Sunday 4:11 AM

As Pone, we need a Dozen Points to WIN this exciting Cribbage Endgame Battle, or Two Points above Pone Average. 🤗

Let's map out at least three ideas to get our bearings:

(109-105*) (As Ac 2d 2c 5h 6s) Cut = 9s, by Lafngas, Nov 17, 2024.

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A) Dump the 5 Card and 6 Card Idea:

Keep (As Ac 2d 2c) and Toss (5h 6s)

Expected Hand Average is 320 DIV 46 = 6.957
(minus) Expected Crib Value (Schell) is 7.470
Total is -0.513 [ Endgame Battle so Use 6.957 ]

04x16=064 - 3333 (Maximum Hand, 4 cuts = 16 Points)
20x08=160 - AA, 22, TTTT, JJJJ, QQQQ, KKKK (24 cuts >= 8 Points)
04x06=024 - 9999 (28 cuts >= 6 Points)
18x04=072 - 4444, 555, 666, 7777, 8888 (Minimum Hand, 18 Cuts = 4 Points)
46 ___ 320

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B) Dump the Aces Idea:

Keep (2d 2c 5h 6s) and Toss (As Ac)

Expected Hand Average is 328 DIV 46 = 7.130
(minus) Expected Crib Value (Schell) is 6.020
Total is 1.110 [ Endgame Battle so Use 7.130 ]

02x12=024 - 22 (Maximum Hand, 2 cuts = 12 Points)
04x11=044 - 7777 (6 cuts >= 11 Points)
04x09=036 - 4444 (10 cuts >= 9 Points)
10x08=080 - 555, 666, 8888 (20 cuts >= 8 Points)
20x06=120 - 9999, TTTT, JJJJ, QQQQ, KKKK (40 cuts >= 6 Points)
06x04=024 - AA, 3333 (Minimum Hand, 6 Cuts = 4 Points)
46 ___ 328

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C) Dump the Deuces Idea:

Keep (As Ac 5h 6s) and Toss (2d 2c)

Expected Hand Average is 252 DIV 46 = 5.478
(minus) Expected Crib Value (Schell) is 6.380
Total is -0.902 [ Endgame Battle so Use 5.478 ]

08x08=064 - 8888, 9999 (Maximum Hand, 8 cuts = 8 Points)
08x07=056 - 4444, 7777 (16 cuts >= 7 Points)
06x06=036 - AA, 3333 (22 cuts >= 6 Points)
24x04=096 - 22, 555, 666, TTTT, JJJJ, QQQQ, KKKK (Minimum Hand, 24 Cuts = 4 Points)
46 ___ 252

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We see immediately that 'Dumping the Deuces' is a bad idea, as it "Maxes Out" at just Eight Points, so it's very likely that we don't have to look any further down the 'Rabbit Hole' for our best candidate. 🐰 🕳

But what about Toss (A A) as compared with Toss (5 6)? These both 'fork over' greater than Six Points into the Dealer's Crib, so it's almost certain that we're in a "Do or Die" situation, although there is some chance we may get to peg out and WIN as the Next Dealer. 🤩

But what about during THIS DEAL? Toss (5 6) has Four Cut Cards (3333) that bring us sudden VICTORY with a Dozen Points, and 4/46 equals 0.087 and thus it shall occur less than 10% of the time. And then the next best prospects for Toss (5 6) are those Twenty Cuts (AA, 22, TTTT, JJJJ, QQQQ, KKKK) that deliver Eight Points, getting us all the way to Hole 117 with certainty. If we combine Four plus Twenty to get Twenty-Four, this means that Toss (5 6) can get us to Hole 117 about 24/46 equals 0.522 and thus it shall occur just over 52% of the time. 🎲

Toss (A A) has only Two Cut Cards (22) that bring us sudden VICTORY with a Dozen Points, and 2/46 equals 0.043 and thus it shall occur less only about 4% of the time. And then the next best prospects for Toss (A A) are those Four Cuts (7777) that deliver Eleven Points, getting us all the way to Hole 120 with certainty, and another Four Cuts (4444) that deliver Nine Points, getting us all the way to Hole 118 with certainty. Finally, after Toss (A A) are another Ten Cuts (555, 666, 8888) that deliver Eight Points, getting us all the way to Hole 117 with certainty. If we combine Two plus Four plus Four plus Ten to get Twenty, this means that Toss (A A) can get us to Hole 117 about 20/46 equals 0.435 and thus it shall occur nearly 44% of the time. 🎯

