January 12, 2022

*** This hand was suggested by Inushtuk1
0*-0  ?
41%
32%
10%
7%
5%
0%
0%
0%
Total votes: 252
Inushtuk1I know Sally wants us to say what the starter card was, but this is a purely hypothetical question Sally. Clearly the best keep is A-A-A-8d((7s-8s), when looking at expected averages *not* to include the pegging. But should we always toss the 8's for a potential bigger pegging bonanza? Even when we are on defense?
JQT
3338 votes

Joined: October 2008

   
Wednesday 3:00 AM
It's very nice to have Mike (Inushtuk1) back here at "Hand of the Day," not just as a daily voter and poster, but one who submits puzzles. May your re-entry into the atmosphere of the 'Daily Cribbage Hand' be one of adventure and education as well!

We begin the game as the Dealer, and lo and behold, we dealt ourselves three Aces and a 7-8-8 trio. Did we shuffle these cards, and if so, perhaps we shuffled them, but not enough? This is how it often looks when we shuffle a brand new deck but do so poorly.

But as humans, we always seek patterns, and we find them even when none exist. And the odds of dealing ourselves this precise arrangement of six cards is actually identical to dealing ourselves any other arrangement! And so, let's let go of any such suspicions. I've seen Mike deal, and he's as honest as the day is long!

We can hold Six Points today in two different ways, while stowing To Points into our Crib, so it's a horse race between Keep (A A A 8) and Toss (7 8) and the alternative Keep (A 7 8 8) and Toss (A A). What we should probably not do is Toss (8 8) from such an arrangement; that's generally a big no-no.

This should not be very difficult, because Toss (7 8) is a much more powerful Dealer Discard than Toss (A A). This is especially the case when we consider the Negative Delta, which might slightly lower the Toss (7 8) in value, but will drastically diminish Toss (A A).

Would I ever actually Keep (A A A 7) and Toss (8 8)? Only perhaps as part of a lesson or a demonstration of just how dangerous it can be for Pone to hold a "Lone" Ace! If such a "Lone" Ace were not 'dumped' early, it could become 'trapped' such that at a Count of Twenty-Seven, we play our first Ace, it gets PAIRED for (29-2), and then we peg willy-nilly (30=6) "go" and (31=14), out-pegging Pone by a 20-to-3 margin!

In fact, Toss (A A) shall have so much Negative Delta, that pegging with those three Aces and the 7 Card after Toss (8 8) may indeed even be better than Toss (A A)! But in any case, both of these are much weaker than our star discard today of Toss (7 8). But oh well, if the score were maybe (102*-116), then what the heck, Keep (A A A 7) and Toss (8 8) and try for the Hail Mary Pegging Play!

Let's begin this game sensibly and Toss (7 8), and hope that Pone leads a Ten (or "X") Card, after which we shall play our 8 Card; if Pone has (X X X X), we shall go-to-town and peg (30=2) and (31=8) or Ten Points in quick succession, while Pone looks on helplessly!

We might even do the same if Pone has either (5 X X X) or (5 5 X X). I would even play the 8 Card in response to an actual Ten "T" Card Lead, since after 8-9-T and Pone's (27-3), we'll parry and score Nine Points, as long as Pone has no Aces, Deuces, or Treys.
JQT says: One of the best ways to avoid falling into the 'Double-Run-Seeking Trap' is to actually examine what those seemingly "magical" Cut Cards will add to both the Hand and the Crib for either Discard Choice, and in doing this simple exercise, you'll see that we get even MORE help after Toss (7 8) from a great portion of those highly-anticipated Cuts. I describe this in much greater detail in my reply to winesteward48 (below). Also, if Pone holds the very common (X X X X) Hand, we shall ALWAYS peg those Ten Points, as long as we reply to Pone's Lead Card with our 8 Card.
Ras2829 says: Hi JQT: Onecan acutally play the 'aces back to back on a 7 lead from hand such as 7-8-9-10 or double run starting with a 7 and upward from there . So, it is worth the small risk to play the 8 on any lead from 7 up, giving dealer opportunity to play A-A-A in sequence.
Sally3
96 votes

Joined: October 2021

   
Wednesday 3:07 AM
Hi Mike, I wish I could see things as clearly as you and John...sigh. I saw and open ended run, more available cut help, plus 2 in the crib. AYyiyi. I'm just very curious about the real starter card lol. Hoep y ou keep coming around again :)
Inushtuk1 says: Hi sally. I *don't* see things as well as John. That's for sure.
mrob2199
852 votes

