Tuesday 3:21 AM

Every cut increases the value of this hand, so I'm guaranteed to be fairly close. I'll lead the 8, keeping the run intact.

   

Tuesday 3:38 AM

I got 8 and need some creative pegging without being pegged out myself. I think the 2 lead might be best. I will have an answer to most responses.

   

Tuesday 4:36 AM

Went with the flush for the extra heart cuts.

   

Tuesday 4:37 AM

I liked the flush today. I think more cuts get us out and I like the pegging flexibility here. If we get a cut that gives us enough, we have a nice disparity of cards and a hand that will be difficult to read. After the cut, since we need 2 pegs, I would lead the 8 and see if we can trap a 5 with our 3-4.

   

Tuesday 5:07 AM

Flush away . Pegging defense and offense. dec

   

Tuesday 5:15 AM

Improves on any cut, and if we still need pegs,lead the off-card 8. The flush does not improve with a non-heart 6 or 9.

   

Tuesday 5:35 AM

Without doing all the work I usually go with the flush. It is often correct as it is hard to read, and there is a 5 card trap. Since we are 2 holes short, lead the 8, preserving the 3-4-five card trap.

   

Tuesday 6:33 AM

My first thought on seeing this - “Oh crap, a JQT puzzle… have I ever even seen him submit a puzzle? This is going to be tough.”

The positional dynamics are pellucid – we need to score 10 in hand and pegging. With dealer at 116*, even someone who started playing last week would probably be laying down their cards with maximal defensitude, so getting points in the play will be tough.

At this score, with these cards, I think pegging two points is a lift. Pegging one would be a little easier, but no sure thing.

This keep has one fewer cuts than the flush for winning outright, but 8 more cuts to hit at least 9… if I counted right. And I think they would be pretty similar in likelihood to get a “go” or “last”. So I’m going to go this way, and even under the pressure of a real game, I would have picked it – it starts with six, it has a nickle, and two Jacks for nob, so it would appeal to the gut. My brain tends to fall asleep at scores like this.

But a decent case could be made for any of 2348 (JJ), which improves on every cut and could trap low cards or even a five; 234Js, which similarly could peg well, and is more likely to score at least eight than 2348 (JJ); or the [348J] flush, which has a five trap, is hard to read, and is ever-so-slightly more likely to win outright.

The problem with 2348 and 234J is that this sort of offensive pegging risks giving up points to dealer. Enough to make up 5? Usually not, but it’s still a risk. The other problem is that a strong opponent will be be wary and wily, both in the discard and the play, and these hands won’t be so likely to succeed here as they would earlier on the board. He will dump his low cards on your mid or J lead, also likely his five if you lead the eight, seeing right through your plot, and it’s just going to be tough to peg much.

Defensive pegging is also a consideration, but I don’t think the differences on that front between these hands will be enough to outweigh the offensive side of things.

The cut leaves me with 9, so I need to get a “go” or “last”. Lead either of the “one-eyed Jacks”, and hope to get a “go” with my 2-3.

Can't discount the possibility that I miscounted something... Jack/flush hands are kinda tricky to work out on pen and paper.

   

Tuesday 7:25 AM

Nice endgame puzzle today by JQT, and haven't seen one in awhile. The power of the flush vs. power of J's in hand seen in action today. Keeping (2 3 J J), there 8 cuts which give no help (6's, 7's, 8',s and 9's which are not a spade or diamond), and 7 cuts which give only 1-pt help (6's through 9's of either a spade or diamond). There are 15 outright winning cuts for 10 pts+ (AhAs,222,333,4s,5555,JJ), and 10 more for 9 pts+ (AA,44,ThTs,QhQs,KhKs). This leaves 6 cuts for 2-pt improvement, (TT, QQ, KK) which are not a heart or spade. As for the flush (3 4 8 J), there are 15 cuts which ALL offer no help (but I more or less put this in the same category as the 15 cuts which offer none or only 1-pt help keeping (2 3 J J), 17 outright winning cuts for 10+ (Ah,222,333,444,5555,888) + 1 for 9pts (7h), and 13 cuts for 8 pts (AAA,6h,777,9h,Th,JJ,Qh,Kh). This clearly seems to give the edge to (2 3 J J) as the best choice, with a total of 25 cuts needing only to peg at MOST 1 point. The power of the J's win out today!

