Tuesday 3:12 AM

Okay, Kmart Shoppers, two 'daze' in a row of my puzzles was 'too much' so let's give Jazzselke a shot at the glory. I'll give this one a thorough review.

We are the Dealer for a change, and trailing by Five Points, but we are only Three Holes 'shy' of embarking upon the critical ZONE 🚧 defined as the Third Street Par Hole 70, and so according to Colvert's "Twenty-Six Theory" of Cribbage, we might be able to remain 'on track' and keep pace in order to 'close out' this game in the next two full CYCLES.

But in order to stay 'on track,' we're going to need a combined 'Pegging plus Hand plus Crib' that totals about Three Points ABOVE our average tally, which is normally Sixteen Points. Let's look 👀 at our cards.

Our first realization is that this bunch is very unlikely to allow us to 'punch above our weight' and pull down those Nineteen Points we need to possibly 'level the playing field' by completion of this deal, but we can still give it our best. Since Pone is already 'In the Zone,' it would be difficult to defend as what's done has already been done!

Two ideas emerge: Either we can Keep (2 4 9 Q) and Toss (5 K), with the idea of splitting up the points in our Hand and Crib, or we could Keep (4 5 Q K) and Toss (2 9) and start with those Four Points in our Hand, and I like this idea a bit more.

In a recent puzzle, exactly one week ago on Sep 12, 2023, I also mentioned sparring with Max Kassler's Cribbage Solitaire, and I was incorrect about it not running on Windows 10 (I was thinking of Tim Schempp's Royal Cribbage, which sadly does not work on the Windows 10 and later platforms). In fact, I have maintained my Kassler "High Scores" list since the Summer of 2007 with this tool, and I have recommended it over the years as a fantastic way to practice Dealer Discards, since this is precisely WHAT IT DOES!

This utility maintains a list of your Top 100 scores, and my best score thus far is 109 and it was played on Jan 3, 2008, which was about seven months after I loaded it. The score totals trail off from there, down to number 100 on the list, when I got a score of 87 on May 27, 2017. After a few hours of effort just four days ago, I was able to post a few games that were added to my Top 100, such as a score of 97, which is now in 22nd place out of 100! The tool allows you to use a discard database from either Hessel, Colvert, Rasmussen, or a combination (average) of all three!

In Cribbage Solitaire, you run through a deck and attempt to optimize Hand plus Crib (pegging is not included, but it's still a great tool). Halscrib helped me to appreciate that sometimes, in a bust arrangement, sending the Small Cards to the Crib is best. But Kassler's Cribbage Solitaire is where it solidified the idea more permanently into my brain. I like to do "speed drills" with this tool from time to time (it's now been a few years!), and I find that when playing a "real" game of Cribbage, these ideas 'jump' out more readily.

And if you recall the recent puzzle I am referring to, it involved a "Garbage Hand" in which I posited my "Good Garbage 🗑 Effect" theory, about placing the Small Cards in the Crib. This is a long and roundabout way of saying that I think we might have a third alternative today, and that is Keep (5 9 Q K) and Toss (2 4)!

Those two Small Cards in the Crib can "catch" a lot of help, and while we know better than to "chase 🏃🏼‍♂️ after" the randomness of the Cut Card, in these instances, when we combine this with also "chasing after" the two cards sent to us by Pone, that adds up to a LOT of chances for help!

More often than not, when we are the Dealer in Cribbage, we should strive to retain the Best 🖐🏼 Hand we can muster, and then 'slough off' the remaining two cards and stash these in our Crib, and that's the reasoning behind Toss (2 9).

By holding both sets of "touching" cards, we hope to get a Cut Card the completes any of the three possible Runs of either: 3-4-5, 4-5-6, or J-Q-K. Also, we would do well with a 5 Card Cut or a Queen or King Cut, so this comprises Twenty-One Cuts (3333, 555, 6666, JJJJ, QQQ, KKK) or about 21/46 equals nearly 46% of the remaining deck that would yield Seven Points or more.

We should also note that many of those same Cut Cards could possibly energize our Crib as well, so we might derive a bit of "synergy" if things go our way. Fourteen Cuts (222, 7777, 8888, 999) however will NOT help our Hand, and yet HALF of those might still help our Crib.

Toss (5 K) has a Crib Value that exceeds Toss (2 9) by about Three Points, which is significant, but in order to stow the 5 Card in our Crib today, it has the immediate 'cost' of decrementing our Hand by Two Points, and the resultant Hand and Crib lacks much of the "flavor" we might enjoy from the aforementioned Cut Cards when we keep the "Touchies."

