Wednesday 3:05 AM

A new Puzzle Contributor, ZulwarnGames, brings us today's puzzle, and it looks like we are down to the final deal as Pone from just Eight Points out. As one who has spent much of my life studying and examining Cribbage Endgames, I can already tell that I will enjoy this puzzle, and hopefully, I will be able to learn something new.

Meanwhile, the Dealer sits at Hole 109 and needs a Dozen Points to reach the end of the board, and since this is Four Holes BELOW the Dealer Average, my previous experience tells me that we should probably attempt to do all we can to MAXIMIZE our own forward progress, and ignore what ends up in the Enemy Crib. We'll examine this in detail soon.

If the Dealer were farther away from the Finish Line, we could afford to discuss the merits and dangers of the Crib today, but from this Relative Score, it's probably best if we aim for the Goal Line, Crib be damned, and come what may.

I say "probably," because some card arrangements are SO BAD that all we *can* do is defend, as in for example, let's say we were dealt (2 2 6 8 9 Q): here we would obviously Toss (8 Q), and hope for the best. If we missed our helpful Cut Cards and came up short, we could maybe still have a very slight chance of pegging out as the Next Dealer.

But however, given an arrangement such as (2 3 7 8 9 K): here it is not so simple! If we don't get our helpful Cut Cards, we could Toss (2 K), lead the 8 Card, and perhaps seek a (31-2) play with our Trey. But some might opt to Toss (9 K) and, at the slight risk of a smaller Hand, try to 'punish' the Dealer's Crib to the maximum! But lo and behold, with a Dealer at Hole 109, it's risky to opt for DEFENSE.

Let's now examine our REAL card arrangement, and see if we can "shoot for the immediate WIN" via our First Hand Show, or whether we need to 'cower' and attempt a Defensive Maneuver.

We were dealt (A 2 4 8 8 J): and at first glance, it's difficult to ascertain whether we should opt for Offense or try to defensively "hedge" somewhat. Let's examine the probabilities of LOSER CUTS, and also of obtaining either Six or Seven Points (or more) during this exercise, which could result in us having to peg One or Two Holes as Pone, a lofty but still reasonable proposition:

If we Keep (A 2 4 8), first we note that we get HELP from ALL POSSIBLE CUTS, and next we see that we shall obtain Six Points or more after Sixteen Cuts (AAA, 222, 3333, 444, 888), which will occur about 35% of the time, and we shall obtain Seven Points or more after Four Cuts (3333), which will occur nearly 9% of the time, and we'll have Eight Points and WIN with certainty after Four Cuts (3333), again about 9% of the time;

If we Keep (A 2 8 8), first we note that we FAIL TO GET HELP from Nineteen Cuts (9999, TTTT, JJJ, QQQQ, KKKK), and next we see that we shall obtain Six Points or more after Eighteen Cuts (444, 5555, 6666, 7777, 888), which will occur about 39% of the time, and we shall obtain Seven Points or more after ZERO Cuts, and thus we'll NEVER have Eight Points and WIN with certainty;

If we Keep (A 4 8 8), first we note that we FAIL TO GET HELP from Eight Cuts (5555, 9999), and next we see that we shall obtain Six Points or more after Eighteen Cuts (222, 3333, 6666, 7777, 888), which will occur about 39% of the time, and we shall obtain Seven Points or more after ZERO Cuts, and thus we'll NEVER have Eight Points and WIN with certainty;

If we Keep (2 4 8 8), first we note that we FAIL TO GET HELP from Nineteen Cuts (6666, TTTT, JJJ, QQQQ, KKKK), and next we see that we shall obtain Six Points or more after Eighteen Cuts (AAA, 3333, 5555, 7777, 888), which will occur about 39% of the time, and we shall obtain Seven Points or more after Four Cuts (3333), which will occur nearly 9% of the time, and we'll have Eight Points and WIN with certainty after Four Cuts (3333), again about 9% of the time;

If we Keep (A 4 8 J), first we note that we FAIL TO GET HELP from Four Cuts (9999), and next we see that we shall obtain Six Points or more after Nine Cuts (AAA, 444, JJJ), which will occur about 20% of the time, and we shall obtain Seven Points or more after just One Cut (As), which will occur around 2% of the time, and we'll NEVER have Eight Points and WIN with certainty;

