April 25, 2017

*** This hand was suggested by Inushtuk1
104-105*  ?
84%
8%
4%
1%
0%
0%
0%
Total votes: 183
Rosemarie44
2052 votes

Joined: March 2016
 
 
 
Tuesday 3:18 AM
By keeping 4-4-5-6 only one cut does not add value to the hand and a safer toss goes to the the dealer. I now have fourteen of the seventeen points needed to peg and count of this hand.
Guest says: A no brainier today
Rosemarie44 says: Unfortunately, Ras and JQT are not in agreement with this choice.
JQT
4143 votes

Joined: October 2008
 
 
 
Tuesday 3:29 AM
Cribbage Endgames can be exceptionally intricate and/or exceedingly tricky sometimes. See Exhibit "A" Above.

And once again, Inushtuk1 delivers us a fine specimen of a puzzle here today! In fact, I had just as much fun working on this as I did watching the latest episode of "Better Call Saul" on AMC early this morning. Let's get to work.

As Pone, we need 17 Points, or more than Half a Street, in order to WIN, while the Dealer only requires 16 Points to get the job done. Typically, while Pone averages about Ten Points per Deal, the Dealer averages closer to around Sixteen Holes.

But Not-to-Worry Folks, because it appears that we have been dealt a real gem of a Much-Greater-Than-Average HAND! And both Keep (4 4 5 6) and Keep (4 5 6 6) look to be about equal, don't they? BUT WAIT: Not So FAST!

We know that we're going to be 'chucking' the Ace 'over the board' here, but for today's recipe, what goes well along with that Ace? Toss (A 6) does seem to be a bit safer than Toss (A 4), but are we really concerned with DEFENSE, or should we concentrate instead on OFFENSE, or WHAT: are we concerned with something else altogether in this puzzle today?

If we Keep (4 5 6 6), we appear to have 15 Cuts (3333, 44, 555, 66, 9999) that produce 16 or more points; and meanwhile we have 11 Cuts (AAA, 2222, 8888) that add NOTHING to the 'D2W2D' which everyone knows is my Shorthand Cribbage Notation for that "Dirty Dozen We Were Dealt!"

However ... If instead we Keep (4 4 5 6), now we only have 11 Cuts (44, 555, 66, 7777) that produce 16 or more points, even though we would then have only 4 Cuts (8888) that add NOTHING to the Original Dozen. In today's predicament however, we're much less concerned with that latter statistic, and we're a whole lot more concerned with the former: this hand of Keep (4 4 5 6) is therefore far inferior to the first choice of Keep (4 5 6 6), mostly because it has four fewer Cuts out of 46 (or nearly 9% fewer ways) to get us 'jacked up' to 16 points or more!

This means that if we lose our focus on what's critical here and begin to worry too much about the slightly-riskier Toss (A 4), we shall then possibly miss out on what's really important in the POSITION given, and that is that nearly 9% added 'gravy train' we get with Keep (4 5 6 6) on our path toward Victory!

What if that's not convincing enough? Well, if we Keep (4 5 6 6), we are also holding onto one of the better Pegging Traps in Cribbage, one that works so well in fact, it has been dubbed, "Old Faithful"! This 'trap' can be used whether we hold the 5 Card ourselves or not, but it does require that we have the (4 6 6) combination.

If the Dealer is holding either (5 X X X) or even holding all four Ten Cards, we can lead a 6 Card from our PAIR, and then 'trap' the Dealer's 5 Card (or even set up our own) for a very powerful 'Pegging Coup' of (31-5) for snagging Five Unanswered Points!

And what could be better for us: we were already dealt Twelve Points, and so Five More Points would give us the Seventeen Points TOTAL that we need in order to WIN! Sure, it is slightly more dangerous if we Toss (A 4), but on the "Positive Side of the Ledger" we have such a compelling case to Keep (4 5 6 6), that it's not even close!

