*** This hand was suggested by JQT

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Total votes: 232

I've spent q lot of time considering what cards to retain and what cards to discard with today's hand. That's not a good sign usually for me - giving too much thought results in the wrong decisions.
Tossing 3-4 to our crib has the best value but leaves a configuration that I am not happy to work with.
Tossing Q-K, while valued less, has a hand that has a higher expected average by about a point than 6-9-Q-K.
Seventeen cuts gives 3-4-6-9 six, eight or 9 points (333, 999; 5555, 666; 222).

No synergy between 6-9 and Q-K, but it's a price I'm willing to pay in order to put 3-4 in my crib.

https://3.bp.blogspot.com/-OOWZCrVymag/UIB3CpoavGI/AAAAAAAAB48/xNfLRby17LE/s1600/image01.png

I had a hand like this yesterday. Earlier in game and tighter positions. Lets put it this way I had a very good day so a course a five was cut and a Jack and King were in it also. Somedays you make the right guestimate. dec

This hand is a better pegger. Down 11, let's peg a bit.

Nice crowd at Brookline. 136 players.

As per Dec. Looking for Lady Luck here not empirical logic. Need a 5 cut and a J and Q/K in the box.

Put the 6-9 in the crib today. Pair of touching cards in hand. A , 2, 4, 5, J cuts help. Maybe 6-9 hits something in the crib.

I have played this hand either way in the past …tossing the Q-K or the 3-4. Over time i have decided discarding the Q-K is best for me. Keep 6-9-Q- K does not have enough cut help imo. Keep 3-4-6-9 is helped by 7/13 ranks and an additional & separate ( do not help the hand ) three more cuts help the crib. With this configuration I like the chances for a three card run too. Rosemarie gives more & better logic detail for our shared choice. As to board position…I am @ #3 threshold & Pone needs 16 to have the deck first @ #4. …if the cycle prevails the last hand of the game may look something close to this ..110-116*..dec explained how he got lemonade out of lemons with this keep.

You guys are killing me with these hands and board positions, lol. So...what's the best of another bad lot for about the 3rd or 4th consecutive day, let's see...hmm. I'd like to have 3 4 in my crib, but to me this leaves a totally unsatisfactory hand keep in the (6 9 Q K). Bad for pegging, and fairly bad for cut improvement as well. So it'll be between the (6 9) and (Q K) discards for me. Clearly (6 9) would be the preferable crib choice between these two, but what about what's left? (3 4 Q K).. I'm leaving ZERO points, admittedly with much better cut chances to improve, with the low and high-end run possibilities. But this keep really does not sit that well with me either. There is a possibility not to improve at all, and this is also a disappointing keep for your peg possibilities. This leaves (3 4 6 9). It is clearly the preferable hand for offense as far as improvement, and MUCH superior for pegging than any of the other holds. And let me tell you, we're in NEED of scoring any way we can after this deal. To me, this overcomes the somewhat sour tone of the (Q K) crib toss. I gotta go with this, once again grudgingly because of the score, but let's hope for something good to happen, being the optimist today :)

I don't know if this puzzle really teaches us anything very conclusive about Cribbage, but I think it can be used to tell us a lot about the Cribbage Player.

We basically have three choices: Toss (3 4), Toss (6 9), or Toss (Q K). It looks simple; it seems meaningless. And yet if you don't enjoy such conundrums, you may not enjoy Cribbage! Much of the game involves what seem like trivial decisions.

The highest Crib comes after Toss (6 9), but it requires us to place ALL of the scoring potential into our Crib. If we have studied the game a bit, we know that Toss (6 9) is considered an "Also Ran" Dealer Discard by RAS, which means it's about the only way we can place points into our own Crib and still be producing a potentially low-scoring Crib.

Toss (3 4) behaves differently, and while it can certainly be grouped within the same end of the scale, in that it contains Zero Points, along with its "cousins" of Toss (6 7) and Toss (J Q), it can often turn NOTHING into SOMETHING. This is maybe how we could turn this "Lemon" of a card arrangement into "Lemonade."

Because it's one thing to Toss (6 9), which begins at Two Points, and reach an Average Crib of about 5.5 Points; but Toss (3 4), and also Toss (6 7) and Toss (J Q), regularly beat some PAIRS in our own Crib, and sometimes reaches an average of Five Points, in spite of starting out with NOTHING!

