Thursday, November 15, 2012

Offense vs Defense Cribbage Strategy

Last week we brought up the idea of choosing your cribbage strategy based on board position (that is, based on your score and your opponent’s score). This week we’ll help you decide when you should play offense and when you should play defense.

What does playing offense mean? It means scoring points at the risk of giving your opponent points: throwing a pair in your opponent’s crib in order to keep a great hand for yourself, or pairing your opponent’s lead at the risk of letting them score three-of-a-kind.

What does it mean to play defense? It’s the exact opposite: keeping a bad hand so that you can throw terrible cards in your opponent’s crib, or ignoring the opportunity to pair or score a run during pegging so that you can keep your opponent’s score down.

How to choose your strategy 

We’ll get to the gory details below, but here’s an executive summary to get you started. When your score is close to your opponent’s (and it frequently is), you can use the table below to help decide your strategy. Follow these steps:

  1. Count the points in your hand.
  2. Make a guess at the points in your crib (if you’re the dealer).
  3. Add in a point or two for pegging.
  4. Look up this end-of-hand score in the table below to decide how to play.

If your score is close to or tied with your opponent’s, and your end-of-hand score is between...
Dealer should play...
Pone should play...
61 to 75
76 to 86
87 to 101
102 to 112
113 to 120

For instance, if you’re playing as dealer and your and your opponent’s end-of-hand scores are between 102 and 113 then you should play offense. If you’re playing as pone and your and your opponent’s end-of-hand scores are between 76 and 87 then you should play defense.

If you’re more of a visual person you might prefer to look up your end-of-hand score on the board below to choose your strategy. Dealer should play offense (and pone should play defense) when her end-of-hand position puts her in a green area, and defense when her end-of-hand position puts her in a red area. Pone should do the opposite -- play offense in the red areas, and defense in the green areas.

We’re going to dig into the gory details now, but if you want some more advice on what exactly “offense” and “defense” mean you can just skip to the end of the article.

Remember, look up your estimated end-of-hand score on the board (and in the table), not your current score.

Dealer’s win probabilities

Where did these strategies come from? Let’s take another look at our chart from last week, which shows the probability the dealer will win based on dealer’s and pone’s scores immediately before the deal:

Remember that the point of offensive play is to score points even at the risk of letting your opponent score. So let’s see what would happen to dealer’s chances of winning if she had played offensively, and each player had pegged an additional two points above and beyond what they would have scored with typical play:

These charts are getting more and more complicated, and this one deserves a little explanation. This chart shows the increase or decrease in the probability that the current dealer would win if both dealer and pone had scored an additional 2 points in a previous deal. Or to put it another way, it tells us whether or not the dealer should have played offensively on her previous hands. The chart is marked green in areas where the dealer is more likely to win when both players scores are increased by two, and red where the dealer is more likely to lose.

Looking at our first (orange/blue) chart, we can see that the dealer has a 59% chance of winning the game when the score is tied at 95 (one line past the one labeled “90”). If the score were tied at 97 (that is, if each player had scored 2 more points), the dealer would instead have a 65% chance of going on to win. (I know it’s hard to tell the difference between a 59% and a 65% on that first chart -- you’ll have to trust me that those are the correct numbers). If dealer had played her previous hand more aggressively she’d be in a better position to win: an extra two points for dealer and for her opponent would actually give dealer an extra 6% chance of winning (65% - 59%). Because of this the chart shows a nice bright green at position 97/97.

The story would be different if the scores were tied at 80 (two lines before the one labeled “90”). With both players tied at hole 80 the dealer has a 62% chance of winning the game. Tied at 82, a red area, the dealer has a 59% chance of winning the game. This time dealer would have been better off if she’d play more defensively in previous hands. She’d have increased her likelihood of winning by 3% if she’d forced her opponent to peg two fewer points, even it had cost her two points.

The red and green blobs in this chart correspond to the white wave running through the first chart. The blobs get fainter and fainter as you move to the bottom left of the chart, but they’re still there -- alternating red and green. An interesting fact is that the areas repeat every 26 points: there’s a green area centered around 95 points, and another 26 points earlier centered around 69 points; and the red area centered around 80 points has an echo 26 points earlier centered around 54 points. This 26 point cycle shows up because players average 26 points every two deals (16 points as dealer, and 10 points as pone), and is the basis for DeLynn Colvert’s Theory of 26.

Use the red and green blobs to your advantage

This red/green chart gives us another method for deciding when to play offense and when to play defense: estimate your and your opponent’s next starting position, find the position on the chart, and base your decision on the chart’s color.