In addition to the first two ideas, we shall now throw Toss (2 4) into the mix for consideration, and it may seem like a weak alternative, since we are trading the "Touching" Cards 4-5 away, and no more Magic Eleven, and we now appear to have just a "gapped" 2-4 in the Crib as our one savior. But such a Hand and Crib could do very well after numerous Cut Cards. While we're not yet choosing to Toss (2 4), I think it's proper to add this idea as our Third Candidate!

This is a difficult Relative Position, and I sense that the discard choice might be reduced to a matter of "style" as opposed to "right" or "wrong," however, in my humble opinion, I believe that there are some clear, concrete lessons we can walk away with here:

I think it's a mistake if we only consider two Discard Candidates today, and so if we were asked to fill out the podium, I would place Toss (2 9) first, and Toss (5 X) second, and Toss (2 4) would be third.

Two things I would NOT DO today are: I would NOT get into a long (or even short) debate over the merits of Toss (5 K) vs Toss (5 Q)! These are essentially the same, and if you are playing with a well-known Opponent and you can justify one over the other, by all means, do so.

But (and this may be heresy 😈 to some) I would NOT spend too much (any...) effort on trying to 'suss' out the minute differences between Toss (5 K) and Toss (5 Q), as it's likely to be negligible, and perhaps just hundredths of a point! Even the differences between Toss (2 9), Toss (5 X), and Toss (2 4), are very likely to be minuscule today; any of these can probably be made to work by a competent player. And, the second thing I would NOT DO today is consider Toss (Q K), since this is Crib Poison.

As a final consideration, we can acknowledge that Keep (2 4 9 Q) would probably be the better Pegging Hand, as it contains a Magic Eleven in the form of 2-9, but all "Magic" is not alike in Cribbage! As a general rule, those two-card "Elevens from 🌟 Heaven" (as RAS often calls them) are best when close in rank, and thus we should tend to prefer them in order from: 5-6, 4-7, 3-8, 2-9, and finally, the least desirable being A-X.

Note that if Pone leads a Ten "T" Card or a Jack, that if we wish to follow through and attempt to pick up the "Thirty-One" score, we are probably more inclined to respond initially with our Deuce instead of our 9 Card, since a 9 Card Reply allows Pone to score a Run! Diving in with the smaller of the two-card duo makes the whole 'Magic Eleven' tactic a lot less effective, although it can still often work. But since this entails weakening our tactic after Eight (TTTT, JJJJ) of the Fourteen extant "X" Card Leads, we might actually consider the (4 5 Q K) Hand to be the Pegging EQUAL of (2 4 9 Q)!

We shouldn't ignore the "Elephant 🐘 in the Room," either, which is that Keep (2 4 5 9) and Toss (Q K) is almost certainly our best Pegging Hand, but I do NOT think Toss (Q K) should be a Discard Candidate today! Toss (2 9) is a weak discard to be sure, and yet at least it allows us to begin with Four Points in our Hand! But Toss (Q K) is a HALF Point weaker, and forces us to begin with just Two Points. This is bad. If all we do today is learn NOT to Toss (Q K), then this will have been a worthwhile puzzle exercise!

Well, so then, what SHOULD WE DO?! I think the fact that our 5 Card in our Hand may allow us to peg just as well as the weakened 2-9 Magic Eleven is the key to this puzzle, and so rather than Toss (5 K), I am leaning toward Toss (2 9), with all of those "MAGICAL" Cut Cards that we examined earlier. All of that work should stand for something, after all!

Let's Toss (2 9) today, and see what kind of delicious ☕ 🍰 🍂 "goodness" Pone will place in our Crib.

After the Jack Cut, we now have a splendid Nine Points in our Hand, with prospects for a 'mysterious' Crib. And, since this is "Hand of the Day" and not a Real Game, we'll sadly never see what that Crib actually is. Those of you who "play it through" on Cribbage Pro or eCribbage can by all means tell us your (horror?) stories! Trivia Question: Since we decided to Toss (2 9), what if we could change that Jack Cut to anything we wish: what is the Maximum Crib we could possibly get today after Toss (2 9)? Could Toss (2 4) exceed this?

Even with that Jack Cut, if Pone gave us something such as Toss (A 3), note that we would have a Crib of Seven Points. But when we dream, we should like to 'Dream Large'; so, let's imagine that Pone gave us a 🍐 PAIR of Tens, to give us a Crib worth Eight Points, because hey: We Deserve It!

