Sunday 3:15 AM

5-9 interests me with 20/46 cuts being an X or a 2, but I'll take the guaranteed eight points.

Four card sixteen could bring 15/2 and 31/4 against the right Pone hand:
X(10)-5(15/2)-5(20/2)-9(29)-go-A(30)-A(31/4).

Sunday 3:50 AM

We are the Dealer sitting One Point 'shy' of being right-smack-dab 🎯 atop the Fourth Street Par Hole 96, and as we are nearly 'fit-to-be-tied' 🥨 with our Opponent, this means that given reasonable cards and after applying a modicum or adequate amount of skill on our part, we should be able to prevail and WIN such a game more often than not. 🤩

In fact, if we deal ourselves an "average arrangement" and get similar-quality cards during our Next Deal as Pone, then in almost all cases I can imagine, we should find smooth-sailing toward VICTORY coming our way, unless we stumble or fumble badly here, which is always possible in Life and in Cribbage (as it is in virtually everything else).

We dealt ourselves two Small Card 🍐🍐 PAIRS: Aces and Treys, alongside a 5 Card and a 9 Card, so it's tempting to instantly "pop" those two Treys into our Crib without any hesitation, and Toss (3 3), and be on our way: 🎼 "Hey-Hey, Ho-Ho, 🎵 Toss Trey-Trey, and 🎶 We're Good-to-Go!"

But I suppose we might also wish to consider Keep (A 3 3 9) and Toss (A 5), although for the life of me, not only is Toss (3 3) worth more, but Keep (A A 5 9) also starts off with more.

We could even look slightly astray and examine Keep (A A 3 3) and Toss (5 9) here, or venture even further afoot and check out Keep (3 3 5 9) and Toss (A A), but I'm not sure what might compel us to 'wander so far' from the 'clear and cloudless' path, because I cannot see how we beat Toss (3 3) today!

But let's look at the score closely, because as the Dealer at Hole 95, we need the proverbial Twenty-Six to go out, and if we test Colvert's Theory and get this much from our pending Three Counts, we should have a good chance of success here unless Pone can traverse Twenty-Five Holes and do it sooner than we can accumulate one more, and as the Current Dealer this seems to be stacked very much in our favor.

Puzzle Poster scottcrib says he chose to Toss (A A), but I'm not sure why we would need to do this, as this seems like a Third Place Idea! In fact, if we felt the need to "roll the dice" on scoring a 'big bundle of joy' here, we would probably have to look more closely at the possible Double-Double Run with Keep (A A 3 3), but I see no need to incur the added risk this entails.

Let's Toss (3 3) today. 🍎 🧀 🥝

After the Queen Cut, we have Eight Points in our Hand, and at least the PAIR of Treys in our Crib.

I'm flummoxed over this puzzle, because Toss (3 3) seems clearly superior, and after this, we could maybe debate whether Toss (A A) would ever compete with Toss (5 9) for Second Place on the Podium, but while that battle between Second and Third Place might be contentious, I see no challenger that comes anywhere close to Toss (3 3).

I'll include a full Hand Mapping (below) of all four main ideas, just to examine whether anything is being overlooked. I fail to see how we can go wrong today by choosing Toss (3 3), but that's certainly not to say that we couldn't lose, which could happen with any discard we make here. But I feel strongly and would predict that such chances of losing should happen LEAST OF ALL after Toss (3 3).

In the actual game, Toss (A A) was chosen, and it was also stated that a Trey Cut occurred, and while that doesn't help my Hand Choice of Keep (A A 5 9) today, it would TRIPLE the Crib since it would yield PAIRS Royal for Six Points, and that's before we even consider any contribution from Pone.

What would concern me most is that after Keep (3 3 5 9) and Toss (A A), there are a whopping Thirty-Three Cuts (AA, 2222, 555, 6666, 8888, TTTT, JJJJ, QQQQ, KKKK) that will yield Six Points or less in the Hand; and yet if we start with Keep (A A 5 9) and Toss (3 3), we always begin with at least Six Points, and we only fail to add more points after Ten Cuts (2222, 33, 7777).

