January 23, 2020

*** This hand was suggested by Ras2829
0-0*  ?
31%
30%
22%
5%
3%
2%
1%
1%
0%
Total votes: 192
Andy (muesli64)
2221 votes

Joined: August 2009

 
 
 
Thursday 3:16 AM
I am on the offensive. Looking for a double run
dec
6326 votes

Joined: April 2008

 
 
 
Thursday 3:48 AM
Its about the seventeen cuts here for me. Begrudgingly I will lead the ten. Do not cut the three. dec
dgergens says: Cheers Dec. Lots of discussion at this site on best possible hand/discard choice, statistical averages, etc. A number of players go the next step and offer to share their lead card (and sometimes some what if scenarios based on an opponent's lead card). But I've not seen any deep discussion on battle strategy (is there an official cribbage term for the card battle portion of play?) Anyway, can you please share why are you leading the 10? Is there no concern opponent is hold a 5? Thanks.
JRCeagle78 says: When leading the first card after the starter card is revealed, playing a matching card can be a good play. This is because the odds of the next card matching the pone's lead at that point, slightly favor the pone. In regards to being concerned about the 5, unless he has a second 5, the dealer may consider an alternative play. In my comments for my blog entry I have given another view.
Ras2829 says: Hi dgergens: Leading any one of the X cards could result in the play of the five. Much worse things happen with this hand if a X-pointer not led. The Ace is the poorest of the small cards to hold with X-X-X as it cannot be reasonably led. If a 10 card is played on the Ace, n/d must make the count 21 (the Ace was your escape card)and 31-4, 31-5, and even 31-8 are often results for dealer. If holding a deuce, trey, or four, this is not the case. The n/d will get hammered frequently if leading the Ace from 3 X-pointers.
dec says: I will add to the above comments that I have a past memory on this type of hand when I lead the Ace. A-A-J-3-10-go-2-2 then the Q on last play. Thats one for me , seven for them. Too many pegs to give up. dec
dgergens
938 votes

Joined: January 2018

 
 
 
Thursday 5:38 AM
At 0-0 today's puzzle doesn't seem complex. But since Ras submitted it, I'm wondering what the object lesson will be.
thelawnet
262 votes

Joined: January 2020

 
 
 
Thursday 6:20 AM
our hand is about the same with TJQ 2 as with TJQ A.

But the A seems obviously better support during pegging, and AA is a good point worse for us in pone's crib as A2, so there's not really any question that tossing AA is a bad play.

otherwise we can try disembowelling our run by tossing 2Q, 2T, or QT. The J can't be tossed because of nobs.

Tossing 2T vs 2Q is an obvious win for 2Q, so we disregard 2T as a choice.

This leaves us tossing either TQ or 2Q. Here TQ has the distinct disadvantage of having a higher maximum score, namely 20 vs 14 points, even if the average is the same. So this seems like a bad play also.

So then we can consider:

ATJQ

vs

AATJ

The latter starts and likely ends up a point worse off, but it saves probably half a point off the crib.

The only question is it worth holding the second Ace for pegging purposes? With Ten cut, we can lead the Ten, and guess that the reply comes back Twenty for two, in which case we reply with the Jack for thirty, then likely a go, and Ace for 31-two.

In that case our remaining Ace doesn't score.

The case AATJ wins in pegging is if we can peg our Aces for a pair for two, one for last, though 31-2 seems unlikely as pone will not play a 9 to our 10 or Jack lead.

We may just as well end up trapped, as if pone is holding a eleven, then we our TJ cost us, e.g., T, 5, J, 6 which is four for pone, zero for us, and then our ace(s) score nothing next round either...

Of course if pone does not have an eleven, then we may be able to get our cards to work for us, e.g., if pone holds 8766, we can score.