I know this was a long haul today (nearly 2000 words, but who's counting?), yet I would be totally remiss if I didn't add a Bonus Trivia Question at the end, to make it even longer: After that Jack Cut, what is another way besides Toss (T T) that Pone could give us Eight Points in our Crib today? (Maybe wait until mid-afternoon to post your answers, and give those 'late-sleepers' a whack at it, too!)

Tuesday 3:22 AM

Yesterday's pegging for 2-3-3-7 playing Defense should have been:

Defense________Dealer Pegging Points
3_____________________(-2.41)
2_____________________(-2.44)
7_____________________(-2.62)

Apologies for the error.

Tuesday 3:44 AM

If JQT is referenced KMart, I’ll go with the Bruce Campbell line: “Shop smart. Shop S-Mart.” I hope I did, though if you know the movie, he rarely was making good decisions.

Tuesday 4:03 AM

Nice puzzle Dan. We all get this arrangement dealt to us every game. We may as well learn to play it correctly. I kept the 45 together just in case a 3 or 6 was cut. The Jack is a nice bonus. I would like to end up close to hole 85, so I will peg if I can.

Tuesday 4:14 AM

Like to get to 79-80 at least. Peg accordingly. dec

Tuesday 5:09 AM

Decided to toss the 5-K which is a top tier offensive toss to own crib. Possibly a little better pegging potential with the 2-4-9. Very close IMO on about 3 or 4 options. 2-4 toss was my second choice and also see the value of keeping the two dual touching cards, but didn’t like the 2-9 discard, especially with one of the 4s out of circulation.

Tuesday 5:24 AM

I'm a huge fan of tossing a 5 in my crib, and, in theory, the 2-4-9 should peg a bit better than the 5-9-Q-K, which was my 2nd choice. Not many people agree with my logic. mfetchCT tossed the 5-K, which I did ponder, and in hindsight after checking the Schell tables maybe I should have tossed 5-K. In either case, J gives us all points, but to those who kept the 5-Q-K together, "nice cut"

Tuesday 5:44 AM

I prefer throwing the the gapper 24 to the crib, rather than keeping the adjoining 45 with the QK. But it's hard to argue against either approach, which is why I posted the puzzle. And a combined 4 points is also achieved by holding 249X, in which case a 3-card 15 is sometimes a savvy strategy as well. So I am intrigued by seeing all the comments advocating the 3 different choices.

Tuesday 5:54 AM

Interesting puzzle Dan-I like the potential of the 2-4 in the crib while we keep our four points in our hand

Tuesday 6:00 AM

I'd keep 5-Q-K together for four points. 2-4 seems the better pairing to discard from the remaining 2,4 and 9.

Tuesday 6:07 AM

I am back in Luxembourg, after visiting Greece for a week. I didn't take my laptop there, so I missed being able to say CONGRATS to SCOTTCRIB on his 28 hand on Sept 16 on eCribbage in ACC play!

Tuesday 6:45 AM

Aiming for the far side of the bell curve at this position. I think this keep's better performance on that metric will outweigh the (relatively) small difference in overall expected averages.

Checking Liam, there is a four-way tie in hand+crib between my keep, toss 5Q, 59QK (24), and 45QK (29), so I'd say we're all smart today. If you look at the histograms, my reasoning is false - toss 24 is actually more likely to score big because of the potential for double runs etc in the crib.

On the side of offensive pegging - yes, a five in hand is better than an 11, but this hits more leads, so I think it will be quite close on that front.

Between heels, and reasonable hopes for a strong crib, I would continue to pursue an offense strategy in the pegging.

Tuesday 7:17 AM

I fully realize that when it comes to discarding, cardfrequency is a tool, but it is down the evaluation list for decision making. That said, be reminded the first 14 top Pone balking discards ( lowest averages) all involve X.
https://www.cribbage.org/NewSite/tips/rasmussen7.asp..

Further..per Ras evidence …of the top ten most frequent Pone crib discards ..eight contain either a Q or K. These six dealt cards are not barn burners…so i lean toward ..starting with two points in hand and two in crib..with optimistic potential to build on my 5-K

Tuesday 8:17 AM

If I thought it over again, I might toss (2 9). I need all the help I can get in my hand, but I ended up picking (2 4), and not sure it can sufficiently pass (2 9) in its superiority. Well, the J cut certainly alleviates any concern I had over the crib throw today.