How else might we remember that Keep (4 5 6 6) is a more powerful hand arrangement than Keep (4 4 5 6)? Well, we all have our own (sometimes secret) methods. In fact, way back in ... I think it was Spring ... perhaps Late March 2013 ... in a serendipitous slip of the keyboard, I believe that our own Coeurdelion once accidentally referred to Keep (4 4 5 6) as a "Double Ruin" (Laugh Out Loud!) and I've never forgotten this!

Let's map out at least these Top Two Contenders and see if we can learn Why and How Come:

25 April 2017 (104-105*) (Ah 4s 4d 5c 6h 6s) Cut = Ks

--

Keep (4 5 6 6) and Toss (A 4)

05x24=120 - 44, 555 (5 Cuts = 24 Points)
02x21=042 - 66 (7 Cuts >= 21 Points)
08x16=128 - 3333, 9999 (15 Cuts >= 16 Points)
20x14=280 - 7777, TTTT, JJJJ, QQQQ, KKKK (35 Cuts >= 14 Points)
11x12=132 - AAA, 2222, 8888 (11 Cuts = 12 Points or NO HELP)
---------
46 702

Expected Average is: 702 DIV 46 equals 15.261 Points

--

Keep (4 4 5 6) and Toss (A 6)

05x24=120 - 555, 66 (5 Cuts = 24 Points)
02x21=042 - 44 (7 Cuts >= 21 Points)
04x16=064 - 7777 (11 Cuts >= 16 Points)
31x14=434 - AAA, 2222, 3333, 9999, TTTT, JJJJ, QQQQ, KKKK (42 Cuts >= 14 Points)
04x12=048 - 8888 (4 Cuts = 12 Points or NO HELP)
---------
46 708

Expected Average is: 708 DIV 46 equals 15.391 Points
JQT says: Even with its slightly HIGHER EXPECTED AVERAGE, and with MUCH FEWER "NO HELP" Cut Cards (about a third as many) to boot, Keep (4 4 5 6) fails us right where we really need the most help: it only has 11 Cuts that produce 16 Points or more, while Keep (4 5 6 6) chalks up 15 Cuts that yield us those precious 16 Points or more, and that is almost a 9% improvement, if we simply choose to Keep (4 5 6 6).
JQT says: In addition to choosing a discard for the "Daily Cribbage Hand," I've often wished we could also examine various Pegging Choices as well. In today's puzzle, a most heartbreaking conclusion to this game for Pone after Keep (4 5 6 6) would be to Cut a Trey or a 9 Card, and thus need to peg JUST ONE MORE HOLE FOR VICTORY, and yet we could still come up short (120-121)! Another torturous finish might occur if, after one of those Eleven "LOSER" Cuts (AAA, 2222, 8888) occurred, now let's say we pegged all four 6 Cards in-a-row and then, with the interim score at a precarious (110-119), it would once again be Our Lead while holding (4 5) in a still-very-contentious Endgame Battle with two cards each remaining and the Count at Twenty-Four, in what I could only estimate to be about-equal odds.
Guest says: phew, lots of stuff, eh Rog
