Monday 3:03 AM

One of the each. Lead the ace.

   

Monday 3:10 AM

1. Don't cut a Jack.

2. Lead the 4 and I can win on responses of Ace, 2,3,5,6,9 and X = 36/46.

Beyond that, it's in the hands of the Fates.

   

Monday 3:32 AM

As Pone in the 'Dead Hole' (it starts out like an old, country song...), we just need just One Measly Point in order to WIN, but the Dealer sits ever-so-smugly on her sun-bleached saddle, with glistening, fiery red hair that bursts out from beneath a torn and tattered cowboy hat, one that has seen way too much for a God-fearing man to even contemplate, at Hole 118, requiring only Three Points to defeat us. This is a very practical Endgame Puzzle by Andy (muesli64), and worthy of our careful study. 👢

Since we were dealt NO Jacks, there is exactly 4 DIV 46 equals 0.087 or almost a 9% chance that a Jack Cut will occur, after which the Dealer would need only One Point to beat us. Therefore, this should not happen over 91% of the time; but since it *could* occur, and since it would drastically alter the nature of this Endgame Battle, we would be very remiss if we ignored the possibility.

In this type of Endgame Scenario, we should not only retain at least One Point, but due to the potential for a Jack Cut, we should also have some kind of plan to Peg Out buried in our back pocket, just in case.

This latter idea will also come in handy if the Dealer scores upon our Lead Card, since doing so will not only tie the score at Hole 120, but will also ensure that, unless we can peg out and WIN and do so FIRST, that the Dealer will then peg out and DEFEAT US!

There are many ways to hold enough points today, because not only do we have several combinations of Fifteen, such as: 5-Q, A-4-Q, and A-5-9, but also since retaining either the 5 Card, or two cards that 'add up' to Five, such as the Ace and the 4 Card, will always guarantee that we shall hold at least Two Points after ANY Cut Card.

In fact, of the "6 choose 2" equals Fifteen unique Discard Choices that we have today, only two of these: Keep (A 8 9 Q) and Keep (4 8 9 Q), could possibly fail to deliver us Two Points after the cut occurs. Ironically, while this fact gives us more options and thus greater flexibility via Thirteen viable Hand Choices, it also tends to make our decision a bit more complicated, and produces what economists sometimes call, "Choice Paralysis."

What to retain in our Hand, and what to stow in the Enemy Crib: those are indeed the issues that concern us today. But if that were the only problem, then this would be identical to any other Cribbage Puzzle. What differs here today is the crucial importance of the Pegging Battle which follows, because a tiny mistake or miscalculation here will cost us not just a point or two: it will cost us the game!

Let's just go over some pegging basics, especially for any newer players: The main reason that the Dealer has the Pegging Advantage in Cribbage is that the Dealer can score with ALL FOUR cards, while Pone can only score with THREE cards, a reduction of 25%. It's as though the Dealer were given an extra "at bat," or tantamount to Pone always getting a "Called Strike" upon the first card played. Is there ANY card that we can lead after which, if it gets PAIRED, we can ALWAYS score? Actually, today there are - gasp! - NONE!

We barely have any retaliatory pegging plays at our disposal here: perhaps the 8 Card Lead gives us a glimpse of hope because if the Dealer were to 'snag' a (15=2) with a 7 Card Reply, we might also be holding our 9 Card in order to score the 7-8-9 Run and WIN. But look at the poor characteristics of such a gambit: we would risk that the Dealer might instead score by PAIRING the 8 Card, and now the score is tied at Hole 120, and the Count is at Sixteen, and it's our turn to play a card!

And notice that in order to 'set up' such lousy odds of scoring, we would have to retain TWO Middle Cards, both the 8 Card and 9 Card, in order to orchestrate such a pathetic plan! Now, if when all is said and done, we happen to be holding both the 8 Card and the 9 Card and maybe we have done so FOR ALTERNATIVE REASONS, if the Cut Card is another 8 Card, then leading our 8 Card is NOT a poor idea! However, deciding NOW to retain both the 8 Card and the 9 Card in order to execute such a plan is a bad idea! Make sure you understand the difference.

