Thursday 3:09 AM

RAS asks us what to do here as First Dealer: in a previous puzzle, back on Feb 2, 2023, he had placed us at (106*-113) with these same cards (except the King was a Heart Suit, and a Trey was the Cut Card, two things which should have NO effect whatsoever upon our Discard Decision). But does this new, game-starting Relative Position: change ANYTHING; or does it change EVERYTHING; or, do some things NEVER CHANGE?!

Before we sharpen our pencils and get to work, let's fling out a 'factoid' for our Newer Players, and then a Thought Experiment. Cribbage uses a standard, fifty-two-card French Deck, and when picking and choosing any discard, we perform the mathematical equivalent of "6 choose 2" which equals Fifteen. (You might have studied the mathematics behind this under the auspices of "Combinations and Permutations" in high-school math, or maybe an early course on statistics.

That is, if all Card Ranks differ, there will be Fifteen Unique Discard Choices. And if one PAIR exists as we see in today's puzzle (and let's ignore FLUSHES just to keep our palate clear), now we shall have Eleven Unique Discard Choices.

But how many possible Discard Combinations EXIST? As it turns out, with Thirteen Ranks (Ace through King) of Four Suits totaling Fifty-Two Cards, there are Ninety-One Possible Discards. And since the VALUE of these differs whether we are Pone or Dealer, the entire "set" of Crib Values for all Pone and Dealer Discard Choices is One Hundred Eighty-Two Unique Values!

A few players will memorize these, but what most players do is "lump" them together in certain groups. RAS, our Puzzle Poster today, has actually grouped all of the Dealer Discards into s "Star Power" system, and you can study it at the bottom of the page: http://www.cribbageforum.com/YourCrib.htm

"But Wait!" you yell -- didn't you promise us a Thought Experiment? Ah, yes! We often discover Hands or Cribs that we can determine will ALWAYS receive help from EVERY or ANY discard. Those are nice, because we can always rely upon those additional points.

Well, I noticed that one of today's Dealer Discards, after seeing the Cut Card, would be helped by EVERY DISCARD . . . EXCEPT ONE! Here, I'll even give you the ANSWER, and just let you think about the question. After my Discard Choice today, only if Pone decides to Toss (A 2) will it NOT help my Crib! Can you "imagine" or picture what I have discarded? Okay, let's move on to the puzzle!

We can hold Four Points in our Hand and Keep (A 2 2 K) and Toss (4 6), or we can begin with Two Points in our Hand, with the "promise" of at least Two Points in our Crib, in a few different ways, the main idea being Keep (A 4 6 K) and Toss (2 2), or we might also try Keep (2 2 6 K) and Toss (A 4), for example, to meet the criteria in the second example.

On the Feb 2, 2023 puzzle, I not only scribbled about 1100 words just for my initial posting, I added several times as much in the discussions and numerous replies that followed, and I also performed dozens of play-outs, and showed several of these. Back in the day, in the late 'aughts' (or two thousand "noughties"), when I wore a younger man's clothes, I would routinely do hundreds of Endgame Play-outs on many puzzles. Today, let's make it simple (and keep it closer to 800 words):

Not only do I think that Keep (A 2 2 K) is *still* the correct way to go, I believe that this is actually an EASIER decision than what we were asked to do nearly two months ago, at (106*-113).

But perhaps not unlike the Endgame Puzzle, I base the decision on the POSITION as well as the supposed VALUE, because on an "open board" without regard to POSITION, Toss (2 2) might actually get us farther down that board! However, when it comes to the Pegging Requirements, I think we are better off holding the PAIR of Deuces, which should help inhibit Pone's Pegging.

For those who choose Toss (2 2), you might have more points in BOTH the Hand and the Crib! I don't think it's a bad choice, either; I'd simply prefer to peg with those Deuces. It's too bad the 4 Card was not a Club Suit! So, let's Toss (4 6) today.

After the 5 Card Cut, we now have Six Points in our Hand, and we hit Crib Paydirt, with a promise of at least Five Points in our Crib!

In fact, only Nine Cards (AAA, 22, 8888) coming from Pone will not help add to our Crib Bounty, and it's actually a difficult task to find those few Pone Discards that will NOT help us: Among the Ninety-One Possible Discards in the entirety of the game, Toss (A 2) might be the only Pone Discard that would not add points to our Crib!

Wordle 649 3/6 (My Streak Rises to 78 Days, and Like Yesterday, I Had a "50% Shot" on Guess Two!)

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Thursday 3:38 AM

Not sure I would have gone this way over the board, but will try this selection today. 4-6 tends to be an underwhelming toss as dealer, as it is helped most by 5s, which the opponent, if dealt any, will be jealously guarding (although the cut has come to the rescue with that today!) 2-2 leaves us with an 11, 16 and possible 5-trap, as well as more flexibility for avoiding a pegging battle.

   

Thursday 3:42 AM

The crib might have some snap, crackle and pop.

   

Thursday 4:11 AM

Cuts for 12-14 points.

   

Thursday 4:25 AM

Thirteen cuts for 8-14 points. Four cuts for at least five in the crib. dec

   

Thursday 4:54 AM

Ras’s small-hand rule today. Keeping the “touching” cards together for chance at max 14 in hand. Like this pegging makeup better as well with a chance to get our three strong pegging cards in at the end of a pegging sequence.