Here is a Hand Mapping of the Top Four Ideas:

(95*-96) (Ah Ad 3d 3h 5s 9c) Cut = Qh, by scottcrib, Nov 19, 2023

Keep (A A 5 9) Toss (3 3)

Expected Hand Average is 380 DIV 46 = 8.261
Expected Crib Value (Schell) is 5.940
Total is 14.201

08x12= 96 - AA, 555, 999 (Maximum Hand, 8 cuts = 12 Points)
28x08=224 - 4444, 6666, 8888, TTTT, JJJJ, QQQQ, KKKK (36 cuts >= 8 Points)
10x06= 60 - 2222, 33, 7777 (Minimum Hand, 10 Cuts = 6 Points)
46 ___ 380


Keep (A A 3 3) Toss (5 9)

Expected Hand Average is 342 DIV 46 = 7.435
Expected Crib Value (Schell) is 5.430
Total is 12.865

04x16= 64 - 2222 (Maximum Hand, 4 cuts = 16 Points)
24x08=192 - AA, 33, 8888, TTTT, JJJJ, QQQQ, KKKK (28 cuts >= 8 Points)
07x06= 42 - 7777, 999 (35 cuts >= 6 Points)
11x04= 44 - 4444, 555, 6666 (Minimum Hand, 11 Cuts = 4 Points)
46 ___ 342


Keep (3 3 5 9) Toss (A A)

Expected Hand Average is 310 DIV 46 = 6.739
Expected Crib Value (Schell) is 5.380
Total is 12.119

06x12= 72 - 33, 4444 (Maximum Hand, 6 cuts = 12 Points)
07x08= 56 - 7777, 999 (13 cuts >= 8 Points)
25x06=150 - AA, 555, 6666, TTTT, JJJJ, QQQQ, KKKK (38 cuts >= 6 Points)
08x04= 32 - 2222, 8888 (Minimum Hand, 8 Cuts = 4 Points)
46 ___ 310


Keep (A 3 3 9) Toss (A 5)

Expected Hand Average is 278 DIV 46 = 6.044
Expected Crib Value (Schell) is 5.450
Total is 11.493

04x14= 56 - 2222 (Maximum Hand, 4 cuts = 14 Points)
02x12= 24 - 33 (6 cuts >= 12 Points)
03x08= 24 - 999 (9 cuts >= 8 Points)
13x06= 78 - AA, 555, 6666, 8888 (22 cuts >= 6 Points)
24x04= 96 - 4444, 7777, TTTT, JJJJ, QQQQ, KKKK (Minimum Hand, 24 Cuts = 4 Points)
46 ___ 278

Sunday 3:55 AM

I went for the guaranteed points and threw 3 3.

Sunday 5:01 AM

I'll keep the points. Need offense to get as close as possible for next deal.

Sunday 5:35 AM

I can get points from the three facets of the game here. Example... eight in hand , four in crib and three in the pegging. Depending on leads, discards and the starter card would probably vary. dec

Sunday 5:36 AM

Something is amiss with this puzzle. Not sure what happened.

Sunday 6:34 AM

Even though these cards aren’t out of this world, and I want to aim for the high end of things, three-three is a strong enough toss that I would adhere to the small hand rule. Also, as I’m sure multiple people have already pointed out, AA59 has the eleven b/w a five, so many hands – not just XXXX, but also plenty of XXMMs and so on depending on pone’s moves – we’ll get a 31-4, or at least parley our aces for two+go, and a 15 in the second series. AA33 just has too many misses/glancing cuts for my liking, I also don’t particularly like 59 in the crib – 33 is much better.

Checking Liam, I’m confident this is right. It beats out toss 59 by a full point in mean hand+crib. 13 points, getting us to 108 by the show alone, is 7% more likely with this toss, and that trend continues (in fact increases) as you go up, so despite the hopenotic potential of the AA33, it’s best for a big score too.

I think an interesting problem is how to handle a X lead. Do you play “greedy” and drop the nine? Or go for a pat two, with some opening to parley the aces anyway? I feel the cut is sufficiently unhelpful that it’d pay to be greedy. But in general – max offense as I’m sure everyone else has said already.

Back to the annotated game. As you’ll recall, the cards had been quite lively. I went from 15*-21, to 41-33* due to great luck in the hand/crib, then the luck flipped and we ended up at 52*-63.