We are still in the mode of choosing our STRATEGY, and a PLAN is NOT a STRATEGY! Our PLAN will come later. Our STRATEGY should recognize that the options for Retaliatory Pegging are dismal with this card arrangement, and therefore we want to hunker down and play in more of a SAFE mode or manner. What does this mean; what does it entail? Our chances for scoring with our Second Card Played, however, becomes a bit more interesting. Is there a Lead Card we can play in Cribbage that will GUARANTEE that we get a 'shot' at scoring (15-2)?

Note that if we lead an Ace, that while it could optimize our chances of obtaining (15-2), it does not necessarily make it a certainty that we shall have a chance to score (15-2) with our Second Card Played. For example, the Dealer could PAIR the Ace, and now, unless we have PAIRS Royal, no matter what we play, it is the Dealer who actually has the opportunity to score (15=2). (Note that for decades now, as part of my own personal convention, just for clarity, I use the "hyphen" to denote all Pone Pegging Scores, and I use an "equal sign" when denoting all Dealer Pegging Scores. I wonder how many people may have noticed this over the many, many years?)

New players sometimes wonder why the 4 Card Lead in Cribbage is so ubiquitous and so powerful, and oftentimes, the seasoned player cannot explain the real reason! And this is it: a 4 Card Lead GUARANTEES that (of course, always depending upon what cards are available to us) Pone will always get a numerical "swipe" at scoring (15-2)! And, after the numerically-superior Ten (or "X") Card Reply, we can easily score (15-2) with our Ace and WIN the game today. But if the Dealer PAIRS the 4 Card Lead, we are probably in the same 'bad boat' as before. The important consideration to remember of course is that: our Opponent cannot see our cards! But is the 4 Card Lead really the best option when we are at Hole 120? More on this later.

That's a lot of "Story Time" and we have yet to even begin choosing our Hand, let alone our Discard! But I think you can see where this is headed: retaining the A-4 duo seems like a no-brainer, and it's so automatic with most players, these might be retained without any thought required. We know these are good pegging cards, and that together, they ensure we have points enough. But newer players should understand WHY, and I hope this helps. And it should become clear that if we can easily choose 50% of our desired Hand so readily and easily today, it should make the choice of those last two cards a bit easier. What shall we retain next?

The Ace, Deuce, Trey, 4 Card, and 5 Card all have high Pegging Value, but when thinking about Opportunistic Pegging, we might not immediately conclude that the 5 Card will help us as much as it may hurt us! This is where this puzzle becomes very difficult, because winning could involve AVOIDING the chances of the Dealer pegging almost as much as it might entail us scoring (or pegging). I say "almost" because, as the score indicates, ANY pegging by us shall give us the WIN, while the Dealer needs either to score twice, or score a RUN. A RUN involves three cards, and since the Dealer plays Second, a RUN cannot be scored by the Dealer until our own Second Card has been played.

These are all basic "building blocks" of the nuances of pegging, and I list just a few of these as they pertain to the starting score today. There's a LOT going on in any Cribbage Endgames, and every point and every card played can and does alter everything, but it's always very straightforward and logical. But along the way, it can become quite deep and complicated. Part of the complication today has to do with the Relative Score, and a thing called BIAS. This may affect the Lead Card we choose; more on this later.

Some players will "latch onto" the 5 Card today, while others (and I'm inclined to be of this group) will 'shy away' from it. I am thinking that Keep (A 4 8 9) and Toss (5 Q) is our best choice, and it's still very difficult to explain why, although I have certainly tried! Keep (A 4 5 8) and Toss (9 Q) may be very popular, and it's definitely a sound idea; many players will simply retain the four lowest-ranking cards in such situations, and doing so is based upon very solid logic. If it didn't have the possibility of Zero Points, I actually like Keep (A 8 9 Q) and Toss (4 5), because it seems like a very defensive idea.

I do strongly believe that some (not all) of our winning chances today could involve a bit of Defensive "Ducking and Dodging" during the pegging, and a 5 Card is often NOT good for this. Obviously, after the cut, we'll need to choose a Lead Card, and while we have few retaliatory ideas at our disposal today, the 4 Card Lead idea, at least prior to seeing the Cut Card, still seems to be likely the best plan we have. There is a hidden danger if we 'ditch' the 5 Card, and that comes when we examine leading either the Ace or the 4 Card: If we lead one of only two Small Cards, we create a Hand with a Lone Small Card; therefore, those who Keep (A 4 5 8) can lead an Ace or a 4 Card with much less danger.