For example, let’s say you’re at hole 85 as pone, with dealer at hole 80. You keep 6-6-7-8 in your hand, and dealer cuts a 10. You've got 10 points in your hand, so you’ll start in hole 95 next turn if you don’t peg. Dealer averages 16 points (between hand, crib, and pegging), so she’ll probably start around hole 96 next turn. Looking at our chart you see that 95/96 points for dealer/pone puts you squarely inside a green section of the chart. You’d like to start further ahead, so if you see the opportunity to peg a few extra points you should take it, even if it means giving your opponent a few points, too.

If the positions were reversed (you as dealer from hole 80, pone starting at 85) you should reverse your strategy and play defensively.

Play for position or play for points?

Note that the strength of the colors increases as you get closer to the end of the game, which means the importance of offensive and defensive play increases as the game goes on. Our chart shows a very faint pink area around 25 or 30 points. That early in the game the effects of correct offensive or defensive play are so small that it’s probably better not to concentrate on offense or defense, and instead to focus on increasing your lead over your opponent (or catching up with her).

Exercise moderate offense or defense between 60 and 86 points
Position really starts to be important after you’re halfway through the game, as shown by the darker green and red blobs. When you and your opponent are between 60 and 86 points you should start practicing moderate offense or defense: try to manipulate your opponent’s position without sacrificing too many points.

Moderate offense means:

  • Pairing your opponent when she leads a 9 or higher
  • Getting involved in a run if you think you’ll end up with as many points as your opponent

Moderate defense means:

  • Not pairing your opponent when she leads a 3 or a 4
  • No getting involved in a run, even if you think you’ll end up with more points than your opponent

Exercise serious offense or defense between 87 and 109 points
Between 87 and 119 points things you've started getting into the endgame, and the importance of positional play has become very important. Proper positional play here can make a big difference in your win rate. Start playing serious offense or defense, depending on where your end-of-hand score puts you on the board.

Serious offense means:

  • Trying to entice your opponent into getting involved in a run. For example, if you’re holding A/2/3/J and opponent leads a 4, play your 3 and hope that she plays a 5 or a 2 (run for three) so that you can make a run of four
  • Lead a ten card from A/J/Q/K, in the hopes that you’ll end up with a 31 for 2 points (even if means you’ll get paired)

Serious defense means:

  • Lead from a card lower than 5, even if you’ve got a pair. For instance, normally you should lead a 7 from 4/6/7/7, hoping for a three-of-a-kind. In defensive mode you should lead the 4, even though you’ll average 0.6 points more when you lead the 7
  • Lead the 6 from 6-7-8-9 (you’ll score more with the 8, but your opponent scores fewer points if you lead the 6)

Exercise extreme offense or defense starting at 110 points
At the very end of the game everything changes. If your opponent is going to be starting as pone next turn within 10 points of winning then you have to do everything in your power to keep them from scoring. This means being willing to peg 0 points and score 0 points in your hand in order to keep them as far away as possible from the final hole. Pone will average 10 points between her hand and crib, so putting her within 10 points of pegging out is a very dangerous situation.

On the other hand, if you’re going to start in this position as pone you shouldn't play particularly offensively. You’ll count first, and you’ll likely go out before your opponent has a chance to count. Giving your opponent more points would just increase the chance that she’ll be close enough to peg out next turn.

Extreme defense means:

  • Don’t play cards that would let your opponent start a run. For instance, if your opponent plays an 8 you shouldn't play the 7 for 15-2, since she could play a 9 or 6 for a run. Even if you have a 9 and a 6 and could make a run of four you still don’t want to do this, since you could give your opponent points
  • Lead low pairs. For example, lead the A from A,A,2,3. You won’t score 15 for 2 if your opponent plays a 10 card, but you cut down on her ability to pair your lead

That’s plenty for this week

That’s the end of a whirlwind tour of a dense topic. Do you have a specific hand you’re interested in analyzing? Would you like some advice on a tricky board position? Let us know and we’ll tell you how and when to play it for offense and defense. Just leave us a comment 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).

Thursday, November 1, 2012

Cribbage Strategy and Board Position

Today we’re introducing a topic that, more than any other, separates casual players from expert players: board position. Expert players take their own score (board position) and that of their opponent into account when deciding how to play. Based on board position an expert player will play offensively (scoring more points themselves at the risk of letting their opponent score), or defensively (limiting their opponents points, even if that means scoring fewer points themselves).

Why play defense?

Why would someone do this? Let’s take an extreme example. The score is tied at 109, your opponent is dealing, you keep 3-3-10-10 in your hand and the cut is a 2:

You lead your 3, and your opponent plays a 3 for two points. What’s your play? Playing your remaining 3 would give you six points, but let’s think about that play a little.

  • You need 12 points to win
  • You’ve got 12 points in your hand
  • Dealer needs 12 points to win
  • You count first
  • So you win as long as dealer pegs fewer than 12 points

The only way dealer is going to win is if he has the fourth 3 and pegs 12 points from four-of-a-kind.  Play the 10 and guarantee yourself the win. Dealer probably doesn’t have the fourth 3, but by not playing your second 3 you’ve gone from “probably going to win” to “definitely going to win”.