In summary: Toss (A A) gets us within Four Holes of VICTORY 44% of the time, but Toss (5 6), with slightly more risk as a Discard Choice, gets us within Four Holes of VICTORY 52% of the time. Is there anything else we left out? YES, THERE IS! Toss (A A) has only Six Cuts (AA, 3333) that are LOSERS, and that add NOTHING, leaving us with just Four Points, while Toss (5 6) has a whopping Eighteen Cuts (4444, 555, 666, 7777, 8888) that are LOSERS, and that add NOTHING, leaving us with just Four Points! That's enough added risk both upside and downside to make this quite a challenging puzzle!

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Let's Toss (A A) today, because when we look at the Hand Mappings, we see that Toss (A A) has a better "pattern" of being filled out with more Cut Cards, from a Dozen Points down to Eight Points, and it has far fewer LOSER CUTS, and it is significantly less risky 'over the board' as compared with Toss (5 6), which of course 'locks in' Second Place. 🍒 🍰 🍷

After the 9 Card Cut, we have Six Points, which is sadly just HALF of what we need to WIN. Let's lead the 6 Card and work a miracle. 👳🏻‍♂️

Just to fill out the "Hypothetical Pegging Dance Card," after virtually ANY Cut Card today, it's probably best to Lead a Deuce, and if a Deuce was the Cut Card, Play Off (avoid giving up any pegs); otherwise, peg as necessary.

When leading a Deuce, we can score after Sixteen Replies (22, 555, 666, 7777, 8888), which is over 35% of the remaining deck. Leading from the Deuce PAIR is likely our best Offensive Lead, since it "keeps our powder dry" (those best pegging cards, the 5 Card and the 6 Card). There's probably little Offensive Value in leading the 6 Card. 🪂

Very nice puzzle for a quiet Sunday Morning!

Sunday 5:30 AM

Another "last train out of town" puzzle. I played it looking for a 2 or 7 starter. Didn't happen. Ugh-h.

Sunday 5:45 AM

Game hole cuts (2) and lets see what our opponent responds with after a two lead. Sixteen points by them is not an absolute. dec

Sunday 6:05 AM

Sunday 7:38 AM

I tried for a hail mary.

Sunday 7:55 AM

I'm doing a hail Mary, too. Decided there's more cuts, and little peggers for hope.
Question: how far out does the dealer have to be before you ignore your toss and just go for the win? Dan says 16 "is no an absolute". I look at it a 8 and 8 without pegging, so I go for it if 16 or less is what they need. How about you???

Sunday 8:00 AM

Tough puzzle today! We’re sputtering towards the finish line and need 12 to go out. I’m keeping A-6. Keeping it this way, we improve with every cut except a 4, and a 3 or 8 would be most preferred. Given our small cards, we need to make hay pegging this hand. If we’re able to do so, and if our opponent fails to go out, we could be in excellent peg out range next hand.

Sunday 8:57 AM

Sunday 9:41 AM

I like this option best of all the choices. Lead a 2 and peg for the border!

Sunday 10:15 AM

I just need a favourable cut and to get the Aces in back to back.

Sunday 12:00 PM

At 109-105* playing an Offense strategy for the pegging the win/Loss %s are:

Offense_____________Win %___________Loss %
2-2-5-6______________25.5____________49.9
A-A-2-2______________15.0____________64.5
A-2-2-5_______________9.3____________38.9

2-2-5-6 is considerably best for Win %s and reasonably low for Loss %s so I'll select the A-A to discard.

After the 9 cut I'll lead a 2 and play Offense:

Lead________________Our Pegging Points
2__________________________1.97
6__________________________1.66
5__________________________1.27

Sunday 2:46 PM

A A to dealer.

Sunday 4:09 PM

Always A-A. Lots of scope with 6522 in hand.

Sunday 11:39 PM

I figured paint gives me 6 outta this mess, 3 even better and lone shouldn't be able to do much with the dregs. Unfortunately I didn't get the cut and gave them 2.