent will peg about 4% fewer points if the cards are suited. If pone’s cards are suited, pone will peg the same as if they weren't suited, but her opponent will peg about 1.5% fewer points. So the pegging advantage to a flush is more about limiting your opponent’s pegging than it is about increasing your own.

Questions?

What do you think, sm15? Is that what you were expecting? Does anyone else have any questions they’d like answered?

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).

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).

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):

Pone	Dealer	Points
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).

What card should I lead? (Part 1)

We talked about some basic dealer pegging strategy in our last post. Let's switch it up a little and talk about pone (non-dealer) pegging strategy. The first pegging question for pone is "What card should I lead?" As usual, the answer depends on your objective at the moment (Score at any cost? Keep your opponent from scoring? Go for most net points pegged?). We’ll focus first on optimizing net points pegged.

For our analysis we'll measure net gain for pone as the average (mean) number of points pegged by pone minus the average number of points pegged by the dealer. So if pone pegs 5 and dealer pegs 3 the pone has a net gain of 2, and if pone pegs 10 and dealer pegs 12 the pone has a net gain of -2 (or a net loss of 2).

If there's enough interest we can examine other metrics in a future post (e.g., probability of pone pegging at least one point; probability of keeping dealer's pegging below some threshold).

6-7-8-9

Our data shows that pone keeps 6-7-8-9 in his hand around 0.7% of the time. That doesn't sound like much, but that actually makes it the third most common hand (after 5-J-Q-K and 5-10-J-Q), so it's worth spending some time analyzing this hand.

6-7-8-9 is the hand that got me interested in analyzing this data. It seems like whenever I play the 8 my opponent plays a 7 on top for "15 two"; and when I play my "9 for a run of three" she's got a "6 for a run of four." Is 8 really the right lead? And if it is, is "9 for run of three" really the right play when the dealer plays "7 for 15 two"? Or should I play "7 for a pair" instead?

John E. Chambers (in Cribbage, A New Concept) suggests that we lead the 6 from this hand. Let's stir up some controversy by respectfully disagreeing with Mr. Chambers!

Lead the 8

There's an ugly truth here that needs to be accepted: the dealer is probably going to outscore us. This doesn't mean that 6-7-8-9 is a bad hand, just that dealer has the advantage when pegging. The best we can hope to do is to keep the gap between dealer's pegging and ours as close as possible.  Cribbage Pro players have played this hand tens of thousands times, and on average they see these results:

Pone lead	Avg pone points pegged	Avg dealer points pegged	Avg pone net points
6	1.84	3.52	-1.69
7	1.93	3.68	-1.76
8	2.07	3.53	-1.46
9	1.87	3.63	-1.75

Leading the 8, on average, gives us a net advantage of 0.23 over the 6 lead (which, to be fair to Mr. Chambers, is the second best lead). The 6 limits dealer’s pegging almost as well, but doesn’t peg as well for pone.

Why does pone score more with the 8 lead? The detailed explanation why is very, well, detailed. If you're interested leave us a comment, and we'll show the gruesome details, with probabilities and results for every possible response to your 8 or 6.

What next?

What should you do when the dealer inevitably plays a 7 on your 8 lead? The answer is (drum roll)... play the 9. Your opponent will have the "6 for a run of four" 42% of the time, but 58% of the time she won't and that's enough to make the 9 the right choice. Average net gain for pone is -2.11 playing the 9 on top of the dealer's 8, -2.80 playing the 6 on the dealer's 8, and -3.17 playing the 7.

Defensive situations: maybe the 6, maybe the 8

Sometimes it’s more important to keep your opponent from scoring than it is for you to score. If your opponent is four points away from pegging out, for instance, you want to maximize the odds that she scores 3 points or fewer. The chart below show probabilities of limiting dealer to any number of points pegged.  It’s interesting to see that the 8 lead is more likely to limit your opponent’s pegging to 5 points or fewer, but the 6 lead increases the chance that your opponent pegs 12 or fewer.

Hail Mary pegging: lead the 8

If you desperately need 10 points to go out, you’re going to need to peg an extra 2 points on top of the eight points already in your hand. The 8 is almost always the best offensive pegging lead. The only exceptions are if you need to peg at least one point (lead the 6), or if you need to peg eight or more points (lead the 7).  The 7 is also your best choice if you need to peg more than ten points -- we've seen pone peg 11 about one time in a thousand when she leads the 7, but we've never seen pone peg 11 with an 8 or 9 lead. The chart below shows the details:

Executive summary

Moral of the story: you should almost always lead the 8 from 6-7-8-9, and feel confident playing that 9 for a run of three. You're probably in for a painful pegging experience, but you're going to get out-pegged no matter what you do.

We'll talk more about pone pegging strategy in the next post. Do you have a hand you're especially interested in? Leave a comment and let us know.

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).

Should You Pair Your Opponent's Lead?

Talk about a classic cribbage question! Should you pair your opponents lead, or is that sly dog planning to sneak in a three-of-a-kind on top of your pair for a big six points? If you stay up late pondering these questions you're in luck: we've got some data to help ease your mind. A word of caution, though. Today's post is nothing but numbers. If you just want the executive summary skip to the bottom of the post.