JQT says: Last but (and I might regret saying this is) certainly not least that might concern us here could be the odd fact that from a score of (104-105*), the discard decision of Toss (A 6) can actually produce a slightly higher Crib for Our Opponent of 16 Points, after say a Dealer Toss (7 7) and an 8 Card Cut, than a discard decision of Toss (A 4), which can only reach 14 Points after say a Dealer Toss (4 5) and a 6 Card Cut! The 6 Card Strikes Again! "This Game of Ours" that we call Cribbage can certainly be a bit maddening at times, can it not?!
Ras2829 says: Hi JQT: You are a man of great influence. You hooked 5% of those responding today. I was hooked even before seeing your bait!
JQT says: Thank you RAS. All credit goes to Inushtuk for a superb puzzle today! And Halscrib helps to clear up some things as usual. This morning, I was thinking that it's perhaps two-thirds due to those extra Cuts we have for Sixteen Points with Keep (4 5 6 6) and one-third due to the improved pegging. Now I believe it's probably more like two-thirds PEGGING and just one-third due to the Cuts and their distribution. It shows up somewhat in the aggregate Expected Average and more noticeably in the Win Rate, but let's try to be clear about WHY Keep (4 5 6 6) is the better choice here. If we look at those DISCRETE additional Cuts that provide a definite Winning Solution (an added 16 Points or more), we can see those Eight Cuts for Keep (4 5 6 6) as opposed to only Four Cuts that similarly help Keep (4 4 5 6). But can this alone make for a better choice? I don't think so, because right near this we have Thirty-One Cuts that provide 14 Points for Keep (4 4 5 6), while Keep (4 5 6 6) has only Twenty Cuts at this level of help. All in all, the Expected Average for JUST THE HAND ITSELF is therefore fairly well camouflaged here among Cuts that produce either Twenty-Four and Twenty-One Points, or among Cuts that offer us NO HELP whatsoever, and those that leave us with just Twelve Points. One way to gain some clarity is to use a Digital Circuit Design Trick and treat both those Cuts that exceed Twenty as well as those Cuts that do NOT help us at all as "Don't Cares" and simply ignore them during our comparison. Then what we're left with is simply those 'Cuts That MATTER' and that are centered closer to the required 17 Points needed to win today. And so if we take into account just the resultant Hand Averages, we have almost an effective TIE here in my opinion. And therefore it is then clearly the PEGGING superiority of Keep (4 5 6 6) that 'clinches' this Discard Choice. Opinions and/or ideas?
Inushtuk1 says: Glad you liked the puzzle JQT. Digital Circuit Design Trick huh. What the hell is.that?
JQT says: not sure why, but earlier today those "don't care" Cribbage Cuts just reminded me of Boolean Logic and design shortcuts using Karnaugh Mapping from my college years ... could be my life flashing before me ; )
dec
6358 votes