Why play offense?

Imagine you have the same hand, but the score is tied at 106.

The equation changes significantly:

  • You need 15 points to win
  • You’ve only got 12 points in your hand
  • Dealer needs 15 points to win
  • Dealer averages 16 points per deal (between pegging, hand, and crib -- see the first post in this series for more details)
  • Dealer will very likely win unless you peg at least 3 points

Executive summary: play your second 3 for six points and you’ll win unless dealer holds that fourth 3 (in which case dealer will score 2 for his pair, 12 for his pairs royal, and score another 1 for a go).

The decisions to play offense at hole 109 and defense at hole 106 both come from straightforward logic, and in both cases the strategy is dictated by board position. A 3 point difference in position completely changes the way you should play your hand.

Winning probabilities

The logic was easy in those last examples because you know you have a 100% chance of winning if you can make it to 121 points. There are opportunities to use this kind of logic earlier in the game. To understand these opportunities better let’s look at another chart built from our millions of hands of Cribbage Pro multiplayer game data. The key to improving your game in this chart: it’s the white wave running along the diagonal line.

The chart shows the probability the dealer will win, based on dealer and pone’s scores immediately before the deal. The line down the middle shows the cases where dealer and pone have the same score, and has ticks marked off every 5, 10, and 30 points. Bright orange means we’ve never seen dealer win from that position, bright blue means we’ve never seen dealer lose, and bright white means that dealer and pone each won 50% of the time. Light orange means pone is favored to win, and light blue means dealer is favored to win. The chart is grey when we don’t have any games in our sample that were at that combination of points.

Of course the chart gets more blue as you move to the right (since the dealer’s more likely to win if his score increases and pone’s doesn’t). And of course it gets more orange as you move towards the top of the chart. But notice that the color changes as you move diagonally up and to the right, because of that white wave. The wave is weak in the bottom of the left, but it repeats itself in 26 points cycles, getting stronger and stronger until it reaches the top right of the chart. The waves are what make board position so important.

Looking closely you can see that the chart is very orange when the score is tied at 115, and very blue when the score is tied at 105.

When the scores are tied at 115 dealer is at a big disadvantage. Pone counts first and only needs 6 points to go out, so pone will usually win if dealer doesn’t peg 6 points. When the scores are tied at 105 the situation is reversed. Pone has to score 16 points to go out, but we’ve seen that pone averages only 10 points between her hand and pegging. We’ve also seen that 16 points is average for a dealer, across hand, crib, and pegging, so starting from hole 105 dealer will usually go out after counting her crib, or will be close enough to peg out the next hand.

Dealer has a huge advantage when the scores are tied at 105, and a huge disadvantage at hole 115. Neither player has a point lead in either of the two positions, but the likely winner has changed. Why? Because the two positions are on different sides of that wave.

How do you ride the waves?

Throughout the game you’re given opportunities to take points at the risk of giving more points to your opponent. Good players will use these opportunities to ride the waves, sacrificing points when necessary to keep their opponents from moving ahead, and giving points to their opponents when necessary to score a few extra points themselves.

Think about your position on the wave whenever you have the opportunity to score points while potentially giving your opponent points. Would you be in a better position if you moved up and to the right in the chart? If so, take the points. If not, turn them down and keep your opponent from scoring, too.

Let’s take a common example. You (as pone) are in hole 96, with dealer in hole 90. You’re holding 5-J-Q-K, for 9 points, so you’ll start from hole 105 as dealer next turn. On average, dealer scores 16 points per deal (between pegging, hand, and crib), so with a typical hand he’ll be in hole 106 at the start of the next turn. 105/106 is a nice blue spot on our chart, so you should peg defensively to keep your position.

You start the play with your Queen and dealer plays a 5 for two points. Should you pair the 5? You’ll be in a good position to win next turn, so you don’t really need the points. Pairing the 5 gives dealer the opportunity to make three-of-a-kind for 6 points, which would knock you out of your sweet spot on the wave. The right play is to turn down the points, and play your Jack or King instead.

If you were starting 10 points back (you at 86, dealer at 80), pairing the 5 would probably be the right play. You’re a little out of position, and you’d really like to move forward at the risk of moving your opponent forward, too.

We’ll go into detail next week, with more precise instructions on exactly when to play offense and when to play defense.


While you’re waiting for next week’s article we suggest reading DeLynn Colvert’s excellent book Play Winning Cribbage. His groundbreaking Theory of 26 gives advice on board position starting from the very first hand of the game, and is well worth studying. Some of his thoughts about the Theory of 26 are also available at the American Cribbage Congress website.

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).