   

Thursday 5:24 AM

Two ways to start with four: A22K with the “meh” 46 in the crib, or A46K with a pair of deuces in the crib, which is also an uninspiring toss. These cards are subpar, and depending on the cut I’ll probably want to pick up some pegs, so I went this way, since it has a two-card 11, a two-card sixteen, and a five trap. A22K might look like a good pegger with its low cards, but 11s and sixteens and five traps are worth more than a LLLX configuration on its own (although obviously it does have an 11).

Checking Liam, A22K (46) averages 10.3 in pure hand+crib, and A46K (22) averages 10 even. I’m pretty sure that the 16 and five-trap will make up the 0.3 points of difference, or at least bring things to a virtual tie.

I’m as sick of writing about the positional dynamics of 0*-0 as other people probably are of reading about them. You can’t presume on your averages, and when you have cards that only average 10 in hand+crib, you probably have to peg a little bit to stay safely in the lead.

The 5 cut definitely makes me play defense, though. It helps the hand a lot, quite possibly helps the crib a lot too, and most importantly it probably helps the pone a lot, making his scoring more of a threat. Luckily, a KA 11 and 46 five trap are ploys that I’d see as both offensive and defensive: the KA 11, besides getting us a 31, shuts out the count, and the five trap is usually a low-risk play.

tl;dr version - A46K is a better offensive and defensive pegger, and that bridges the small difference in pure hand+crib.

   

Thursday 5:44 AM

Not too keen on A-4 or 2-2 from these six.
The hours of cutting practice have paid off.

   

Thursday 6:10 AM

Not a fan of 4-6 in my crib, as my opponent has a low probability of tossing me a 5. Don't really see a better way here, since the 6 does not work well with the K so I want to toss the 6 to my crib.

   

Thursday 6:15 AM

It’s a Ras puzzle ..and it’s appropriately so after a complicated eye procedure was a success yesterday ..from late yesterday

Ras2829 says: After 1 hours 20 minutes of a ars plan vitrectomy surgical procedure, surgeon had three words: "everything went well!" Great relief as have had 12 medical appointments since January 16, and have more scheduled between now and 4/5. All's well that ends well as William Shakespeare declared long ago. I give thanks to a Forgiving Lord, the advances of medical science, Kaiser Permanente, and those who offered their support in many ways over the past few weeks.

   

Thursday 6:34 AM

Hate 46 to the crib but first hand of the game I believe we need to hold the A22X. For an end-game situation such as Feb 2nd it is MUCH more conplicated and I'm still not convinced of the preferred approach.

   

Thursday 7:32 AM

I am going along with the crowd today for the same reasons already expressed.

   

Thursday 9:49 AM

I saw the 2-2 and 4-6 as pretty similar overall, and decided as first dealer that A-4-6-K looked like it would be better for defensive pegging than the more tightly bunched A-2-2-K.

I will again renew my request for any suggestions on a pegging program with decent quality AI that you can just peg with the same hand over and over against opponent hands to better test two choices.

   

Thursday 12:10 PM

I think the results are actually close in hand+crib, and I am not a huge fan of toss (4 6). But I would like to keep the starting 4 with potential for a double run, and the 5 cut may be even MORE beneficial, as really the only cut (or discard) which substantially helps this. I also feel that with the high card, I can adequately defend a little better with the pair of deuces, thus this is my overall choice today.

   

Thursday 1:45 PM

I think it's between A-2-2-K (4-6) and A-4-6-K (2-2):

A-2-2-K: 4pts + 4pts (Schell: 3.85) = 8pts

A-4-6-K: 2pts + 5¾pts (Schell: 5.72) = 7¾pts

Potential:

A-2-2-K: Improves with AAA, 22, 3333, 4444, 5555 + 15xXs = 32 cuts = 32/46 = 69.6% up to 8/12/14pts with AAA, 22, 3333, KKK = 12 cuts.

A-4-6-K: Improves with AAA, 444, 5555, 666, 8888, 9999 + 15xXs = 36 cuts = 36/46 = 78.3% up to 6/8/9pts with AAA, 444, 5555, KKK = 13 cuts.

Position:

As First Dealer positional hole is at 8pts so I'll play Defense but try to score the average 16pts or more.

Pegging:

I think both hands will peg well and A-4-6-K has a 3-card magic eleven while A-2-2-K has 3 low cards and a high card. Playing Defense with a pair I think A-2-2-K will have the edge in the pegging.

Summary:

A-2-2-K is slightly better for starting value by ¼pt and although it has fewer cuts for improvement it has 12 cuts for 8-14pts compared to 13 cuts for 6-9pts. So I'll throw the 4-6.

   

Thursday 3:19 PM

At 0*-0 playing a Defense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

_______________Pone's
Defense___Hand_Pegs____Crib_Total___W9 %____W10 %
A-4-6-K____4.52+(-1.91)+5.46=8.07____31.6____44.7
A-2-2-K____6.57+(-2.33)+3.73=7.97____31.8____45.0
2-2-6-K____3.78+(-2.02)+5.35=7.11____28.3____42.6

Defense______L9 %____L10 %
A-4-6-K_______26.7____28.8
A-2-2-K_______26.2____28.3
2-2-6-K_______25.5____30.1

A-4-6-K is best for expected averages by 0.10pt. but A-2-2-K is very slightly best for Win %s and lowest for Loss %s. However as it's the start of the game I'll decide based on expected averages so I'll select 2-2 to discard.

After the 5 cut I'll play Defense to the lead.

   

Thursday 8:44 PM

This is why I win at cribbage 🤣