5.) At 52*-63, unless my cards are pretty bad, I’m on defense. I was dealt A249TK – damn, those *are* fairly bad cards. Ofc tossed 29 in the crib and hoped for the best.

Bozo got 368JKK and (imo) correctly risked the 68 to hold 3JKK. He wasn’t deterred by how badly that worked out for me when I did the same dang thing last hand :)

The cut was… an 8.

For me, with 289?? In the crib, and a four point hand – I’m still basically inclined to defense, but would try to get some safe pegs. I have *some* hope that I’ll have a few points in there, and Bozo’s position is threatening.

For Bozo, with a two point hand, and a cut that hits his 68, he played maximum offense. He didn’t think there was much hope of slowing me down with that cut/toss, so he wants to at least get as near par as possible. Indeed, he played what MtE would call “disgusting offense” and pulled some shenanigans on me.

Pegging went: J-A(11)-3(14)-T(24)-“go”-4(28-1)//K-K(20-2)-K(30-7)

I think Bozo’s Jack lead was gutsy but clever. He’s aiming at either a two-on-none with his Kings (not at all impossible with the configuration he held), or a two-on-one trapping my lone King as a best case scenario. Leading the Jack drives my own king off the play, if I have one – which in this case I do.

So to the Jack lead, my cards are weak enough that I have half a mind to entice a run again for the 31. But playing the Ace instead seems to work something like ~75% as often (that’s gut math) and doesn’t immediately give up points.

Bozo plays the white knuckle three, risking a run, risking all sorts of things.

Now I can play my ten or my king. Of course I play the ten because kings are harder to trap in a two-on-one… in theory. Then I’m forced to play my four letting Bozo steal last card.

And next came the rattle – Bozo’s dream has come to life.

I think it’s worth looking a little more closely at how Bozo played this. What if he had led, say, the King instead? First off that misses out on the two-on-none possibility. But even in a two-on-one – say the second series goes K-?-J. Four queens out there would give him four; two jacks would give him three. That makes 22 points, statistically. In K-?-K two kings will give him 7 – that’s only fourteen points. But when you weigh that against the possibility of parleying his kings, I think it would probably bridge the gap, especially holding a hand that’s relatively favorable for a two-on-none (remember, LLLX is the most common dealer configuration, occurring about 10% of the time, and that’s not the only one that would allow this).

Also, leading the Jack might get him an immediate run if I’m holding XXXX, though the odds of this are only about 1 in 20.

What if he had led the three? That’s what I would have done, frankly. You have a chance to pair a Jack or King response, and it still leaves an opening for a two-on-none or trap in the second series. But Bozo was aiming high – the Jack lead drives my king off the play. So it was certainly a wild move, but perhaps justifiable under the circumstance, and it worked out well for him. I’ve experimented with the same maneuver holding similar LXXX hands in similar situations with some success, so I think I actually learned something from the guy.

I had a four point hand. My crib was 26988 – four points, a lame-o. And I only pegged one. So I’m at 63.

Bozo had two points in hand but pegged *seven*. So he’s dealing at 72*.

6.) 63-72* - a double marginal, very good situation for him, very bad for me.

I will play defense if the cards are strong enough, but with weaker hands will be compelled to play at least some offense. I was dealt 234779. Well… what would *you* do? Anyone who reads my posts knows what I’d do – toss the 77.

If you think that’s nuts, consider, 2347 would leave me short of par or teetering around it with most cuts. And 79 is not a safe toss, although I wouldn’t deny that 77 is significantly more dangerous. Still, the means are distorted by the fact that 77 scores a min of two. Consider – 77 is “only” about 20% more likely than 79 to give up a good-to-great crib of 6+ points. It’s about 17% more likely to score 8+. It’s 8% more likely to score 10+.

Yeah, that’s a big swing, but it’s not a *massive* swing. I know I need defense here, but I also know that it’s extremely hard to play defense without a surplus in the back, ie without being hopefully a few points past the next par of 69*, the more the better. So I’m playing offense now to play defense later.

Meanwhile, consider the hands, 2347 vs 2349. 2347 will score six or more only 54% of the time. 2349 will do so about 96% of the time. It will score 8 or more about 44% of the time, to 2347’s 20%. The offensive upside is too great to pass up. 63-72* is a losing score, and you can’t win a losing game without taking risks.