Before we show the numbers, let's talk about what we're measuring. We looked through our games and found all the hands (hundreds of thousands of them) where the dealer had the opportunity to pair their opponent's lead. We didn't include hands where the dealer could score a 4-of-a-kind in response if the non-dealer scores 3-of-a-kind. In those cases we'd consider the dealer the trapper, not the trappee. We did, however, include hands where the dealer had two cards 8 or higher, since the count would have to go past 30 for them to score their 4-of-a-kind. Perfectly clear? Then let's see some data:

Probability dealer would be trapped if they paired opponent's lead

Lead card	Trap %
A	49.9%
2	37.9%
3	26.9%
4	23.3%
5	45.2%
6	35.4%
7	31.9%
8	28.5%
9	34.0%
10	34.6%
J	35.4%
Q	31.8%
K	32.1%

(Don't use these numbers, though. We've got more useful stuff coming up soon).

So if you're the dealer, you're sitting on an ace, and some random opponent starts play by laying down an ace, then there's a 49.9% chance that he's got at least one more ace in his hand.

The cut card has some bearing on these odds. If the you've got an ace, your opponent leads an ace, and the cut is an ace, then it's less likely that the your opponent has an ace in reserve. The normal case is that the cut card is a different rank than your opponent's lead. Let's see what the probabilities are in that situation:

Trap probability when lead is different rank than cut

Lead card	Trap %
A	50.6%
2	38.8%
3	27.5%
4	23.8%
5	45.1%
6	36.3%
7	32.6%
8	29.0%
9	34.7%
10	35.4%
J	36.3%
Q	32.6%
K	32.8%

(Don't use these numbers yet, either)

Turns out that doesn't make that much of a difference. That's mainly due to the fact that the lead card is usually a different rank than the cut, though, so the averages are weighted heavily in that case's favor. We'll talk about the other case (lead is the same rank as the cut) a little later in the article.

What are the A players doing differently?

We talked a lot about the A players in our first post. Let's look at this first table to see what the A players are doing, and how we should respond to their fancy pants play:

Trap probability when playing A level players, lead different rank than cut

Lead card	Trap %
A	47.4%
2	38.5%
3	28.9%
4	24.5%
5	52.5%
6	40.3%
7	35.9%
8	31.7%
9	44.1%
10	41.6%
J	44.3%
Q	35.8%
K	35.5%

Use these numbers!

The A players are less likely to try to trap with aces or twos (especially aces), but more likely to try to trap with everything else, especially nines and jacks. We see two lessons here: one is that the A players are more likely to lead from a pair, and that's a good sign that we should do that, too. Another lesson is that we should be nervous about pairing a good player's lead.

What if an A player's lead is the same rank as the cut?

Trap probability when playing A level players, lead same rank as cut

Lead card	Trap %
A	29.4%
2	16.2%
3	17.8%
4	12.5%
5	-
6	24.0%
7	13.0%
8	14.4%
9	23.4%
10	19.4%
J	16.4%
Q	17.9%
K	20.3%

(Note that we've left out statistics for the "5" case. We've got a lot of data, but that particular situation is so rare that we don't have a large enough sample to feel confident reporting on it)

The lead card is a lot less likely to be a trap when its the same rank as the cut. In particular, notice that all the probabilities are lower than 33%.

How should we play against A+++ players?

The keys to taking your game to the A level are study and practice. Getting from A to A+++ is going to take psychology and creativity. Here's a fun story from DeLynn Colvert, four time national champion and author of Play Winning Cribbage, about a game against former national champion Duane Toll:

The game with Duane Toll was a 4th round match in the Grand National in Lincoln City, OR. With the score 2-2 best 3 of 5, Toll was dealing from about 28 out and I was standing about 23 out with first count. Toll has studied my habits consistently leading from a pair. My hand was 3-3-4-k and well short of game. I lead from the single 4!! Toll was also short of winning with first count the next deal and was forced to play offense...and he played a 3 on my 4 lead! I paired his 3 and knowing I consistently lead from a pair immediately played the 3rd 3 for 6!! When I played the 4th 3 for 12 he was stunned, threw his remaining cards in the air and conceded the match. I went to the championship and $5,000! Toll took home $200 for the 4th round! His play of the 3rd 3 was a good play as he would have been 15 or so short otherwise!

Colvert and Toll are possibly the two best players in the world, and it's great to see how they approach a decision as common as "should I pair my opponent's card?"

Executive summary

Should you pair your opponent's lead? This data is an important piece of the answer, but there are other factors to take into account when making a decision of this magnitude. If you need two points to go out then of course you should pair the lead. And if your opponent always, 100% of the time, leads from a pair then you should be even more cautious about pairing their lead.  Your current board position also plays a big part (We’ll talk more about that soon in another article).

But you'll frequently find yourself in a position where you don't have a read on your opponent and you'd like to take a chance at some points as long as you're more likely to come out with more points than the other player. That's where this data comes in handy.

In a large fraction of hands we're happy to take a guaranteed two points for ourselves as long as our opponent will average less than two points in response. That means we should take the pair for two as long as there's less than a 33% probability that our opponent is going to get three-of-a-kind for 6 in response.

When you just want to come out ahead in the exchange, the executive summary is that you should pair your opponent's lead of a 3, 4, or 8 (the three leads with a < 33% trap probability). And if your opponent's lead matches the cut you should feel free to pair it.

Have any insights you'd like to share on this topic? Questions about the data? Suggestions for future posts? We'd love to hear from you. Leave your comments below.

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).