Thursday, August 1, 2013

Cribbage Strategy Discard Quiz - Pone Edition

It’s early August, and that means it's time for a Cribbage Pro discard quiz! We've listed some common hands below. See if you can figure which discard gives the best results for pone. Note that in all cases you're playing as pone, so you'll be discarding into your opponent's crib.

We chose the hands below because they show up fairly often, and are frequently played in a suboptimal way. Before you take the quiz, you might want to review the Cribbage Pro discard table. In particular, note that you can minimize your opponent's crib by giving her K-10, Q-9, or K-9; and you'll maximize the points in your opponent’s crib by discarding 5-5, 7-8, or 2-3.

We rate each discard by its net effect on pone's points:
points pegged by pone
+ points in pone's hand
- points in dealer's crib
- points pegged by dealer

We don't take into account points scored in dealer's hand since pone's discard doesn't affect those points.

2 3 9 10 J Q


Should you keep the run and give dealer your 2-3? Or should you break up the run in order to poison your opponent's crib? We've seen the best results for the players who split up the run and give their opponent the Q-9. Only 44% of players get this one right, though. Keeping 2-3-10-J leaves you you two fifteens, good pegging (lead the 3), and on average gives dealer a terrible crib.

Here's a breakdown of the average points scored for each of the two discards. Keeping 2-3-10-J gives pone slightly more points, but the real advantage is that discarding 9-Q lowers dealer's average crib by more than three points (compared to the 2-3 discard).


Discard
9 Q 2 3
Pone points pegged
1.78
1.63
Pone points in hand
7.04
6.76
Dealer points pegged
3.06
3.78
Dealer points in crib
4.05
7.39


A 2 3 4 7 8


Would you toss A-7? If so you're an elite discarder: only 37% of players get this right. A lot of players toss the 7-8 into their opponents crib in order to keep their run of four. Don't do that: the 2-3-4-8 gives you a 15 for two, and lessens your opponent's crib by 3.3 points!


Discard
A 7 7 8
Pone points pegged
2.34
2.98
Pone points in hand
8.32
8.21
Dealer points pegged
2.90
3.41
Dealer points in crib
4.42
7.79


7 8 9 10 J K


What's the right move here? Go for the run of four (7-8-9-10) and toss your opponent J-K? Or break up your run and put 10-K in your opponent's crib? Very few players get this right, but the correct answer is: toss the 10-K. On average dealer ends up with 1.7 fewer points in his crib, which makes 10-K the right discard.


Discard
10 K J K
Pone points pegged
2.34
2.98
Pone points in hand
8.32
8.21
Dealer points pegged
2.90
3.41
Dealer points in crib
4.42
7.79


2 4 5 8 9 J


Everyone's got a different way to play this one. Discarding 2-4, 2-8, 4-9, and 8-J and are all popular discards. The most popular choice is to discard the 2-4, but the best discard is 4-9. Compared to 2-4, the 4-9 discard limits dealers pegging and stifles her crib.


Discard
4 9 2 4
Pone points pegged
1.81
2.08
Pone points in hand
6.31
4.76
Dealer points pegged
3.26
4.11
Dealer points in crib
4.31
5.00


A 2 4 5 6 10


Most players toss A-2, but they can do better than that. The 2-10 discard gives dealer fewer points on average, and keeping the A-4 combination gives you an extra 1.6 points of pegging on average. This holds for any card that counts 10: pone should discard 2-J from A-2-4-5-6-J, 2-Q from A-2-4-5-6-Q, and 2-K from A-2-4-5-6-K.


Discard
2 10 A 2
Pone points pegged
3.07
1.72
Pone points in hand
8.86
9.75
Dealer points pegged
3.49
3.77
Dealer points in crib
4.31
4.77


2 3 5 6 9 J


It seems counterintuitive to give your opponent a 6-9, but that's the right play here. A lot of players toss the 2-3 in this situation, but our discard data shows that 2-3 is a more dangerous discard than 6-9.


A 2 3 4 6 9


A lot of players are throwing 6-9, but they'd gain a few points if they kept 2-3-4-6 and discarded A-9.


