Annotated game: HALSCRIB - Rest Of The World (Internet, June 2003)

This game is taken from the second HALSCRIB vs. the Rest Of The World match, which was held June 19, 2003 at MSN Games by Zone.com. Hal Mueller took one side of the table, using a beta version of HALSCRIB 5.1 to play the cards dealt him by the Zone. A team of human players, captained by myself, took the other side and played by consultation, discussing our discarding and pegging choices on the chat lines. As always, it was great fun and an opportunity to play a couple of instructive games while seeing the world's most powerful computer cribbage program in action.

Take out your cribbage board and a deck of cards, and follow along. To get the full instructional value, I recommend going through the game twice, once from the perspective of the humans and once from the perspective of HALSCRIB. On each deal, try to decide what you'd have done with the same cards. Then read the accompanying text to see why the actual players did what they did.

Deal 1

The Rest Of The World (ROTW) deals first, and receives 2-5-8-9-J-K. Following the addition method, we keep 2-5-J-K, which returns about 1 points more between hand and crib than 2-5-8-K. Interestingly, both Schempp and Mueller rate 2-5-8-K significantly higher as a pegger, though the difference is not enough to make up for the better scoring potential of 2-5-J-K.

Keep  Toss 

  Average  
hand

Own crib:

   

   Expected   
average

    

Pegging (Schempp): 

    

Pegging (Mueller): 
  Static    Delta   Dynamic  Net (pone/dealer) Net (pone/dealer)
2-5-8-K     9-J 6.00 3.97 +0.01 3.98   9.98 +1.6 (1.9/3.4) +1.6 (1.6/3.2)
2-5-J-K 8-9 6.36 4.72 -0.01 4.71   11.07 +0.9 (2.2/3.1) +0.8 (1.8/2.6)
PONE  (0):
HALSCRIB
 
 

A-A-6-8  (2-Q)

 play:
   8  J  6  5  A  A (31-4)    2  K (12-1)   
  crib:   2-Q
8-9		 cut:  7        
2-5-J-K  (8-9)
 
   
DEALER  (0*):
ROTW
 		  

When the bot leads an 8, we play our J. Why the J and not the K? Because of this:

8  K  6  5  2 (31-2)    9  J  10 (29-4)

And this:

8  K  5  5 (28-2)  2 (30-1)    9  J  10 (29-4)

Playing the J first is more likely to give up a pair, since pone is far more likely to be holding a J than a K, especially if he also has an 8. But by saving our K for last we're less likely to give up a run, both because the K is an edge card that can only be trapped by one combination (J-Q) and because it's further away in rank from pone's lead card. In the long run, the J and K should average out the same, and either one would be a good play here. We chose the J, feeling that in this position the risk of a run was more threatening than the risk of a pair. See deal 5 for another example of this concept.

After HALSCRIB plays its 6 we must decide between our 2 and our 5. The 5 is vulnerable to a 2 or a pair of As. The 2 is vulnerable to a 2 or a 5, gives up a go to a lone A, 3 or 4, and gets clobbered by A-3 or 2-2 (as unlikely as those seem). Also, it saves us only one point against A-A. Put it all together and the odds favor the 5. When the count gets up past 19, just play as high as you possibly can unless you have a clear reason not to.

Now let's look at this deal from HALSCRIB's side of the board. The bot has a straightforward discard decision, and after a favorable cut it decides to play aggressively, leading its 8. This allows it to score a run on a 7 reply, and saves the pair of As for later hoping for the kind of play that materialized in the game. The strategy works, as the bot moves all the way to 17*, only only point shy of the First Street positional hole.

Deal 2

At 10-17* the humans need a bit of defense, but we also need to make sure we don't falter offensively, since we're starting out in marginal position ourselves. We draw A-2-3-3-8-Q.

Keep  Toss 

  Average  
hand

Opponent's crib:

   

   Expected   
average

    

Pegging (Schempp): 

    

Pegging (Mueller): 
  Static    Delta   Dynamic  Net (pone/dealer) Net (pone/dealer)
A-2-3-3     8-Q 11.83 4.31 +0.07 4.38   7.45 +0.3 (4.0/3.7) -0.7 (2.3/3.0)
A-2-3-Q 3-8 7.74 5.05 -0.07 4.98   2.76 -0.9 (3.1/4.1) -1.1 (1.7/2.8)
2-3-3-8 A-Q 6.09 4.33 +0.04 4.37   1.72 +1.0 (4.0/3.0) -0.4 (2.3/2.7)
2-3-3-Q A-8 9.52 4.85 +0.05 4.90   4.62 +0.2 (3.4/3.2) -0.9 (1.9/2.8)
DEALER  (17*):
HALSCRIB
 