   

Tuesday 9:04 AM

This was hard, although "it pays to flush". The 2-3-J-J has a better chance at 9 points. Both flush and 2-3-J-J are close for 8 points or 10 points.

When in doubt, it pays to flush!

   

Tuesday 11:29 AM

Guaranteed hit and an 11 maybe for the two needed.

   

Tuesday 3:21 PM

I think we're just looking for the hand most likely to score 10pts or more:

2-3-4-8: 10pts+ 222, 333, 444 = 9 cuts
9pts 888 = 3 cuts
8pts with AAAA, 5555 = 8 cuts

2-3-J-J: 10pts+ ASAH, 222, 333, 4S, 5555, JJ = 15 cuts
9pts AA, 44, 10S10H, QSQH, KSKH = 10 cuts
8pts 1010, QQ, KK = 6 cuts

3-4-8-JH: 10pts+ AH, 222, 333, 444, 5555, 7H, 888 = 18 cuts
8pts AAA, 6H, 777, 9H, 10H, JJ, QH, KH = 13 cuts.

I think it will be close between 2-3-J-J and 3-4-8-JH. 2-3-J-J has 15 cuts for 10pts+ and 10 cuts for 9pts and 6 cuts for 8pts while 3-4-8-JH has 18 cuts for 10pts+ and 13 cuts for 8pts. I think I'll go with the flush which has the most cuts for 10pts+ and should peg well and be hard to read. So I'll throw 2-JS.

   

Tuesday 3:24 PM

At 111-116* playing an Offense strategy for the pegging the Win/Loss %s are:

Offense___________Win %s______Loss %s
2-3-4-8____________79.3________20.7
2-3-4-JS___________73.2________26.8
3-4-8-JH___________65.9________34.1
2-3-J-J____________61.3________38.7

2-3-4-8 is considerably best for Win %s and lowest for Loss %s so I'll select J-J to discard.
After the A cut I'll lead the 2 and play Offense:

Lead__________Our Pegging Points
2____________________1.58
3____________________1.34
8____________________1.31
4____________________1.12

   

Tuesday 3:54 PM

Today, we are concerned not so much with trying to obtain the highest Expected Average, as we are with getting a specific number of points, while also having to defend as well, a monumental struggle. This is a Colossal Cribbage Conundrum, and so it entails a little saga about how we might solve a giant Endgame Battle with a FLUSH: but ironically, our FLUSH today involves FLUSHING AWAY a few Jacks!

I used to frequently show what I call the "Hand Mapping" for many puzzles here at "Hand of the Day," and I believe it's a wonderful exercise for developing a familiarity with the cards that will help us to discern the necessary cards that can get a job done.

We naturally do not have time for this at the board, but it's the kind of "homework" that allows us to develop a better "feel" for which groups of cards can yield a given number of points. I've also said very frequently that in many Cribbage Endgame Battles, we are not necessarily looking for the MOST points; as in today's puzzle, we are looking to score Ten Points.

The Discard Value is what we call a "Don't Care" today, because the Dealer is so close to going out, that if the Crib ever comes into play and gets tallied, we've already LOST in such a game. But rather than fret or despair over such a reality, we can use this bit of information to direct our thinking and reason away from the Crib and ignore any dangers there; since we "Don't Care" about the Crib Value today, we can focus ALL of our energy on choosing the most powerful Hand to bring us VICTORY!

Crib Values tend to vary slightly, since different players have developed slightly different tables, or have collected real-world data. But if we make a careful observation of the Hands in every Cribbage Puzzle, we should notice that the Expected Value of every resultant Hand is identical, right down to the last decimal place. This makes sense, because it is actually a known, calculated result, as we look at ALL of the possible Cut Cards, and how much each and every Hand will be with any of these, then add these all up, and finally we divide that number by the number of remaining cards in the deck, or forty-six.

