Thursday, December 20, 2012

Cribbage Strategy - Test Your Pegging I.Q.

Looking for a way to pass the time between games of cribbage? How about playing a game about cribbage!

This week we've got a quiz for you to test your pegging instincts. We've scoured hundreds of thousands of cribbage games to analyze the pegging potential of each cribbage hand. How well does your intuition agree with our data?

Chose your role (Dealer or Pone), and your strategy (Offense: score as many points as possible; Defense: keep your opponent's pegging as low as possible; or Net Points: maximize your points while minimizing your opponent's).

Have a question about one of our answers? Can't figure out why 5-K-K-K is such a lousy pegging hand for dealer? Send us an email or comment below, and we'll give more detail on your question in a future blog post.

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 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).