After this extensive (but still not entirely exhaustive or completely comprehensive, even after nearly 2800 words!) analysis, let's Keep (A 4 8 9) and Toss (5 Q) today. Why so much dialog and effort spent when we're at Hole 120? Because winning THIS game is *just as important* to me as winning ANY OTHER GAME, is it not?!

After the 7 Card Cut, we now have Five Points in our Hand, but One is as good as Fifty, and while we could still WIN if we peg One Point before the Dealer can peg Three Points, we can also prevail and WIN with our First Hand Show, as long as the Dealer does not accumulate Three Holes during the pegging. Ah, the pegging. A lot of players who post here take "Hand of the Day" too literally, and sometimes do not even mention which card they wish to lead! But that's at least half of the challenge, or maybe more, in a puzzle like this.

Since the Cribbage Statistics tell us very clearly that the Dealer tends to peg an average of about 3.5 Points, we should approach the pegging in what I call an "Opportunistic Mode," and this simply means that if the Dealer has an opportunity to score upon our Lead Card, we wish to make it such that, as Pone, we have a very high probability of scoring if the Dealer scores. Since the Dealer can only score Two Points at most after any single Lead Card, as long as we can parry the Dealer, this will secure a WIN for us.

Since a Jack Cut did NOT occur, with the Dealer still at Hole 118, we have just enough "wiggle room" to 'give up' Two Points and still WIN, as long as we can immediately retaliate and score or 'parry' the Dealer. All players seem to "know" that the 4 Card Lead is usually optimum, but while our calculators are still warm, let's examine WHY:

After we lead the 4 Card, we can score and WIN the game after Thirty-Two Replies (AAA, 2222, 3333, 888, 999, TTTT, JJJJ, QQQ, KKKK), or 32 DIV 45 equals 0.711 or about 71% of the remaining deck. Note that if we led the Ace, we can still score after Thirty-One Replies (444, 555, 6666, 888, 999, TTTT, JJJJ, QQQ, KKKK), or 31 DIV 45 equals 0.688 or about 69% of the remaining deck. It's exceedingly close, but the Ace probably serves us better later on during the pegging, since even a "go" clinches this game in our favor. But WAIT!

Because, it's not so simple, and if you thought the Discard Decision was complicated, we're just getting started! Now, we have to really give some additional thought to the Relative Score, and a phenomenon called "bias." The Relative Score says the Dealer needs to either score TWICE, or score a RUN, and we need merely a "go" or Last Card to walk away with a WIN. This might lead some players to lead from the "higher ranking" side of the ledger, rather than leading the 4 Card! Sure, we have 71% odds of scoring upon the Dealer's Response to our Lead Card, IF the Dealer were to shuffle the cards and play one! "Bias" means that our Opponent is TRYING TO REMAIN ALIVE and also WIN the game!

If we lead an Ace or 4 Card, the Dealer SHOULD assume we have the alternate or respective card that 'adds up' to Five; similarly, if we lead a Deuce or a Trey, the Dealer SHOULD predict that we have the other, respective or 'complementary' card. Now, if we lead a 9 Card, we can score and WIN the game after Nineteen Replies (AAA, 2222, 444, 555, 777, 888), or 19 DIV 45 equals 0.422 or about 42% of the remaining deck.

But notice that MOST of these are seemingly a lot "safer" or a bit more difficult for the Dealer to assess the danger of playing! That is to say, if we lead a 4 Card, the Dealer KNOWS that any Ten (or "X") Card has a high "bias" for being scored upon; however, after the lead of a 9 Card, at least a Dozen of the dangerous replies are fairly well-hidden, and thus lower "bias" in terms of what the Dealer can predict.

I'm a bit worried if the Dealer, using BIAS as a guide, responds to our 4 Card Lead with a 7 Card. Do we have a logical reply? Now we have fully "switched gears" from STRATEGY, which mostly preceded the Discard Decision, to PLANNING! A PLAN is something that is more concrete, like "What do we do if...?" Some further logic here tells me that we might be in trouble if we lead EITHER of our Small Cards (the Ace or the 4 Card)! It all has to do with the extreme "BIAS" that the Dealer is forced into using when we are at Hole 120. It also has to do with simple Hand Composition: If we begin with two Small Cards, and lead one of these, now we have created a remaining hand that has a Lone Small Card, and at the given score today, this could likely become a liability.