But either way I don't particularly like this, and think we are best off with ATJQ for the most points....
thelawnet says: Regarding the leads, we should consider the possible scoring replies. There are 4 fives, and let's assume that they are equally likely to be in hand as crib, if dealt to pone. This is a 31.5% chance, call it in 1 in 3. Then there are 3 Jacks, which is 24.4%, call it 1 in 4, finally there are 2 Tens, which is 16.8%, call it in 1 6. With a lead of Ten, Jack or Queen, then 1/3 of the time we get a 5 reply for 15-2. If we lead Ten, then if pone does not have a 5, then he will likely reply with a Ten if he has one, since his read on us is that we are only leading Ten because of the turn up. So that's two more points in that case, or roughly half the time. If we lead Jack, then pone may read that we hold a second Jack, and hold back on playing the pair, for fear of thirty for six. So it seems that the Jack is the better lead, albeit that 1/3 of the time we immediately incur 2 points. If we hold one Ace, then we cannot lead the Ace, because if a ten card comes back we are in deep trouble with 31, runs and three-of-a-kinds. But if we hold two Aces, then we can lead an Ace, and if a ten card comes back then we can play the other Ace for 12, and we may still end up with last, i.e. if pone plays an 8 (he is not likely to play a 9 on 12)
james500 says: Hi Lawnet, hope all's well. A very thorough analysis yet again, but if I may, I'd like to take issue with some of the things you've said. For instance, I agree with your statement, "There are four fives, and let's assume they are equally likely to be in hand/crib if dealt", but this "if" needs to be quantified for the likelihoods you later quote to be valid. 1-((42/46)*(41/45)*(40/44)*(39/43)*(38/42)*(37/41)) = 0.439 or 44% chance they have a 5 in the first place, and then it's 50:50 whether they keep/discard it as you say, so only a 22% chance they can make 15/2 on an X lead. Roughly 1/5 rather than the roughly 1/3 you suggest. The same sort of downgraded adjustments should also be made to your quoted odds for responses of a 10,J or Q.
thelawnet says: I don't think I can concur with your analysis. Two statements are certainly true here: there is 32% chance of 4 randomly chosen cards containing a 5, and a 44% chance of 6 randomly chosen cards containing a 5. now if we discard blind (which is what I was getting at really) then the chance that our hand contains a 5 remains 32%. for me that is a good number to use as a starting point, but I suppose you would need to consider all possible combinations of 6 cards for pone, and then of those that contain 5s, how often that 5 ends up in the crib. It does seem that certain cards are more likely to be tossed to crib and others less. So it might indeed turn out that a 5 is more likely to be tossed given that it is a powerful card and if our hand does not support it, we should likely toss it.But it does not follow from that the same applies to say Q. Because it seems that other things being equal in the case that our hand is basically trash we will toss 5s and middle cards to our crib more often, and say K, less often. I think it's probably ok however to just consider 4 cards, but that we should probably try to work out whether in fact a 5 is more likely to remain in the dealers hand, less, or is roughly equal
thelawnet says: the basic point of course being that we toss 1 in 3 of our cards, which if done blindly is the same thing as only drawing 4 cards and then dealing 2 directly to the crib
Gougie00
5701 votes

Joined: March 2008

 
 
 
Thursday 6:31 AM
Keeping the 3-run. Lead the Jack.
james500
3894 votes

Joined: June 2013

 
 
 
Thursday 7:01 AM
Had planned to lead the Jack. After cutting another 10, I'll lead mine.
Rosemarie44
2051 votes

Joined: March 2016

 
 
 
Thursday 7:09 AM
Best discard and retention with these cards today. Lead the ten. Ras will explain reasons for this submission.
JRCeagle78
1054 votes

Joined: June 2016

 
 
 
Thursday 7:30 AM
With the Td starter card, I'll match it with my ten. If the ten was NOT the starter, I'd lead with my Jack since it is in the middle of my 3-card run. If the dealer is forced to play 2 5's on the opening plays of the hand, the Ace may give me a 31-2 to counteract his 15-2. The dealer would probably jump at the first 15-2 if he has two 5's on the chance that the pone pairs his 5 to leads into his pairs royal.
horus93
1271 votes

Joined: December 2017

 
 
 
Thursday 8:03 AM
I always think of a-2 as "the worst bilk" but it's probably best today. I'd play offense to the cut and lead the ten.
usacoder
968 votes

Joined: August 2019

 
 
 
Thursday 8:19 AM
I'm surprised by the outcome from my Monte Carlo program. Which said to put the aces into the crib. The program gives this an average score of 8.42.

While myself I would have tossed one of the aces with the deuce. The program gives this an average score of 7.79.

As is I'll start the pegging with the 2.

BTW the program averages the whole phase of each hand; which includes turning a jack for a starter, pegging and counting.
RubyTuesday
896 votes

Joined: January 2019

 
 
 
Thursday 8:34 AM
I wanted to keep the run, but expected that all of you clever players would have found something much cleverer to do!
travelingman2019
513 votes

Joined: December 2018

Thursday 9:18 AM
Keep the most points AND those combos that could lead to a good point count with the cut.......the 10 here makes it 8, which is good........
JQT
4135 votes

Joined: October 2008

 
 
 
Thursday 9:50 AM
The real "meat" of this arrangement is the (A A 2) trio, and not the RUN, at least not if it forces us to relinquish Toss (A 2) to our Opponent!

We'll lead the Jack, and look to work those two Aces into the pegging, and this should easily 'make up for' any supposed 'lost' point from busting up the RUN.

The combined odds of getting a Double Run (or getting a 5 Card Cut) with T-J-Q are precisely the same odds that we shall get a Cut of either an Ace, Deuce, Trey, or 4 Card to boost the (A A 2 J) hand in a similar fashion!

Meanwhile, we jettison Toss (T Q), a Real BOAT ANCHOR, into the Opponent's Ocean, which is far superior to placing two 'Small' cards into that realm.