If we Keep (A 2 4 J), first we note that we FAIL TO GET HELP from Eight Cuts (6666, 7777), and next we see that we shall obtain Six Points or more after Sixteen Cuts (AAA, 222, 3333, 444, JJJ), which will occur about 35% of the time, and we shall obtain Seven Points or more after Five Cuts (As, 2s, 3333), which will occur nearly 11% of the time, and we'll have Eight Points and WIN with certainty after Four Cuts (3333), again about 9% of the time;

After looking at just six of the possible Pone Hands that appear to be the best of the bunch, it is quite surprising that if we ignore those LOSER CUTS that do not help in any way, Keep (2 4 8 8) appears to just barely rise to the top of the class today! But this may be very deceptive, because this Hand will fail to receive any help whatsoever after Nineteen Cuts (6666, TTTT, JJJ, QQQQ, KKKK), or greater than 41% of the time! Ouch!

What stands out as being the most remarkable trait? This one is easy to see: Keep (A 2 4 8) gets HELP from ALL POSSIBLE CUTS! Also, it has a 9% chance of getting us an immediate VICTORY, and this is equal to or better than all of the other candidates! Let's Toss (8 J) today, and make it unsuited, just out of habit.

Choosing the Second-Best Hand is a task that is perhaps no easier than picking out the BEST! I would maybe place Keep (A 2 4 J) next up on the podium, because I like the figures it yields, and I also like it as a Pegging Hand. It's important for us to realize that the Dealer cannot defer to the most Defensive Pegging Hand today, because the Dealer still needs a Dozen Points, and the Dealer cannot "coast" this far and rely upon merely holding the strongest Pegging Hand.

The composer of the puzzle, ZulwarnGames, further says, "I worked so hard to come from behind on this one, and then I got paralyzed trying to think of the best options for this hand." Any one of us can identify with such a feeling! I'm approaching 1500 words on this puzzle, and it's a tough nut to crack!

Cribbage is difficult, and none of us can take the time to dissect an arrangement of cards as I have just done while sitting at the table! But by doing such an exercise, we learn things. What CAN we do while sitting at the Cribbage board?

I contend that it is possible to at least see and determine that Keep (A 2 4 8) has NO LOSER CUTS! That calculation should only take an average player a few seconds, and most importantly, it's a calculation that ought to be performed. Players with more skill might even conclude that while Keep (A 2 4 8) has just Four Immediate Winners (3333), that no other Candidate Hand under consideration here can exceed this.

After the Queen of Hearts Cut, we now have Four Points in our Hand, and we'd like to peg Four More. This will be very difficult. Let's lead the 8 Card.

Remember what I just said four paragraphs ago: the Dealer at Hole 109 is almost with certainty *forced* to hold a relatively strong Hand, in order for the Hand and Crib tally to traverse those Dozen Holes needed to reach the Finish Line. Thus, the Dealer should be able to be exploited for a few Pegging Holes if we go about this Pegging Exercise wisely.

Wordle 648 3/6 (Had a 50% chance to get it on Guess Two)

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Wednesday 3:52 AM

With no chance to hold more than 2 points, go with a low scoring discard (8-J fills that bill). Choosing offense to include the pegging lead the 8, take any pegs offered. With a four-point hand after seeing the starter card, n/d needs four pegs, Don't despair, play with confidence as there are many scenarios which would allow n/d to peg those four holes. Could this be one?

   

Wednesday 4:00 AM

The last train out of town. What combination gives me the best shot to get 8? This does if I cut a 3. An A,5,or 7 would be nice. The Q cut means I just lost. Ugh. Lead the 8 and hope the dealer pairs it.

   

Wednesday 4:07 AM

When holding this sort of configuration, where you can hold an a4+mid 15, or an a4 15 with a x and toss mid-low or mid-mid, it's best to just throw the one of the mids and the x to balk the crib at most scores and with most hands of this sort. You still have a 15, you still have a nickle, and you have touching low cards both for pegging and cuts. Even here, where balking the crib is less of a concern (though not totally off the radar either, since a 0 crib could just let us peg out next hand), it's the way to go. 8 lead for sure.

   

Wednesday 4:34 AM

3-2-A dem are the cuts. Lead the eight and just maybe we can parlay the Ace-Two. dec

   

Wednesday 5:42 AM

Along with A347 my favorite 2-point hands as pone. A248 improves on any cut as already highlighted; A347 can peg well and only misses with a 6 or 9 starter card.

   

Wednesday 5:44 AM

This question is for all of you statistics wizards, I'm especially interested to see what Gandalf says.

"What are the chances that the opening dealer will also deal the last hand of the game?"