Regardless of what we THINK we should lead here, is there a Cut Card that would change our minds and cause us to lead a different card today? Remember the earlier idea or 'whim' we covered that after an 8 Card Cut, we might like to try leading our 8 Card (as long as we have the 9 Card ready to claim VICTORY)? But does such an idea really make sense when we have the 4 Card Lead? It's debates and discussions such as these that make Cribbage such an exciting, intoxicating game!

Maybe with the 7 Card Cut that actually occurred, the Dealer would be slightly more inclined to "pounce" upon an 8 Card Lead with a 7 Card, thinking the odds that we have another 7 Card are now reduced; but the danger of either a 6 Card or 9 Card Reply entails up to Eight Cards, or nearly 18% of the remaining deck! Do we revert to the Old Stand-by 4 Card Lead? Or do you prefer the "deception" tactic of leading the 9 Card?! I think I'll lead the 9 Card, just for the LULZ! (Does anybody over age fifty even know what THAT means??)

Wordle 702 3/6 (There's no place like Nome!)

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Monday 4:40 AM

Thank goodness the cut wasn’t a Jack 😅

   

Monday 5:18 AM

As mentioned above looking for as many possible responses to get two points after our Ace lead. If twos or threes get involved on their next play we might get the count high enough to get a go and game. dec

   

Monday 5:20 AM

I considered and discarded arguments for a few of these. If going for win by “go”, it makes sense to keep the highest ranks, but dealer may hold a couple of low cards and peg out before we steal last card. I decided to go this way as a hybrid between offense and defense. Ace lead could easily draw an 8 or 9, and the 4 could help prevent dealer from making trouble with low cards at the end of the first sequence. I can see the case for other choices, but went this way because it’s what I would’ve done under the time constraints of a real game, and I’m not sure it isn’t really best, anyway. Good arguments for other picks too, though.

   

Monday 5:26 AM

I forgot when making my selection that I had the opening lead, and for some reason I was looking at this from the vantage of responding to all opening leads...(Was going to say I shouldn't keep the A as a pegging liability, so this is clearly wrong)... This would be the best keep I believe as dealer, but clearly I should have kept the A as pone. My re-selection as pone would be (A 4 5 9)!

   

Monday 5:38 AM

I’ll lead the ace. Win with a 4,5,6,8,9,10,J,Q,K response.

   

Monday 6:01 AM

Today's excellent puzzle seems to be the thunderdome of end of gam pegging. I find myself at the fabled and feared hole 120. There is no time to bewail the fates that left me one short of victory. Then again the enemy was stranded at 118.

Top concerns, not to give up points on a "go" and spreading out the hand. Also not to cut a jack....

mmmm 7 cut is better than a Jack... Am I in the "herd" today since I kept A-4-5 and there seems to be several permutations?

   

Monday 7:29 AM

Today’s puzzle has nothing to do with point count in the hand but how can I peg 1 as leader before O pegs 3. So I need to come up with my pegging plan and throw what I don’t need. I have no concern about counting my hand because I probably won’t.

I won’t lead an A, 5 or Q from this hand since the O will probably get 2. I would keep an A and face if I were dealer in this hand. If nothing else it increases my chance of a 31 and a guaranteed win if I can keep O from pegging.

My first card to consider is the 8. If dealer throws the 7 I’ll get a run with the 9. If opponent pairs the 8 we’ll be at 16. 25 at this point does not seem too dangerous since the dealer keeping the 6-7-8 at this point is meaningless. This keeps the 8-9 in my hand and moves me toward keeping the A-5 or maybe A-4 but the 5 will get me closer to 30 so I can play my A. If dealer keeps an A I’m always in a bad situation unless I can hit 31, which is never a given, especially with 2 cards.

What if I throw the 4 first? I’ll assume the dealer will not throw a 10 counter so my A won’t win the game. I’ll also discount a 3, 5 & 6 as the next play, that leaves me the 2, 7, 8 & 9 to counter. On a 2 I’ll win with the 9. The 7 puts it at 11 which isn’t likely but I could make the count 20 with my 9 in that case also. Dealer and I will then be playing for the next peg. (I’m assuming I must be the first to peg last card or 31). If opponent throws an 8 or 9 I win it with a pair. It seems the best throw to the crib is the Q-5 since the dealer will avoid allowing me to use either of these cards to win.