Tuesday 8:31 AM

I think CribEDGE also liked the opportunity to put a 5 (and a 15 at that) into its crib. The score of the game wasn't quite far along enough to trip any special logic. Here's CribEDGE's result for today:

Keep: Two of Clubs, Four of Diamonds, Nine of Clubs, King of Hearts
Toss: Five of Spades, Queen of Diamonds
Worth: 2 / Bonus: 11

Tuesday 9:56 AM

Choosing offense out of the gate, discards of 5-K and 2-9 are nearly identical in combined value. Considered only 5-K or 2-9 as discards. The 5-K has far greater crib potential 6.726 (1,762) compared to 2-9 3.905 (538) and has a slight edge on pegging. Picked up two for turning the Jack (likely to result in 8-9 points in crib) which would have been scored in the hand with 2-9 discard. Dealing from hole 67 (3rd street CPZ 69-73), will take any pegs offered. With two points from Jack, a guaranteed peg, two points in hand, and 5-K average of 6.726 in crib, am likely to reach hole 79. Need to have my next deal from 4th street CPZ (95-99). Peg and likely to be playing offense for the rest of this game. It is what it is though despair cannot be part of the equation.

Tuesday 10:33 AM

Interesting puzzle Jazz! 11 of 13 cards help hand our crib, and our position says offense-but not ludicrous.
I like my points where I can see them, so I’ll toss the 2-9, and hope for a 6. Or a Jack!

Tuesday 4:46 PM

I'll consider 4-5-Q-K (2-9), 5-9-Q-K (2-4), 2-4-9-K (5-Q) and 2-4-5-9 (Q-K):

4-5-Q-K: 4pts + 3¾pts (Schell: 3.71) = 7¾pts

5-9-Q-K: 4pts + 4½pts (Schell: 4.52) = 8½pts

2-4-9-K: 2pts + 6½pts (Schell: 6.63) = 8½pts

2-4-5-9: 2pts + 3½pts (Schell: 3.46) = 5½pts

Potential:

4-5-Q-K: Improves with AAAA, 3333, 444, 555, 6666 + 14xXs = 32 cuts = 32/46 = 69.6% up to 7/8/9/10pts with AAAA, 3333, 555, 6666, JJJJ, QQQ, KKK = 25 cuts.

5-9-Q-K: Improves with AAAA, 555, 6666, 999 + 14xXs = 28 cuts = 28/46 = 60.9% up to 8/9/10pts with 555, JJJJ, QQQ, KKK = 13 cuts.

2-4-9-K: Improves with AAAA, 222, 3333, 444, 555, 6666, 999, KKK = 27 cuts = 27/46 = 58.7% up to 6/7pts with 222, 3333, 444, 999 = 13 cuts.

2-4-5-9: Improves with AAAA, 222, 3333, 444, 555, 6666, 8888, 999 + 14xXs = 42 cuts = 42/46 = 91.3% up to 6/8/9pts with 222, 3333, 444, 6666, 999 = 17 cuts.

Position:

We're 3pts short of 3rd street positional hole while Pone is 13pts short of where they'd like to be, so I'll play Offense but with caution.

Pegging:

I think 2-4-5-9 will peg best with two low cards, a 5 and a high card plus a 3-card magic eleven. Playing Optimally I think 2-4-9-K and 4-5-Q-K will also peg quite well.

Summary:

5-9-Q-K and 2-4-9-K have the best starting value with 8½pts each. However, 4-5-Q-K is only ¾pts behind and has the second most cuts for improvement and 25 cuts for 7-10pts. So, I'll throw the 2-9.

Tuesday 4:47 PM

At 67*-73 playing an Offense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

_______________Our
Offense___Hand_Pegs_Crib_Total____W3 %___W4 %
4-5-Q-K____6.70+2.85+3.69=13.24____2.3____21.3
2-4-9-Q____3.83+2.87+6.49=13.19____2.4____22.1
2-4-9-K____3.83+2.87+6.48=13.18____2.4____22.0
5-9-Q-K____6.00+2.67+4.38=13.05____2.7____22.2
2-5-Q-K____6.17+2.57+3.65=12.39____1.9____19.6

Offense_______L3 %___L4 %
4-5-Q-K________7.4____49.4
2-4-9-Q________6.4____46.9
2-4-9-K________6.4____46.9
5-9-Q-K________7.0____47.9
2-5-Q-K________6.9____49.5

4-5-Q-K is best for expected averages but only by 0.05pt over 2-4-9-Q. 5-9-Q-K is very slightly best for Win %s but is high for Loss %s. On balance I think the best compromise is 2-4-9-Q (although 2-4-9-K is almost the same) so I'll select 5-K to discard.

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