 

6-7-8-K  (10-J)
  crib:   10-J
8-Q		 cut:  7        
play:
   3  K  2 (15-2)  8  3  A (27-1)    6  7 (13-1)   
A-2-3-3  (8-Q)
 
   
PONE  (10):
ROTW
 		  

A-2-3-3 is the obvious keep, but is it too dangerous for us to hold four bunched-up cards? How about saving 2-3-3-Q instead? This gives up ½ point more in the crib, but provides us with an "out" card if dealer tries to trap us into a series of runs. Can the bots, with their computer-generated pegging averages, enlighten us here? Maybe. The problem is that their pegging averages are based on simulations of balanced play, rather than purely defensive (or purely offensive) play. Thus holding 2-3-3-Q in the following situation:

3  4  ?

the simulators will invariably take the run with the 2 instead of breaking with the Q. This distorts the defensive side of the ledger when the results are tallied up. Mueller's numbers suggest that keeping a high out card will reduce dealer's pegging by about point. Schempp's numbers for this particular hand are all over the map, though they do rank the candidates in the same order as Mueller. My best guess is that holding a high out card in situations like this will save you ½ to ¾ points on defense. If that seems too low, keep in mind that a single out card might not be enough to keep you out of trouble:

3  4  Q  4  2  4  3 (30-3)  A (31-6)

3  3 (6-2)  3 (9-6)  4  2 (15-5)  A (16-4)  Q  5 (31-2)

3  3 (6-2)  3 (9-6)  4  Q  2  2 (27-2)  2 (29-7)

At any rate the question is pretty much moot in this position. Needing both points and defense, the humans have no choice but to keep the double run and hope not to get killed in the pegging.

HALSCRIB has a much easier discarding decision: 6-7-8-K clearly outperforms 6-7-8-10 when you factor in crib potential.

Keep  Toss 

  Average  
hand

Own crib:

   

   Expected   
average

    

Pegging (Schempp): 

    

Pegging (Mueller): 
  Static    Delta   Dynamic  Net (pone/dealer) Net (pone/dealer)
6-7-8-10     J-K 7.33 3.96 +0.03 3.99   11.32 +1.0 (2.1/3.1) +1.6 (1.6/3.1)
6-7-8-K 10-J 7.24 4.61 +0.09 4.70   11.94 +1.0 (2.0/3.0) +1.5 (1.5/3.0)

The play of the K on our 3 lead is an aggressive tactic designed to keep the bot's touching cards together. Note how the bot can retaliate with the 8 if the K is paired. After we take our 15-2 the bot is reluctant to make the count 21 with its 6, so it plays its 8, hoping to trap a 5 with its remaining 6-7.

Deal 3

At 23*-35 the ROTW deals itself 3-5-6-8-J-K, presenting a choice between 3-5-J-K and 5-6-J-K. The former scores more in the crib, but the latter includes a magic eleven which should give us better pegging defense against ten-cards (on a favorable cut we could even play the 6 on a ten-card lead). Although we need to slow down our opponent, who goes into the deal +1, we're only five points beyond the previous positional hole and we're staring at a mediocre starting hand. In the end we decided that the defensive edge of 5-6-J-K was too slight to justify the sacrifice in crib scoring.

Keep  Toss 

  Average  
hand

Own crib:

   

   Expected   
average

    

Pegging (Schempp): 

    

Pegging (Mueller): 
  Static    Delta   Dynamic  Net (pone/dealer) Net (pone/dealer)
3-5-J-K     6-8 6.67 4.63 -0.05 4.58   11.25 +0.9 (2.1/3.0) +0.8 (1.8/2.6)
5-6-J-K 3-8 6.76 3.92 +0.02 3.94   10.70 +1.1 (2.2/3.2) +1.1 (1.8/2.9)
PONE  (35):
HALSCRIB
 
 

9-10-J-Q  (A-7)

 play:
   10  5 (15-2)  9  3 (27-1)    J  J (20-2)  Q (30-1)    K (10-1)   
  crib:   A-7
6-8		 cut:  6        
3-5-J-K  (6-8)
 
   
DEALER  (23*):
ROTW
 		  

When the bot leads a 10 we have to decide whether or not to take the 15-2. There was some sentiment for ducking with the K. If HALSCRIB can pair our 5, then it could well have about eight points in hand, in which case a couple extra pegs would make a lot of positional difference. And if the bot does have 5s and ten-cards, there's an increased likelihood that it threw an A, 6, 7 or 9 to our crib, thereby reducing the need for us to peg. The flip side of the argument is that we're only staring at four points in our hand, and despite the 6 cut we could also be disappointed in the crib if pone didn't throw us any of those "magic" ranks. We're not too happy about it, but we decide to take the 15-2, hoping that the bot doesn't have a 5, or that if it does, it at least didn't benefit from the cut.