The 9 is the only card left to lead. I’ll discount dealer playing an A, 6 or 9 on this since they are the cards O would most likely want to see. I only need 1 point so a pair or 15 wins it for me. 8 and 10 would be dangerous for the dealer to play since I may be playing from the middle of a run, which would not be a bad strategy given the choice. This leaves 2, 3, 5, 7 or face. Any face card puts me in a bad spot since I have to either play my A or put the count between 22 and 29 which give the dealer an opportunity for a 1 card 31. If I were dealer, I would play a Q or K if possible but avoid the J since my possible 10 would win it for me. And as dealer I would be inclined to keep a Q or K in this situation since the opponent would be inclined to throw them in my crib. Therefore, they can pair them. The 5 & 7 are both winners for me. The 2 or 3 would get my 8 so dealer is stuck putting us in the 22-29 range. I only have the 4 & A left at this point and I’m not fond of the odds of playing either for a 31. I don’t like the 9 lead at all.

I really need to win by getting the first peg or some sort of points before the first peg. The A in my pocket will help me with this. If dealer has nothing but a bunch of small cards, I’m probably toast unless I can hit 15. As dealer I would definitely save any Aces for last or guaranteed points.

Dealer always has the advantage in cases like this and all you can do is keep cards you THINK will give you the best chance of pegging.

When I fist looked at the hand, I thought the 8 might be the best lead, but it turns out to be my favorite lead when I don’t know what else to do – the 4. Oh, by the way, did I mention I’m throwing the Q-5?

Now that I’ve seen the 7 cut, I’m more comfortable with all of my considerations. I can afford to give up a pair for any pegging and my 4 lead stands for the reasons above. I think a J cut is the only thing that should affect the dealer’s play.

   

Monday 8:33 AM

My choice is predicated on what will the dealer probably not play on my first card. So I am going to try for a go with the Q lead. I think most opponents are afraid to pair or make it 15. I also like the A-4-8-9 keep

   

Monday 9:03 AM

Do see the five as a liability needing one peg. None among these six cards averages a full peg point for n/d; so why not hold the cards that give best chance to score on 2nd card pegged. After the cut n/d knows that game is won if dealer pegs no more than two. So if unable to peg as response to dealer's first card, grab any two or pay off in a way to minimize dealer pegs. N/D has two ways to win this game - dealer has only one. Approach with confidence - no time for timidity.

   

Monday 11:33 AM

I won a tournament, waiting for an A lead. Too common.

   

Monday 1:26 PM

We need to stop Dealer pegging 3pts and preferably peg 1pt first. I think we need to keep A-4 for the lead and a possible 15 with a ten card reply. I don't think we should keep the 5 and I feel it is better to separate the 8 and 9. So for me it's A-4-8-Q or A-4-9-Q. I think I'll go for A-4-9-Q and throw the 5-8.

   

Monday 1:31 PM

At 120-118* playing an Optimal strategy for the pegging (cautious offense) the Our Peg Out %s and Dealer Peg Out %s are:

Optimal______Our Peg Out %_____Dealer Peg Out %
A-4-8-9__________78.8________________19.3
A-4-5-8__________76.3________________18.6
A-8-9-Q__________75.3________________21.0
A-4-9-Q__________73.5________________24.7
A-5-9-Q__________72.8________________22.4
A-5-8-Q__________72.7________________22.6

A-4-8-9 is best for Our chances of pegging out by more importantly, I think, A-4-5-8 is lowest for chances of Dealer pegging out. So I'll select 9-Q to discard.

After the 7 cut I'll lead the 8 and play Defense:

Lead_______Win %_____Loss %
8__________36.1_______5.1
4__________31.3_______7.4
A__________31.3______10.4
5__________28.3_______9.9

   

Monday 4:11 PM

Four lowest cards for me!

   

Monday 5:45 PM

Oh boy, what an enjoyable endgame conundrum this hand has become! My thought process was simple. Definitely keep the Ace, keep the 4 to lead, no idea why I kept the 5 (it seemed a little dangerous) but it also seemed like a decent idea and I kept the Queen because of this magic 11 I keep reading about. All in all, should the game get to counting the hands, I wanted a 15-2.