Again, let's Lead the Devilish Knave: The Jack. That's often the best way to 'rid ourselves' of him!
Ras2829 says: Hi JQT: Like your thinking and the 10-Q is one of 6 discards among the 91 that score 0-2 in excess of 40%. Yup, the 10-Q scores 0-2 40.972%. The other 10 point combinations in that group of six are 10-K and Q-K. Many players avoid the 10-K, Q-K, 10-Q because they fear the dreaded 5 discard and accordingly miss a large number of 0-2 cribs on the other side of the board. A five spot is seldom discarded by dealer. In fact dealer may play a few games before can turn loose a five. A five works with A-4, A-9, 2-3, 2-8, 3-4, 3-7, 4-6, 5-5, 6-7, and all those X-pointers. A five does not appear in the ten most frequent dealer discards (2-3 though is #2).
thelawnet says: what's the significance of a 0-2 score of 41%? That doesn't seem to tell us much without the mean? i.e. if we have a choice between a pone crib that always scores 4 points, or one that scores 2 points 90% of the time and 22 points 10% of the time, say, it is not obvious that that is a better choice? Because presumably 10% of the time we have all but lost the game, whereas say the other 90% of the time we have merely gained a small edge I am prepared to accept of course that situationally it must make sense to make very risky plays at say big deficits, but it does not seem obvious that TQ is a wonderful discard simply because it is often a cheap.crib for us, given that it sometimes may be a very expensive one.
Ras2829 says: HI thelawnet: Discards are not equally tossed to either crib. A 10-K to opponent crib is often the discard even when either 10 or K might fit better with the remaining cards. Nondealer will often give up two points in hand score to toss 10-K. In this case the 10-Q is chosen for a variety of reasons delineated later in this reply. Even so the discarding in no way matches the availability. RAS plays by the numbers only with very good results either in live play or electronically. So if the 10-Q is 9 times likely to score 0-2 than 12 or more, why should the 4.722% at 12 or more frighten me? Have great confidence in my discard averages since have discarded in live play over 250,000 recorded cribs. The 10-Q has been discarded to opponent crib 1,440 times in live play with the results recorded. I have great confidence in those numbers any time I've tossed them more than 1,000 times. Your earlier contention that all cards are equally available does not take into account discard bias, Choice of offense or defense strategy, board position, need for pegging cards, and other considerations before and up to the time of actual discard.
Coeurdelion
5573 votes

Joined: October 2007

 
 
 
Thursday 1:01 PM
I think this is between A-A-2-J (10-Q) and A-10-J-Q (A-2):

A-A-2-J: 2pts - 4½pts (Schell: 4.61) = -2½pts

A-10-J-Q: 3pts - 5pts (Schell: 5.07) = -3pts

Potential:

A-A-2-J: Improves with AA, 222, 3333, 4444, 5555, JJJ = 20 cuts = 20/46 = 43.5% up to 6/8/12pts with AA, 222, 3333, 4444 = 13 cuts. Plus 11 hearts for 1pt extra for his nob.

A-10-J-Q: Improves with AA, 4444, 5555 + 13xXs = 23 cuts = 23/46 = 50.0% up to 8/9 with 4444, 5555, 101010, JJJ, QQQ = 17 cuts. Plus 11 hearts for 1pt extra for his nob.

Position:

As First Pone positional hole is 18pts. I'll play Offense.

Pegging:

A-A-2-J should peg better than A-10-J-Q.

Summary:

A-10-J-Q has a starting value ½pt more than A-A-2-J and has more cuts for improvement and more cuts for an average hand although the maximum is less. So I'll select A-2 to discard.
HalscribCLX
5296 votes

Joined: February 2008

 
 
 
Thursday 1:06 PM
At 0-0* playing an Offense strategy for the pegging the dynamic expected averages and Win/Loss %s are:

_______________Our
Offense___Hand_Pegs__Crib___Total___W9 %____W10 %
A-A-2-J___4.41+2.07+(-4.56)=1.92____19.8____19.1
A-10-J-Q__5.52+1.17+(-4.82)=1.87____19.3____19.4

Offense______L9 %____L10 %
A-A-2-J______38.1____54.1
A-10-J-Q_____37.2____53.6

A-A-2-J is better for expected averages by 0.05pt and is very slightly better for Win %s. Although A-10-J-Q is lower for Loss %s even so I'll select 10-Q to discard.

After the 10 cut I'll lead the J and play Offense:

Lead____________Our Pegging Pts.
J____________________2.02
2____________________1.44
A____________________1.33
Ras2829
5124 votes

Joined: November 2008

 
 
 
Thursday 2:27 PM
If playing offense with no more than three points made up by X-X-X, considering the discard of two small cards or two mid cards, holding two points is preferable and has the greater value. Such cho0ices also leave the better pegging cards in hand. This statement is true most of the time. If you have been hanging on to the X-point run with three small cards in hand or three mid cards (2-6-7-10-J-Q, 6-8-9-J-Q-K, 6-7-9-J-Q-K,or similar try it this way. The increased pegging value and the decreased crib score of opponent will more than compensate for the 1 point loss in hand score. If playing offense with cards like this, lead the large card. Lead the Jack here. The cribbot automatically recognize such scenarios. We humans have to reprogram our brain and occasionally recall the reasons for doing so.