Thursday 3:03 AM

Too tough to break up 456 -especially for its pegging value for the dealer and the powerful 23 discard to our crib

Thursday 3:03 AM

We are "Ahead and Dealing," which is the working title of the Cribbage Novel I have yet to start, or have I?! Here, we are looking to leave First Street behind us, and possibly obtain a dominating lead against our Opponent, who currently is already trailing us by Eleven Holes.

With a Deuce-through-6-Card, Five-Card Run, and an 8 Card "kicker," we have several discard choices, ideas such as: Toss (2 3), Toss (5 6), Toss (5 8), or Toss (6 8). Any of these will leave behind a Hand that could aspire to become a Dozen Points, but some will do it more easily and readily than others. As Cribbage Puzzles are studied and examined over a period of time, the better card combinations will stand out the way a good move or combination stands out to a Chess player.

We're going to concentrate most on Keep (4 5 6 8) and Toss (2 3), as well as Keep (2 3 4 8) and Toss (5 6), not only because these are the two strongest themes, but because they also allow us to begin with Hands that will grow to at least Seven Points with certainty, while those other 'contenders' would have us begin with just Four or Five Points, and possibly only end up with Six Points!

Toss (5 6) is a very powerful Dealer Discard, and is perhaps half-a-point better than Toss (5 8), and yet it is surpassed by Toss (2 3) by nearly half a point. Toss (6 8) is not in the same "ZIP Code" as any of those others, so I think we can "discard" this as a potential discard right away. Every idea that can be easily rejected saves us time and effort.

The closer in rank two cards are when they 'add up' to Eleven, generally the more powerful a Magic Eleven they make, and this is especially important when we are choosing to adopt an Offensive Posture during the pegging; therefore, 5-6 is typically the best duo, followed by 4-7, then 3-8, and 2-9, and finally A-X. Does this mean that (4 5 6 8) will be a better Pegging Hand as compared to (2 3 4 8)? In most respects, yes.

But it's difficult to say for certain, as it will depend upon Pone's Hand, and the latter arrangement of (2 3 4 8) has more Small Cards in it, which tend to have higher Pegging Value. Against four Ten (or "X") Cards for example, (4 5 6 8) will likely out-peg Pone 5-to-1, while (2 3 4 8) will probably only out-peg Pone 3-to-0.

As far as extremes: it surprises some players to learn that Toss (2 3) can only reach a Maximum Crib of Eighteen Points, while a whopping Five Discards from this arrangement can actually reach the coveted Twenty-Four Points. Can you recite them all? (Answers Below).

Okay, we're at that stage where we must pick and choose between Toss (5 6) and Toss (2 3). Yesterday, we had a FLUSH that was a double-edged sword, in that it was probably better for Offensive Pegging, but the Relative Score implored us to prevent our Opponent from pegging as best as we could, since our Opponent was only a Dozen Points 'shy' of reaching the Fourth Street Par Hole 96, and Pone's average tally is Ten Holes! Any small 'slip up' during the pegging could have meant surrendering a tremendous Positional Advantage to our Opponent.

Today, we are once again the Dealer, but not only are we Ahead and Dealing, but we have already surpassed our "target" 🎯 by Half-a-Dozen Holes, and so the sun is out, we are "Home on the Range, and the Skies are not Cloudy All Day! This not only means possible copyright infringement, but means we shall gladly adopt a more Offensive Posture today, and that comes if we Keep (4 5 6 8). But when we look even further, I think this is simply the Better Hand, regardless of the Relative Position, and regardless of whether we seek Offense or Defense.

So it goes, let's Toss (2 3) today, because if Toss (2 3) is wrong, we don't want to be right! Good Old Toss (2 3), just how bad could that be?! Sounds like a Midwesterner talking to himself. Yah. Got that right. Could do a lot worse.