But the score is of concern, as we are not only trailing by Eleven Holes, but we are One Hole 'shy' of the Third Street 'par' Hole 70. And that may call for a balanced approach, whatever that may mean. I think it probably warrants Toss (Q K), as we might peg a bit better. But we may do so at the expense of our Crib. We may end up with a lousy Crib today, regardless of what we throw!

I think there are Relative Scores, or places on the board, that would call for Toss (Q K), and that this may be one of them. But I'll be honest: I think as long as we choose either Toss (3 4) or Toss (Q K), we are making a good decision, and the discard that you choose today maybe tells me more about you as a player than it indicates a clear right or wrong choice.

For the RAS article on "Star Power" see: http://www.cribbageforum.com/YourCrib.htm

When looking at the pegs (69*-80), seeing these six cards, have nothing to defend, yet cannot bring myself to choose aggressive offense to include the pegging. So an optimal strategy feels just right (pegs are net). In order to gain +1 peg (none of the cards reach 1.5), need to hold 3-4-6. That solves the choice for RAS. Goodbye Q-K! Once seeing the starter card will shift to offense as seems of no benefit to Q-K in crib and only adds two points to hand score. Would pair a trey or four if led. Play the 9 on a deuce lead and play the trey on an Ace or five lead. On 6 or 9 lead, would score the 15-2, on an 8 lead would play the six, on a 7 lead, would play the 9. Don't want a X-point lead would play the 9 on Q-K , keeping 3-4-6 intact, and play the trey on 10-J. Actually even though Q-K is very low scoring ot own crib (3.483), the hand potential of 3-4-6-9 is so superior to 6-9-Q-K that combined values favor this choice by nearly two points. Looks like will be choosing an offense strategy for the remainder of this game. Don't despair - there's a faint glimmer of light at the end of the tunnel.

Here to learn. But again, my gut is differences between choices are matters of degree and look forward to Hal's numbers to confirm or deny my feelings.

I think the hand naturally breaks 3 ways - 6-9-Q-K (3-4), 3-4-Q-K (6-9) and 3-4-6-9 (Q-K):

6-9-Q-K: 2pts + 5pts (Schell: 4.91) = 7pts

3-4-Q-K: 0pts + 5¼pts (Schell: 5.13) = 5¼pts

3-4-6-9: 2pts + 3½pts (Schell: 3.46) = 5½pts

Potential:

6-9-Q-K: Improves with 5555, 666, 999, JJJJ, QQQ, KKK = 20 cuts = 20/46 = 43.5% up to 5/6/8pts with 5555, 666, 999, JJJJ = 14 cuts.

3-4-Q-K: Improves with AAAA, 2222, 333, 444, 5555, 8888, JJJJ, QQQ, KKK = 32 cuts = 32/46 = 69.6% up to 3/4/7pts with AAAA, 2222, 5555, JJJJ = 16 cuts.

3-4-6-9: Improves with 2222, 333, 444, 5555, 666, 8888, 999 = 24 cuts = 24/46 = 52.2% up to 6/8/9pts with 2222, 333, 5555, 666, 999 = 17 cuts.

Position:

We're 1pt short of 3rd street positional hole and opponent needs 16pts to reach 4th street positional hole. So I'll play Defense.

Pegging:

Playing Defense I think all these hands will peg well but I prefer 3-4-6-9.

Summary:

6-9-Q-K has a starting value 1½pts more than 3-4-6-9 but it has the least number of cuts for improvement and only 14 cuts for 5-8pts. 3-4-6-9 has the second most cuts for improvement and 17 cuts for 6-9pts compared to 16 cuts for 3-7pts. So I think 3-4-6-9 will catch up the 1½pts and I'll throw the Q-K.

At 69*-80 playing a Defense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

________________Pone's
Defense___Hand__Pegs___Crib_Total___W3 %___W4 %
6-9-Q-K____3.39+(-2.02)+4.93=6.30____2.5____16.3
3-4-6-9____4.35+(-2.15)+3.37=5.57____2.6____15.5
3-4-Q-K____2.52+(-2.33)+5.19=5.38____2.1____14.6

Defense______L3 %___L4 %
6-9-Q-K_______24.4___71.6
3-4-6-9_______26.6___73.3
3-4-Q-K_______23.9___73.1

6-9-Q-K is best for expected averages by 0.73pt. and is slightly best for Win %s and appreciably lowest for Loss %s. So I'll select 3-4 to discard.

After the 4 cut I'll play Offense to the lead.

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