A 2 4 8 10 K


Once again, 10-K is the right discard. Your hand will score fewer points, but you'll peg more and your opponent's crib will have fewer points. A-2-4-8 pegs well, so when you're dealt A-2-4-7-8-K you should keep the A-2-4-8 and throw 7-K into opponent's crib.


A 3 4 7 10 K


You've guessed it: 10-K is the way to go. Keeping the A-3-4-7 is good for pegging (if you lead the 4), and the 10-K discard shuts down dealer's crib.


3 4 6 7 9 J


The wrong (but most common) discard is 7-J. You'll score better if you discard 3-J: better pegging and a lower scoring crib for the dealer.


2 3 4 8 9 10


Oh, here's a good one. The right move? Toss the 8-10. A lot of players toss the 8-9 here, but that sets dealer up for a nice crib. Some players toss 2-3, but that leaves them with too few points in their hand. 2-3-4-9 strikes the right balance of a poor crib for dealer, with a good hand and good pegging for pone.


A 2 3 5 5 9


Tossing the 2-3 is pretty scary, but it leaves you with six points. Tossing the A-9 gives dealer fewer points in her crib, but leaves you with only four points in your hand. Hmm.. What's the right choice? Toss the A-9. Discarding 2-3 almost guarantees your opponent a great crib. Keeping the 2-3 increases your pegging potential, especially if you lead the 3. So on balance A-9 is the right discard here.


2 3 7 8 9 10


Don't toss that 2-3!!! Toss 10-3 or 10-2 instead. You'll score fewer points in your hand, but you'll more than make up for that by shutting down dealer's crib.

How can we help you?


Do you frequently run into a hand that flusters you? Leave us a comment below and we'll tell you what our data suggests.



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).

5 comments:

  1. Handful of sixes and nines lead with the six or the nine ?

    ReplyDelete
    Replies
    1. I lead with the six, if your opponent has a 9 for 15, you can follow with a 9 for a pair. Count is 24 and they can't triple you up. If you use the same play theory and lead with a 9 then 6 for 15, 6 for a pair, 21 count. Your opponent can play 6 to triple up or 10 for 31, two points.
      Definitely lead with the 6.

      Delete
    2. Hi Adrian,

      The Cribbage Pro data shows that there's a slight advantage to leading the 6. We've seen tens of thousands of 6-6-9-9 hands played with a 6 lead and tens of thousands with a 9 lead. When pone leads a 6 she averages 2.0 points of pegging and gives up 3.0 points to dealer. When pone leads a 9 she averages 1.9 points and gives up 3.0 to dealer. So lead the 6 and you'll average an extra 0.1 points of pegging.

      Delete
  2. You mention a couple of times here to lead the 3 when hold 2-3 as pone. I almost always go for the "reverse psychology" play in that situation and lead the two. I haven't done the detailed analysis you have, but I think I get a 10-value on a 2 way more often than a 3, allowing for the 15-for-two play. Thoughts?

    ReplyDelete
  3. Hi Thomas.

    The 3 lead actually gets a 10-value response a little more often than the 2 lead. I looked specifically at the case where pone is holding 2-3-10-10 (or any two 10-count cards instead of the 10). In those cases dealer plays a 10 card 34.6% of the time on the 3 lead vs. 31.5% on the 2 lead.

    Why is that? Well, dealers are less likely to respond to a 3 lead with a 4, 5, 6, 7, or 9 than they are with a 2 lead. The data doesn't say why the players are doing that, but my personal feeling is that the 4 and 5 are scary because pone could turn them into a run; 6 is scary because pone could score 15 for 4 if she has a 6; 7 is scary because pone could score 15 for 2 if she has a 5; and 9 is scary because pone could score 15 for 2 if she has a pair of 3s. Eliminating 4, 5, 6, 7, and 9 as a response doesn't leave as many options, so dealer is more likely to respond with a 10 count card.

    That said, the results are actually pretty similar: the 3 lead gives a very, very slight edge over the 2 lead, and if you're getting good results leading the 2 then I wouldn't suggest you change.

    ReplyDelete