After the 5 Card Cut, we now have a Delightful Dozen Points in our Hand, and prospects for a very good Crib. We're hittin' on all cylinders! Those who decided to Toss (5 6) MIGHT have a Twenty-Four-Point Crib, but we ALREADY have the certainty of a Twelve-Point Hand, and it takes a multitude of possible Twenty-Fours to equal the certitude of a Dozen!

Trivia Answers: We could obtain Twenty-Four Points in our Crib today after: Toss (5 6), Toss (4 5), Toss (6 8), Toss (4 6), and Toss (3 6). Both Toss (3 4) and Toss (3 5) are 'wannabe' candidates, as these peak at Twenty-One Points, while Toss (5 8) and Toss (2 5) can reach Twenty Points. Next, we find Toss (2 3) and the 'Cinderella Kid,' Toss (2 4), which on a good day can both attain Eighteen Points. Guess which one does it more often!

Further down the totem pole are Toss (2 6) and Toss (2 8), which, if given the proper nurturing, will boast Sixteen Points. And, to round out the collection, only able to produce the 'Minimum Maximum' of Fourteen Points that *ANY* two cards can attain in Cribbage, are Toss (3 8) and Toss (4 8). The only way to guarantee that any Cribbage Discard can never reach Fourteen Points is to hope that your Opponent is bad at counting!

This says nothing about the odds of actually being able to obtain such an outcome, and as you might imagine, getting Twenty-Four Points after Toss (3 6) is going to happen a LOT LESS frequently than it will happen after Toss (5 6). However, if you need Twenty-Four Points in your Crib to WIN a game (or to avoid a SKUNK), then any discard that has a chance is better than one with no chance!

This is why we shouldn't base our decisions on the extremes, unless we are forced to do so. For example: Our average maximum daily temperature a few miles upstream of Niagara Falls, New York during the first week of October is 60 degrees F (16 deg C), but seventeen years ago this week, we had the "Bomb Cyclone" and "Thunder Snow" in an October Surprise ⛄ storm that dumped several feet of snow during this very week, as the leaves were still clinging to the trees, causing what was dubbed "Arborgeddon" in the city, while yesterday, it was 85 degrees F (29 deg C) outside my door! We expect tee-shirt weather this time of year, but in our emergency kits, we are prepared for the extremes. If we Toss (3 6) in Cribbage, Twenty-Four Points is possible, but it's an extreme outcome that is exceedingly rare.

Applying this knowledge to Cribbage: Once you see enough of these Crib Maximums, you begin to develop a 'feel' for what cards work together, and those that do not. If you remember nothing else from such an exercise, notice that there tend to be 6 Cards in many of those higher-scoring Cribs, something that it doesn't hurt to know in a pinch when you need that Barn Burner of a Crib to secure (or avert) a surprise SKUNK! 🦨

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Ref: Brandon Mitchell: https://www.youtube.com/@ukraine_tbic
Ref: The Future of Ukraine - Meet Nika: https://youtu.be/SGGIZFqkw4I
Ref: October Storm: https://en.wikipedia.org/wiki/Lake_Storm_Aphid
Ref: Year 2006, remember 240p resolution?!: https://youtu.be/ecF3E4nzB4g

Thursday 3:28 AM

Hoping for something like an A-2 or A-3 for a discard or/and the 4-5-6 gets a lift with a cut. dec

Thursday 3:28 AM

2-3 is second best discard to dealers crib and I save the 4-5-6 for pegging.

Thursday 3:37 AM

I don't like the dangling 8. I tossed 56 in my crib, and should end up with 12+ combined points.

Thursday 4:18 AM

23 to the crib and the 456 run in the hand is hard to dislike

Thursday 4:26 AM

Some people would (understandably) read this score as defensive – after all, we have a significant advantage. Shouldn’t we “defend” it by playing cautiously?