Joined: February 2009

   
Wednesday 3:22 AM
Full agreement with JQT today-the triple aces combined with the 8 has monster pegging potential as dealer,and the 78 discard has the bingo potential of a 6 cut which gives us a 12 point hand and 678 working in the crib
Sally3 says: Etching it into my brain!
james500
3111 votes

Joined: June 2013

   
Wednesday 3:40 AM
In agreement with those above,
X(10)-8(18)-X(28)-A(29)-go-A(30/2)-A(31/8) would be most welcome, especially in conjunction with a 6 cut.
Jazzselke
1985 votes

Joined: March 2009

   
Wednesday 4:43 AM
Ditto, agree, copy, etc. 2225 would be a similar example: X5X222, 12 pegs to 0.
Sally3 says: copy that...
Gougie00
4894 votes

Joined: March 2008

   
Wednesday 4:54 AM
Suited 78? Seem the most logical toss. Excellent shot at parlaying at least 2 aces.
zeke76
1127 votes

Joined: August 2018

   
Wednesday 5:26 AM
I’ll take my lumps and hopefully learn.
scottcrib
811 votes

Joined: August 2019

   
Wednesday 5:28 AM
Triple aces are not often achieved, but worth trying for at the end.
smokeytroll42
107 votes

Joined: January 2021

   
Wednesday 5:37 AM
Keep the aces, nice suited toss to the crib.
dec
5514 votes

Joined: April 2008

   
Wednesday 5:46 AM
Alex can I buy a six of spades ? Pegging for a three pointer at end, maybe six/seven? dec
scottcrib says: Hey Dan, are you and damonsmom related?
Gougie00 says: Not exactly related but ...
mfetchCT425
1042 votes

Joined: February 2009

   
Wednesday 6:20 AM
Keep your eyes open as dealer for these particular 4-card magic 11s (A-A-A-8, 2-2-2-5, 2-3-3-3, 2-2-3-4)They can peg big-time for dealer. 7-8 more powerful in crib than A-A.
Sally3 says: Thanks for the lesson, champ!
Ras2829 says: Hi mfetchCT425. Shold have read your post first and could have saved a line or two in mine. Good Job!!
wasa
2225 votes

Joined: November 2014

   
Wednesday 7:33 AM
Briefly pondered tossing the A-A but I really don't like tossing pairs to my crib (except 5-5!). 7-8 works well with those 6s and 9s my opponent likes to toss. I've seen better cuts at the butcher's!
fentesk
400 votes

Joined: January 2021

   
Wednesday 8:10 AM
I didn't like the prospect of pegging defensively with A-7-8-8, and would toss the 7-8 here even without fully appreciating just how strong the A-A-A could peg for us as dealer.
Fender Bass
210 votes

Joined: July 2021

   
Wednesday 8:22 AM
Unless you cut a 6.7.8 or 9 I think you're better off here for hand, crib and pegging
Fender Bass says: and a 6 cut would be good for this hand, too.
MiketheExpert
302 votes

Joined: April 2021

   
Wednesday 8:50 AM
No question in my mind today, I am going to toss (7 8) suited to my crib. Much stronger crib throw than a pair of aces....And even without this fact, I would probably do it just for this line of pegging chance:

X-8-X-A-A-A!! for 10 unanswered pegging points!
MiketheExpert says: If I needed a "Hail Mary", I may actually keep the 7 instead of the 8, and hope to trap pone's A for 20 pegging points...However as 1st hand of the game, no reason not to toss your strongest crib discard with this hand. :)
winesteward48
96 votes