Therefore, what an Expected Average for any specific Hand tells us is that on an infinitely-long board, when we choose that particular Hand of four cards from the six we were dealt, if we examine our movement down that imaginary, infinite board after let's say a thousand random Cut Cards, that when we now divide that resultant number by the number of Cut Cards looked at (or one thousand in this case), we will actually get the number of that is defined as the Expected Average!

It's akin to saying that if we flip a coin one thousand times, we shall have reached a total result of "Heads" very close to 500, and "Tails" should also have occurred about 500 times. For those who understand simple Calculus and Limits, we can say that after an INFINITE number of Cut Cards, when we integrate the total by that same infinite number of trials, we shall obtain an exact, precise value or number, and this is defined as the Expected Average.

The probabilistic nature of any endeavor that involves randomness is important to understand, and this includes any game that involves cards or a dice. A few comments recently have lamented the fact that we don't get to know the value of the Cut Card in Cribbage ahead of time, but one could argue that we do know what it will be: The Cut Card in Cribbage will always be one of those forty-six cards that was NOT dealt to us! That's a fairly well-defined value if you approach it from the perspective of Quantum Mechanics! And regardless, the value of the Cut Card is always as mysterious to our Opponent as it is to us. As Richard Feynman might advise us: "I'm very comfortable not knowing some things."

We need Ten Points as Pone, so let's look at the four obvious choices we have today, all of which shall tend to exceed Eight Points as an Expected Average: These are: Toss (4 8), Toss (2s Js), Toss (J J), and Toss (8h Jh).

(111-116*) (2s 3h 4h 8h Js Jh) Cut = Ad, by JQT, 30 May 2023.

Keep (2s 3h Js Jh) and Toss (4h 8h)
Expected Average is 405 DIV 46 = 8.804

02x13=026 - 2h, 3s (Maximum Hand, 2 Cuts = 13 Points)
06x12=072 - 22, 33, JJ (8 Cuts >= 12 Points)
02x11=022 - 5s, 5h (10 Cuts >= 11 Points)
05x10=050 - As, Ah, 4s, 55 (15 Cuts >= 10 Points)
10x09=090 - AA, 44, Ts, Th, Qs, Qh, Ks, Kh (25 Cuts >= 9 Points)
06x08=048 - TT, QQ, KK (31 Cuts >= 8 Points)
07x07=049 - 6s, 6h, 7s, 7h, 8s, 9s, 9h (38 Cuts >= 7 Points)
08x06=048 - 66, 77, 88, 99 (Minimum Hand, 8 Cuts, NO HELP = 6 Points)
46 ..... 405
--------------------------------------------------------

Keep (3h 4h 8h Jh) and Toss (2s Js)
Expected Average is 385 DIV 46 = 8.370

02x13=026 - 2h, 5h (Maximum Hand, 2 Cuts = 13 Points)
05x11=055 - 22, 555 (7 Cuts >= 11 Points)
11x10=110 - Ah, 333, 444, 7h, 888 (18 Cuts >= 10 Points)
13x08=104 - AAA, 6h, 777, 9h, Th, JJ, Qh, Kh (31 Cuts >= 8 Points)
15x06=090 - 666, 999, TTT, QQQ, KKK (Minimum Hand, 15 Cuts, NO HELP = 6 Points)
46 ..... 385
--------------------------------------------------------

Keep (2s 3h 4h 8h) and Toss (Js Jh)
Expected Average is 381 DIV 46 = 8.283

09x12=108 - 222, 333, 444 (Maximum Hand, 9 Cuts = 12 Points)
03x09=027 - 888 (12 Cuts >= 9 Points)
08x08=064 - AAAA, 5555 (20 Cuts >= 8 Points)
26x07=182 - 6666, 7777, 9999, TTTT, JJ, QQQQ, KKKK (Minimum Hand, 26 Cuts = 7 Points)
46 ..... 381
--------------------------------------------------------