On the contrary, the best way to defend an advantage is to increase it by playing offense, when this is feasible. To “defend” an advantage with conservative play makes sense in football, but not cribbage. Our surplus is 8 points (or 7 or 6 depending on who you ask). That’s not really a large buffer on first street. A bad hand or two will knock us right down, and the odds of that happening over the course of the next ~8 hands are pretty high. Ras will quote odds of dealer scoring 8 or less, but his math is wonky, because it is not a matter of scoring 8 or less now, but underscoring our averages by 8 points over the course of many hands.

Meanwhile, pone has a huge deficit, 19 points, i.e. he would have to score 29 points to get into even a theoretically marginal position in the front. So fireworks in the pegging (barring something really extreme and unlikely like picking up 9 points through a nasty run chain b/w a great hand) are not really threatening there.

I would toss 23. It’s the best crib toss, it leaves us with the double-barrel 56 eleven, and there are non-negligible odds for a huge cut. Then again if I looked into the puzzles a couple of hours before everyone else, then spent some hours more plugging away at it, as JQT claimed a few months ago to do, I might come up with a better answer.

Checking Liam, I think this is best, but 56 is not far off at “14.7” to this keep’s “15.1”. That would technically be within the margin of error but the eleven should push this on top.

The cut is great, but not so much as to push me away from offense.

One thing I’ve been musing about is the relative importance of the members of the tripartite anatomy – discard, pegging, and strategy. I used to think discard and strategy were most important because discarding is worth the most points. But consider: most discards are completely automatic. A DCH worthy hand occurs maybe once every four games or so. In those DCH-tier hands, even if you get it wrong, it will probably only be a matter of some tenths of a point, and the odds of this deciding the game are extremely low. But in pegging – multiple times a game will I see a hand and think “yeah, I would have played this differently a few years ago,” or come across a decision that I’m not at all sure about. And in board strategy too – someone who thinks that 71*-84 is a “defensive” position because we have a “positional advantage” is making seriously subpar moves in every game. Strategy and pegging are always relevant, but the fine points of discarding, assuming you know the “basics” (small hand/big hand rules and famous exceptions, relative crib values, etc) are relatively unimportant. Barlow didn’t think pre-endgame discarding was worth studying at all; he was surely wrong in this, but it is true that it is only worth so much. I would say it is my weakest area, but I don’t lose any sleep over it.

Thursday 4:42 AM

2-3 all the time with this hand makeup.

Thursday 5:32 AM

Rob..starts us off today by taking the words right out of my mouth!

Thursday 5:32 AM

The 8 does seem misplaced, but the hand does improve on any cut, and the powerful 23 is then available for the crib. At one time I would play the 2348, which still allowed for a top 5 throw of 56. So this would be a hand where my strategy has evolved over the years.

Thursday 5:52 AM

Both 2-3 and 5-6 look good. I think you'd do alright choosing either, but perhaps a wee bit better after 2-3?

Thursday 7:06 AM

Toss 2-3 is at 57% of all votes and about 90% for those bothering to comment. Looks like I'm in lockstep with the majority today which is reassuring, as is the 5 cut. Hopefully, will make 20+ points on this hand - I'll play CribPro and see what happens.

Thursday 8:19 AM

I decided to try 5-6 in the crib versus 2-3. This keep also has a magic 11.

Thursday 8:26 AM

Wondering if CribEDGE made a mistake today. This choice does not seem popular:

Keep: Two of Clubs, Three of Spades, Four of Diamonds, Six of Clubs
Toss: Five of Hearts, Eight of Spades
Worth: 5 / Bonus: 8

Thursday 8:51 AM

In 2-3 I trust. Well, 2-3 to crib and 4-5-6 in hand. Going this way today.

I need to go find a treatise on pegging with 4-5-6 as dealer given the multiple comments about it today.

Thursday 11:19 AM

The reason for the submission was twofold. First, the Cribbage Pro app said 2-3-4-8(5-6) was best for expected averages, with an average hand of 8.26, and an average Crib of 6.05. 4-5-6-8(2-3) has an average hand of 8.22 and an average Crib of 5.80. The average hands are fixed. But the average Cribs are not static, and therefore subject to the negative delta of the other 4 cards dealt. Halscrib performs these calculations while us mere humans are forced to apply memorized averages. It looks like Cribbage Pro gives the (2-3) a lot more negative delta holding 4-5-6-8 than it does (5-6) holding 2-3-4-8. I wanted to see Halscrib's numbers. I am sure they will not agree with Cribbage Pro's.