Joined: April 2021

   
Wednesday 9:37 AM
It is tempting to toss 7,8 to the crib, but, I preferred the chance of the double run in the hand. Perhaps it is the group I play with, but they seldom give me the chance to play three consecutive A's. With the 4 cut I might get 10 in the crib when pone puts K, 10 into the crib. Their frown is worth the price of admission.
JQT says: The desire to obtain the splendid Double Run of 6-7-8-8 or 7-8-8-9, or to get the almost-magical 7-7-8-8 hand can make it difficult for us to see that those Cuts that indeed produce such wonderful combinations shall boost our 'Hand plus Crib' Total EVEN MORE if we 'split up' the 7-8-8 and stow the powerful Toss (7 8) into our Crib! Let's examine some of the finer details here: In Crib Value alone, Toss (7 8) is worth One Full Point (Schell) MORE in our Crib than Toss (A A), and so let's examine the 'static' value of which Cut Cards add what amount of points to these two Hands and potential Cribs. After Keep (A A A 8) and Toss (7 8): Cuts of (4444, 9999) add 2 points; Cuts of (A, 5555, 777, 88) add 6 points; and, Cuts of (6666) add 9 points. Meanwhile, after Keep (A 7 8 8) and Toss (A A): Cuts of (A, 88, 9999) add 6 points; Cuts of (777) add 8 points; and, Cuts of (6666) add 10 points. If you tally the aggregate totals for each, it reveals that Toss (7 8) actually yields 5.6% more to the Expected Average, not to mention what the contribution of Pone's discard might also add, which as Schell's numbers show, will actually boost Toss (7 8) more than Toss (A A).
JQT says: Slight Correction: Cuts of (9999) add 3 points (not just 2) to the Toss (7 8), and therefore Toss (7 8) actually yields 9.4% more overall to the Expected Average Total (not just 5.6% more).
jmath714
1041 votes

Joined: January 2012

   
Wednesday 9:45 AM
It’s interesting to see the differences between the percentages of commenters versus the overall number.

I wonder if this problem were to be given at say, a 100-person ACC event, if the percentages would be similar to what shows above, or more similar to the ~75% for AAA8 in the comments here. (82.3% by my count)
Rosemarie44
2005 votes

Joined: March 2016

   
Wednesday 11:02 AM
This retention and discard seems easy for me as I don't like pairs in my crib as a general rule. So suited 78 leaves these four cards in my hand as pictured!
Ras2829
4343 votes

Joined: November 2008

   
Wednesday 11:43 AM
Choosing defense as dealer of hand one, it all falls into place. Keep that mighty four card magic 11. Play the 8 on all leads from 7-K. Play off other leads except for an Ace.
Ras2829 says: I qualified for All-American team a couple of times by holding A-A-A-8 as dealer and pegging those Aces back-to-back which is often the case. Works that way all most all the time on a 9 or X- lead. and sometimes even works on 7/8. Go for it. Other four card 11's from heaven that work well for dealer are 2-2-2-5, and 2- 3-3-3. Look for them if oodles of pegs will make you well.
Coeurdelion
4801 votes

Joined: October 2007

   
Wednesday 3:20 PM
I think its between A-A-A-8D (7-8S) and A-7-8-8 (A-A):

A-A-A-8D: 6pts + 6½pts (Schell: 6.53) = 12½pts

A-7-8-8: 6pts + 5¼pts (Schell: 5.38) = 11¼pts

Potential:

A-A-A-8D: Improves with A, 4444, 5555, 6666, 777, 88 = 18 cuts = 14/46 = 30.4% up to 12pts with A, 5555, 6666 = 9 cuts.

A-7-8-8: Improves with A, 6666, 777, 88, 9999 = 14 cuts = 14/46 = 30.4% up to 12/14/16pts with 6666, 777, 88, 9999 = 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:

A-A-A-8 is a 4-card magic eleven and I think will be the better pegger playing Defense but A-7-8-8 should also peg well.

Summary:

A-A-A-8D has the better starting value by 1¼pts. A-A-A-8D has more cuts for improvement but A-7-8-8 has 13 cuts for 12-16pts while A-A-A-8D only has 9 cuts for 12pts. So I think A-7-8-8 will catch up the 1¼pts therefore I'll throw A-A.
HalscribCLX
4531 votes

Joined: February 2008

   
Wednesday 3:23 PM
At 0*-0 playing a Defense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

_______________Pone
Defense__Hand__Pegs___Crib_Total____W9 %____W10 %
A-A-A-8D__7.57+(-2.15)+6.43=11.85____41.8____54.3
A-7-8-8___8.22+(-2.00)+4.98=11.20____39.1____52.0
A-A-A-7___7.43+(-2.07)+5.10=10.46____38.0____50.9

Defense______L9 %____L10 %
A-A-A-8D______25.5____20.8
A-7-8-8_______25.4____22.5
A-A-A-7_______25.7____23.4

A-A-A-8D is best for expected averages by 0.65pt. and is appreciably best for Win %s and lower for Loss %s. So I'll select the suited 7-8 to discard.

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