Bozo dealt himself A457JQ and correctly tossed the 57.

The cut was… an 8! A wave of nausea passed over me, followed by a sense of impending doom. That’s the absolute last cut I wanted to see – it only adds two to my hand, and now he has ??778 in the crib. I decided to switch to damage control and play defense – my hope is that his hand isn’t *too* good, and maybe the score next hand will be like 71*-86, and then I get really good cards, and he gets bad cards…

Bozo, meanwhile, plays a balanced game. He understands he can win in the front or the back, and though the 8 makes him hopeful for his 57 toss, he only has a four point hand, so he doesn’t want to go ape.

Pegging went: 3-Q(13)-2(15-2)-J(25)-4(29)-A(30-1)//9-4(13-1)

Magic five has offensive and defensive upsides for me here, and I got the 15. Bozo doesn’t entice a run. The rest of the play was straightforward.

So having pegged two and with a seven point hand, I continue in marginal position dealing at 72*. Bozo had a four point hand (maybe nob too I forgot to write down nob this game), and 57778 in the crib for 12 points. So the score next hand is a brutal 72*-91. Weylaway…. do I have any chance at all?? We’ll see tomorrow.

Sunday 6:36 AM

Don't ever get rid of REAL points in situations like this. This should be best offensively in ALL 3 categories if my calculations serve me correctly (hand, crib, AND pegs). The only possibility for me today!

Sunday 7:58 AM

I really like holding the magic 11 with two aces and a 9.

Sunday 8:57 AM

This strikes me as a "no brainer", and an 83% concurrence reinforces this observation. I have three counts to make 26 points for the win, which I think is the statistical average. We'll see how this goes with CribPro...

Sunday 9:10 AM

Here are a few good playouts, very representative of this critical Relative Score:

(95*-96) (Ah Ad 3d 3h 5s 9c) by scottcrib, Nov 19, 2023

REX = Pone = Keep (9s 9d Td Jc) and Toss (3s 7h)
JQT = Deal = Keep (Ah Ad 5s 9c) and Toss (3d 3h)
Cut = Jd
Pone Hand = 16 Points
Dealer Hand = 8 Points
Dealer Crib = 6 Points

Pegging:
9 (9) 9 (18=2) 9 (27-6) A (28) A (29-3), J (10) 5 (15=2) T (25-1), Pone = 7; Dealer = 9

With Two Points for "His Heels" tallied as part of the pegging, I am seemingly off to the races, not knowing how dire the situation really is. Even after allowing Pone to peg PAIRS Royal, I keep moving, which is crucial, and yet even with PAIRS Royal in the Crib, I am still a few holes 'shy' of closing out the game. Every Point Matters!

and score is now (118-119*).

JQT = Pone = Keep (4h 8s Td Qh) and Toss (2h Kc)
REX = Deal = Keep (As 7h 9s Qs) and Toss (8d Th)
Cut = 6c
Pone Hand = 0 Points
Dealer Hand = 2 Points
Dealer Crib = 0 Points

Pegging:
4 (4) Q (14) Q (24-2) 7 (31=2), Pone = 2; Dealer = 2

and score is now (120-121*), and I LOSE.

- - -

(95*-96) (Ah Ad 3d 3h 5s 9c) by scottcrib, Nov 19, 2023

REX = Pone = Keep (2s 2d 3c Ts) and Toss (9s Kc)
JQT = Deal = Keep (Ah Ad 5s 9c) and Toss (3d 3h)
Cut = Jc
Pone Hand = 10 Points
Dealer Hand = 8 Points
Dealer Crib = 4 Points

Pegging:
2 (2) 9 (11) 2 (13) 5 (18) T (28) A (29) "go" A (30=3), 3 (3-1), Pone = 1; Dealer = 5

and score is now (112-107*).