Secondly, does anyone think on Defense the (5-6) toss deserves serious consideration? But at this score I am +6, and my opponent is -21. So the (5-6) definitely stays in my hand.

Thursday 11:27 AM

(2 3) for me too. Let's go for the throat right here and see if we can put this game out of reach, and threaten to skunk. The 5 cut certainly creates all the more room for optimism.

Thursday 1:43 PM

I think it's between 4-5-6-8 (2-3), 2-3-4-8 (5-6), 2-3-4-6 (5-8) and perhaps 2-3-4-5 (6-8):

4-5-6-8: 5pts + 6¾pts (Schell: 7.00) = 11¾pts

2-3-4-8: 5pts + 6½pts (Schell: 6.63) = 11½pts

2-3-4-6: 5pts + 5½pts (Schell: 5.48) = 10½pts

2-3-4-5: 4pts + 4½pts (Schell: 4.63) = 8½pts

Potential:

4-5-6-8: Improves with AAAA, 222, 333, 444, 555, 666, 7777, 888, 9999 + 16xXs = 46 cuts = 46/46 = 100.0% up to 8/9/12pts with 333, 444, 555, 666, 7777 = 16 cuts.

2-3-4-8: Improves with AAAA, 222, 333, 444, 555, 666, 7777, 888, 9999 + 16xXs = 46 cuts = 46/46 = 100.0% up to 8/9/12pts with AAAA, 222, 333, 444, 555, 888 = 19 cuts.

2-3-4-6: Improves with AAAA, 222, 333, 444, 555, 666, 7777, 888, 9999 + 16xXs = 46 cuts = 46/46 = 100.0% up to 9/11/12pts with 222, 333, 444, 555, 666, 9999 = 19 cuts.

2-3-4-5: Improves with AAAA, 222, 333, 444, 555, 666, 7777, 888, 9999 + 16xXs = 46 cuts = 46/46 = 100.0% up to 7/8/9/10/12pts with AAAA, 222, 333, 444, 555, 666, 8888 + 16xXs = 39 cuts.

Position:

We have a good lead after probably two deals so I'll play Defense.

Pegging:

All these hands will peg very well. Perhaps 2-3-4-5 the best.

Summary:

4-5-6-8 has the best starting value by ¼pt over 2-3-4-8 but 2-3-4-8 has 19 cuts for 8-12pts compared to 16 cuts for 8-12pts with 4-5-6-8. Also I think 2-3-4-8 will peg better than 4-5-6-8 so I'll throw the 5-6 to my box.

Thursday 1:45 PM

At 24*-13 playing a Defense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

_______________Pone's
Defense___Hand_Pegs____Crib_Total____W7 %____W8 %
4-5-6-8____8.22+(-2.02)+6.76=12.96____41.0____69.2
2-3-4-8____8.26+(-2.15)+6.52=12.63____38.7____67.3
2-3-4-6____8.46+(-2.17)+5.48=11.77____36.6____65.3
2-3-4-5____8.54+(-2.07)+4.66=11.13____35.4____63.5
3-4-5-6____8.46+(-2.15)+3.65=10.98____35.7____64.2

Defense_______L7 %____L8 %
4-5-6-8________5.1_____6.3
2-3-4-8________5.4_____7.2
2-3-4-6________5.5_____8.0
2-3-4-5________5.6_____8.6
3-4-5-6________5.1_____7.9

4-5-6-8 is best for expected averages by 0.33pt. and is slightly best for Win %s and very slightly lowest for Loss %s so I'll select 2-3 to discard.

After the 5 cut I'll play Optimally to the lead (cautious offense).