I know that the opening dealer has a slight advantage of winning. And as we all know, the closing pone counts first and has a slight advantage. What do the averages say about this being the same person?
This straw man is based on those tight end games.

   

Wednesday 6:06 AM

The potential bonus point from the Jack may be decisive. Better cuts were available. I'll lead the Jack and play on.

   

Wednesday 9:06 AM

"Well isn't this a fine mess" I decided to keep the pair just in case I get a chance to use them, or the opponent feels the need to pair an 8 lead because they need points.

   

Wednesday 9:42 AM

Good pegging cards, assured points, best position to add points in a cut.

   

Wednesday 12:47 PM

Difficult decision....I went with (A 4 8 8). More cuts and pegs to get us closer I think...I'm not too concerned about the A being a pegging liability, in fact I am considering max offense in order to close 8 pts, with general disregard for crib throw and any inherent danger in pegging hand. This is the best way I can see combined with cuts to improve plus pegging.

   

Wednesday 2:29 PM

I'll examine A-2-4-8S (8H-J), A-2-4-J (8-8) and 2-4-8-8 (A-J):

A-2-4-8S: 2pts - 4½pts (Schell: 4.59) = -2½pts

A-2-4-J: 2pts - 6¾pts (Schell: 6.82) = -4¾pts

2-4-8-8: 2pts - 4¾pts (Schell: 4.68) = -2¾pts

Potential:

A-2-4-8S: Improves with AAA, 222, 3333, 444, 5555, 6666, 7777, 88, 9999 + 15xXs = 46 cuts = 46/46 = 100.0% up to 6/8pts with AAA, 222, 3333, 444, 88 = 15 cuts.

A-2-4-J: Improves with AAA, 222, 3333, 444, 5555, 88, 9999 + 15xXs = 38 cuts = 38/46 = 82.6% up to 6/8pts with AAA, 222, 3333, 444, JJJ = 16 cuts. Plus 10 spade cuts for 1pt extra for his nob = 10/46 = 0.22pt.

2-4-8-8: Improves with AAA, 222, 3333, 444, 5555, 7777, 88, 9999 = 27 cuts = 27/46 = 58.7% up to 6/9pts with AAA, 3333, 5555, 7777, 88 = 17 cuts.

Position:

At 113pts we need 8pts to get out. So I'll play Offense.

Pegging:

I think A-2-4-8S and A-2-4-J will peg well but A-2-4-8S has a 3-card magic eleven so I think will peg best.

Summary:

Starting value is less important than the hand plus pegging potential in this position:

I'll count cuts for 8pts+, 7pts and 6pts:

A-2-4-8S: 3333 = 4 cuts for 8pts
AAA, 222, 444, 88 = 11 cuts for 6pts.

A-2-4-J: 3333 = 4 cuts for 8pts
AS, 2S = 2 cuts for 7pts
AA, 22, 444, JJJ = 10 cuts

2-4-8-8: 3333 = 4 cuts for 9pts
AAA, 5555, 7777, 88 = 13 cuts for 6pts

2-4-8-8 has the most cuts for 6/9 at 17 but A-2-4-J has 16 cuts for 6-8pts and 6 cuts for 7/8pts. It should also peg better than 2-4-8-8 so I'll throw the 8-8.

   

Wednesday 2:47 PM

At 113-109* playing a BOLD strategy for the pegging the dynamic expected averages and Win/Loss % are:

_______________Our
Offense___Hand_Pegs_Crib____Total___Win %___Loss %
A-2-4-8S___4.83+1.70+(-4.55)=1.98____41.1____58.9
A-4-8-J____4.43+1.35+(-4.67)=1.11____26.0____71.4
2-4-8-8____4.09+1.35+(-4.64)=0.80____27.1____67.3
A-4-8-8____4.39+1.28+(-4.97)=0.70____25.4____70.6
A-2-8-8____4.00+1.37+(-4.76)=0.61____23.3____67.6
4-8-8-J____3.65+1.30+(-4.84)=0.11____18.9____69.0
A-2-4-J____4.72+1.63+(-6.32)=0.03____40.8____59.2

A-2-4-8S is best for expected averages by 0.87pt. and is slightly better than A-2-4-J for Win/Loss %s so I'll select 8H-J to discard.

After the Q cut I'll lead the 8 and play Offense:

Lead______________Our Pegging Pts.
8_______________________1.75
4_______________________1.71
A_______________________1.62
2_______________________1.43