JQT = Pone = Keep (8s 8h 9s Th) and Toss (4s 4c)
REX = Deal = Keep (Ts Qs Qd Kh) and Toss (Ah 6s)
Cut = 4d
Pone Hand = 8 Points
Dealer Hand = 2 Points
Dealer Crib = 12 Points

Pegging:
8 (8) K (18) T (28-1), Q (10), 9 (19) Q (29=1), 8 (8) T (18=1), Pone = 1; Dealer = 2

I only pegged One Point as Pone, but with 8 Points in Hand, pegging One Hole was all I needed to WIN! REX only had Two Points, but still defended well, and as it turns out, REX would have defeated me even without any pegging, due to a Dozen Points in the Crib! But since I pegged One Hole and had First Hand Show, I didn't have to incur such a loss.

and score is now (121-109*), and I WIN.

Sunday 10:55 AM

Can't think why I would not throw 3-3??

Sunday 11:26 AM

It matters not the strategy, A-A-5-9 with 3-3 toss has the edge convincingly. My choice is aggressive offense with n/d at hole 95. Need to chew up some of the board after seeing the starter card. Have hopes for crib as if n/d had a deuce, A-2, or 2-4 not a likely fit in hand and just might have been deposited in the crib. Dealer has to hope for such or will need to peg a bunch. Dealer should grab every peg possible to vet down the board. If dealer were to only score that guaranteed peg, hand + a four-point crib would put at hole 109. Would like to end this game on next deal with first count. Alas, 3-3 does score two points 21.272%.

Sunday 2:09 PM

I'll look at A-A-5-9 (3-3), 3-3-5-9 (A-A), A-3-3-9 (A-5) and A-A-3-3 (5-9):

A-A-5-9: 6pts + 5¾pts (Schell: 5.94) = 11¾pts

3-3-5-9: 4pts + 5¼pts (Schell: 5.38) = 9¼pts

A-3-3-9: 4pts + 5½pts (Schell: 5.45) = 9½pts

A-A-3-3: 4pts + 5¼pts (Schell: 5.43) = 9¼pts

Potential:

A-A-5-9: Improves with AA, 4444, 555, 6666, 8888, 999 + 16xXs = 36 cuts = 36/46 = 78.3% up to 12pts with AA, 555, 999 = 8 cuts.

3-3-5-9: Improves with AA, 33, 4444, 555, 6666, 7777, 999 + 16xXs = 38 cuts = 38/46 = 82.6% up to 8/12pts with 33, 4444, 7777, 999 = 13 cuts.

A-3-3-9: Improves with AA, 2222, 33, 555, 6666, 8888, 999 = 22 cuts = 22/46 = 47.8% up to 12/14pts with 2222, 33 = 6 cuts.

A-A-3-3: Improves with AA, 2222, 33, 7777, 8888, 999 + 16xXs = 35 cuts = 35/46 = 76.1% up to 8/16pts with AA, 2222, 33, 8888 + 16xXs = 28 cuts.

Position:

We're 1pt short of positional hole but would like to be as far past 111pts as possible to maximize our winning chances. So I'll play Offense.

Pegging:

I think all the hands will peg quite well but A-A-5-9 and 3-3-5-9 have 3-card magic elevens so I think A-A-5-9 will peg best with two low cards, a 5 and a middle card.

Summary:

A-A-5-9 is best for starting value by 2¼pts over A-3-3-9 and it has the second most cuts for improvement although only 8 cuts for 12pts. It also ahould peg well so I'll throw the 3-3.

Sunday 2:10 PM

At 95*-96 playing an Offense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

_______________Our
Offense___Hand_Pegs_Crib_Total____W1 %___W2 %
A-A-5-9____8.26+3.70+5.53=17.49____2.2____50.4
A-A-3-3____7.43+3.22+5.36=16.01____1.7____41.3
3-3-5-9____6.74+3.63+4.96=15.33____0.6____36.1
A-3-3-9____6.04+3.13+5.32=14.49____0.4____31.7
A-A-3-9____4.74+3.48+6.04=14.26____0.3____29.9

Offense_______L1 %___L2 %
A-A-5-9________0.4____25.9
A-A-3-3________0.5____30.3
3-3-5-9________0.4____34.6
A-3-3-9________0.4____36.2
A-A-3-9________0.5____39.0

A-A-5-9 is best for expected averages by 1.48pts. and is very much best for Win %s and considerably lowest for Loss %s. So I'll select 3-3 to discard.

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