Joined: April 2008
 
 
 
Tuesday 4:20 AM
Add the two cut. Those four more cuts weighs out odds wise over 6-5-4 pegs. dec
LoneStarPegger
811 votes

Joined: January 2008
 
 
 
Tuesday 4:49 AM
Going for the trap. Only need 3 pegs, so would lead from the pair anyhow.
Samgash
402 votes

Joined: November 2016
 
 
 
Tuesday 4:57 AM
Bravo JQT. Entertaining and informative.
james500
3924 votes

Joined: June 2013
 
 
 
Tuesday 5:03 AM
Chose A-6, although having now read JQT'S excellent post, I realise I shouldn't have. Bravo sir.
BigFoot Bob
624 votes

Joined: April 2016
 
 
 
Tuesday 5:16 AM
My first thought was not sending a 1-4 to the dealers crib in case I couldn't peg enough to go out and to kill the crib if a face card is cut. . . . .which it was to my benefit. I still need three points to peg.
glmccuskey
4102 votes

Joined: April 2011
 
 
 
Tuesday 5:20 AM
Waned to play the 6-6-4 trap. If it works, I'm out.
Ras2829
5155 votes

Joined: November 2008
 
 
 
Tuesday 5:28 AM
Who counts first next time? The challenge it seems to me is to win the game this deal. So it is to lead form the sixes and RAS will choose the spade. Have queried this hand before with the Cribbage Prof and the 4-4-5-6 has a very slight edge on potential hand score of .13. The offensive pegging of 4-5-6-6 has an edge of a full point based on my scant empirical data. So if looking at combined value alone, 4-4-5-6 with A-6 has the edge. Even so, my chances of winning are enhanced by holding 4-5-6-6 with A-4 discard. See JQT posting for the rest of the story.
Ras2829 says: BTW am interested in HalscribCLX analysis as the cribbot seems to play defense in situations on fourth street where I would choose offense or optimal. If that should be the case, those who have chosen 4-4-5-6 will have a very potent ally.
Ras2829 says: For those who might not be familiar with the pegging power of this hand, if dealer is playing 5-X-X-X, 5-5-X-X, or XXXX. By leading the six spot, RAS scores five pegs. If dealer plays a five on my six lead, I score 15-5 (not likely). If dealer plays a 10 on my six lead, advance the count to 22 with the remaining 6 spot. What happens then? Non-dealer scores 31-5 (run of three and 2 for 31). The chances are quite good that dealer will be holding one of those hands needing 16 points to win. If you've not been playing for this frequent highly efficient pegging trap, add it to your playbook.
cwed
1355 votes

Joined: October 2014
 
 
 
Tuesday 5:38 AM
I am playing offense in order to win the game on this deal, so I'll hold the pair of 6s and run the "5-trap." I don't really care about the crib, so A-4 to the dealer's crib doesn't bother me in this position.
Gougie00
5731 votes

Joined: March 2008
 
 
 
Tuesday 5:47 AM
Despite getting a good hand, I'm still vulnerable. 456 is tough to defend. Lead the 4.
The_Bee_Mann
306 votes

Joined: November 2016
 
 
 
Tuesday 7:53 AM
I went with 4456 to avoid A4 to crib. After reading the Ras and JQT comments I change my mind.
bbaer1
3693 votes

Joined: February 2011
 
 
 
Tuesday 8:02 AM
Most likely will need a decent cut and some pegs to win. This is the better pegger.
Coeurdelion
5595 votes

Joined: October 2007
 
 
 
Tuesday 2:42 PM
Is it worth keeping the better pegger 4-5-6-6 but having to throw A-4 instead of A-6?:

4-5-6-6: 12pts - 6pts (Schell: 5.72) = +6pts

4-4-5-6: 12pts - 4¾pt (Schell: 4.91) = +7¼pts

Potential:

4-5-6-6: Improves with 3333, 44, 555, 66, 7777, 9999 + 16xXs = 35 cuts = 35/46 = 76.1% up to 21/24pts with 44, 555, 66 = 7 cuts.

4-4-5-6: Improves with AAA, 2222, 3333, 44, 555, 66, 7777, 9999 + 16xXs = 42 cuts = 42/46 = 91.3% up to 21/24pts with 44, 555, 66 = 7 cuts.

Pegging:

4-5-6-6 will peg better as we can set the trap for a 5 by leading the 6s.

Position:

We need 17pts to win so need the hand with the best chance to score this and peg any shortfall.
Coeurdelion
5595 votes

Joined: October 2007
 
 
 
Tuesday 2:45 PM
Summary:

4-4-5-6 starts with 1¼pts more and has many more cuts for improvement. So despite the better pegging of 4-5-6-6 I'll choose the A-6.
HalscribCLX
5318 votes

Joined: February 2008
 
 
 
Tuesday 3:22 PM
At 104-105* playing an Offense strategy for the pegging the dynamic expected averages and Win %s are:

________________Our
Offense___Hand__Pegs__Crib___Total____Win %
4-4-5-6H__14.46+1.07+(-4.34)=11.19____43.1
4-5-6-6___14.33+1.96+(-5.70)=10.59____52.5

4-4-5-6 is better for expected averages by 0.60pt but 4-5-6-6 is significantly better for Win %s. This is because the negative influence of the crib is quite likely not to play apart in the out come and the expected averages for just Hand and Pegs are:

________________Our
Offense___Hand__Pegs_Total
4-5-6-6___14.33+1.96=16.29
4-4-5-6H__14.46+1.07=15.53

So I'll select A-4 to discard.

After the K cut I'll lead a 6 and play Offense:

Lead____Our Pegging Pts.___Win %
6___________2.23___________40.1
5___________1.10___________15.2
4___________1.01___________13.8