Keep (2s 3h 4h Js) and Toss (8h Jh)
Expected Average is 376 DIV 46 = 8.174

01x13=013 - 3s (Maximum Hand, 1 Cut = 13 Points)
05x12=060 - 222, 33 (6 Cuts >= 12 Points)
01x11=011 - 4s (7 Cuts >= 11 Points)
02x10=020 - 44 (9 Cuts >= 10 Points)
04x09=036 - As, 5s, JJ (13 Cuts >= 9 Points)
12x08=096 - AAA, 555, 6s, 8s, 9s, Ts, Qs, Ks (25 Cuts >= 8 Points)
17x07=119 - 666, 88, 999, TTT, QQQ, KKK (42 Cuts >= 7 Points)
01x06=006 - 7s (43 Cuts >= 6 Points)
03x05=015 - 777 (Minimum Hand, 3 Cuts, NO HELP = 5 Points)
46 ..... 376
--------------------------------------------------------

The Hand Mapping clearly shows us that if we examine the number of Cut Cards that will either deliver us directly to the Finish Line, or that could allow us to WIN if we can peg One or Two Holes, we have the following data:

Toss (4 8) will allow Fifteen Cuts (As, Ah, 222, 333, 4s, 5555, JJ) or 32.6% to yield Ten Points or more, and an additional Sixteen Cuts (AA, 44, TTTT, QQQQ, KKKK) or 34.8% that will give us Eight or Nine Points;

Toss (2s Js) will allow Eighteen Cuts (Ah, 222, 333, 444, 5555, 7h, 888) or 39.1% to yield Ten Points or more, and an additional Thirteen Cuts (AAA, 6h, 777, 9h, Th, JJ, Qh, Kh) or 28.8% that will give us Eight Points;

Toss (J J) will allow Nine Cuts (222, 333, 444) or 19.6% to yield Ten Points or more, and an additional Eleven Cuts (AAAA, 5555, 888) or 23.9% that will give us Eight or Nine Points;

Toss (8h Jh) will allow Nine Cuts (222, 333, 444) or 19.6% to yield Ten Points or more, and an additional Sixteen Cuts (AAAA, 5555, 6s, 8s, 9s, Ts, JJ, Qs, Ks) or 34.8% that will give us Eight or Nine Points.

If that's all there is to this endgame, then the FLUSH wins, hands down! But did we ignore something? With the FLUSH, or after Keep (3h 4h 8h Jh) and Toss (2s Js), we begin with only Six Points, and after Fifteen Cuts (666, 999, TTT, QQQ, KKK) or 32.6% of the time, we'll need to peg a staggering Four Holes! Quite a few Cut Cards offer us NO HELP.

And after Keep (2s 3h 4h Js) and Toss (8h Jh), we begin with only Five Points, and after Four Cuts (7777) or 8.7% of the time, we'll need to peg a staggering Four or Five Holes! Again, we have some Cut Cards that could leave us in the lurch.

What about after Keep (2s 3h Js Jh) and Toss (4h 8h), the Hand with the highest Expected Average? Here we will begin with Six Points, and yet after Eight Cuts (66, 77, 88, 99) or 17.4% of the time, we'll need to peg a gargantuous amount of Four Holes! Once again, we are prone to the NO HELP Gremlin, since several Cut Cards leave us 'stuck in the mud.' And, there's another potential nasty ointment on this fly: Brace Yourselves! 👹

One other spanner that we might drop into the finely-oiled logic of our thinking machinery today is that for any and all of those roughly 4% occasions after which a Jack is the Cut Card, this will enable the Dealer to enjoy a "40% Off Sale" on the amount needed to peg out and WIN after scoring "Two for High Heels." This has the interesting effect of "putting a thumb on the scale" and adding favor or bias to any discard that involves us 'dumping' one or more Jacks here!

It's not quite so pronounced a disastrous effect as when the Dealer is sitting at Hole 118 or higher, but it will make any calculation that we relied upon earlier which involved a Jack helping us WIN a lot less effectual or certain. Like the Moon and the Tides, the Jack is a card in Cribbage that adds an occasional bit of spice and nuance to the game, but once in a (I'm trying to avoid saying "Blue Moon"), it can gum up the works. The Jack Giveth, but the Knave Taketh Away! Just be aware that that ostensibly "winning" Jack Cut when you Keep (2 3 J J) may send a dagger through (Rhymes with Ribs) and out your backside.

Let's look at Keep (2s 3h 4h 8h) and Toss (Js Jh) once more, shall we? While the mapping data seems to have a bit of a weakness (read: gaping hole) in the "What can you do for me?" department, we can also see that, while we begin with just Five Points, this will ALWAYS get boosted to at least Seven Points by ANY AND ALL Cut Cards! In the worst-case scenario, this means that just under 57% of the time, we shall need to peg Three Holes.

No other Hand possesses that quality today in which every Cut Card adds help! Yes, pegging Three Holes as Pone is a rather Tall Order, but I think you'll agree that it's better than needing to peg Five Holes! Could this 'informational nugget' actually make Toss (J J) the best option today? Does the fact that we shall never need to peg more than Three Holes after we Toss (J J) give us "The Answer" to this puzzle? I believe that it does!

In addition to having a Hand that ALWAYS gets help from EVERY Cut Card, I think that all we need now is just some small indicator or deciding factor to add a bit of certainty and make Toss (J J) the most favorable option, and so as in many things related to Cribbage, where shall we look? The PROSPECTIVE PEGGING, that's where! Keep (2 3 4 8) is just energetic enough in that it might be able to reliably peg Two Holes and "clinch" this game for us! Let's Toss (J J) today.

After the Ace of Diamonds Cut, we now have Eight Points in our Hand, and we now still have two tasks that remain and that face us: We need to peg Two Holes, which is Average Pegging for Pone, but let's be realistic: the Dealer will be HIGHLY MOTIVATED to stop us. Our remaining task is that, even if we can and do peg those Two Holes, all the Dealer alternatively needs to do to defeat us is peg Five Holes before we get to tally First Hand Show, and all will be for naught. Unfortunately, we still do need to peg, and we must entail some risk.

The reason I like this puzzle is that both the Dealer and Pone (that's us) very likely have opposing forces at work. The Dealer wants to defend and 'coast out' by counting Hand and Crib, but must realize the danger that our First Hand Show poses; the Dealer could also play opportunistically, and peg out and WIN in a sudden surge. In a close Endgame Battle, if a Dealer is within Half-a-Dozen Holes of the Finish Line, that Dealer should ALWAYS look for an opportunity to score PAIRS Royal and end the game, or, if forced to consider grabbing or allowing a RUN, maybe look for ways to entice extending it even further, and thus WIN the game!

Let's lead our Deuce, which will allow us to SCORE those two remaining and potentially-winning points (unless the Dealer pegs out) after a whopping Thirty-Four Dealer Responses (AAA, 333, 444, 5555, 888, 9999, TTTT, JJ, QQQQ, KKKK), or about 34/45 equals 75.5% of the remaining cards in the deck. We're going to try to peg Two Holes any which way we can!

This is really as much of a Pegging Puzzle as it is a Discard Puzzle. And this Hand we latched onto today is well worthy of some careful study in BOTH respects. Notice how we ALWAYS start with Seven Points after ANY Cut Card, and also be aware of just how many Dealer Responses to our Deuce Lead shall allow us to "clinch" this game! In spite of NOT being a FLUSH, our chosen Hand is very well-suited and up to the task of winning such an endgame as this.

Those who are interested in delving further into the intricacies of such Cribbage Endgames might also wish to look at a puzzle from three years ago, as I explored various ideas even more passionately back in the pre-pandemic period on January Last, 2020 when we struggled with a somewhat similar scottcrib scenario, when we were at (115-117*), whereas today we begin at (111-116*). The puzzle dated December 22, 2019 also has some good information, and on that day, we found ourselves at a relatable score of (111-110*).

Ref: https://www.dailycribbagehand.org/show.php?date=2019/12/22 and https://www.dailycribbagehand.org/show.php?date=2020/01/31

   

Tuesday 4:32 PM

I need 10 points. I thought this was my best option until you pros tell me otherwise.