HALSCRIB again has an easy discarding decision, but its lead of the 10 from 9-10-J-Q is peculiar. The standard lead from this hand is the 9, both because it is thematic to lead from the end of a four-card run when you're playing on, and because the 9 lead will drive out a lone 6 in dealer's hand, making it safer to subsequently bring the count to 25 with a ten-card. The fact that the 6 is out of play should make the 9 lead even more attractive.

After our 15-2, the bot correctly drops its 9 next, saving the J-Q combo for last. Our 5 makes us more likely to have ten-cards than mid-cards, and when you're playing on you should try to maximize contact with your opponent's cards to facilitate scoring pairs and runs.

The bot leads its J to start the second play series. We pair it rather than risk giving up either a run or a pair with our K. In part this was a psychological decision. It was difficult for us to believe that the bot would have led the 10 from 9-10-J-J in a non-endgame situation. Silicon players rarely do anything as rash as that, and HALSCRIB, as sneaky as it can sometimes be, is no exception. Pairing the J also carries the lowest objective risk of the two plays: 2 · 6 = 12 (ignoring the go) compared to (4 · 3) + (3 · 2) = 18 for the K. And of course the pair is worth an immediate two points. Even against most human players it would be right to pair the J. Only if your opponent is clearly desperate for six points, or else has previously displayed a proclivity to lead away from a high pair, would it be right to play the K instead.

Deal 4

DEALER  (43*):
HALSCRIB
 
 

A-4-J-J  (9-Q)
  crib:   9-Q
6-10		 cut:  3        
play:
   Q  J  Q  A (31-2)    9  J  5  4 (28-1)   
5-9-Q-Q  (6-10)
 
   
PONE  (47):
ROTW
 		  

The bot's cards have faltered a little, and it now deals -1. It has an easy toss of 9-Q from A-4-9-J-J-Q. The humans benefited from a fourteen point crib last deal, moving them three points past the positional hole with their first count as pone still to go. Now they're thinking defense. From 5-6-9-10-Q-Q, the clear choice is to toss 6-10. Note that keeping 5-10-Q-Q and cutting a 5 or J would still leave the ROTW seven points short of the Third Street positional hole.

The 3 cut helps neither side. When the humans lead a Q, the bot, desperate for points, plays a J in hopes of enticing a second ten-card. In this position it's worth giving up a three-card run to retaliate with the A for 31-2. Despite this, the ROTW plays their second Q next. The 9 would be vulnerable to a 2 or a pair of As (neither of which we'd like to see with a 3 cut), and the 5 would be vulnerable to a 5, 6, or a combination like A-2-3, 2-2 or 2-2-2. Again, when the count is over 19, play as high as you can unless there's a good reason not to.

On the second play series, HALSCRIB plays its second J on our 9 lead. This is perfectly safe, as we have already demonstrated that we have no 10 or J.

Our defensive discard pays off as the bot scores only two in the crib. Now HALSCRIB is -6 and the ROTW +9.

Deal 5

PONE  (54):
HALSCRIB
 
 

5 8 9 Q  (8 K)

 play:
   8  J  Q  A (29-1)    9  Q  5  4 (28-1)   
  crib:   8-K
2-7		 cut:  A        
A 4J Q  (2 7)
 
   
DEALER  (53*):
ROTW
 		  

Both sides have straightforward discards, but there are a couple of noteworthy decisions in the pegging. The first is the bot's choice of lead from 5-8-9-Q. Leading the Q, the bot can score two points on a 5, 8 or 9 reply, perhaps earning an extra point for go in the latter two cases. Leading the 8, though, it can score two or three points on a 2, 5, 7, 9, 10 or Q reply (perhaps adding a go in the latter three cases), and it stands a decent chance of scoring a go on a J or K reply. As I've noted elsewhere, when you have a 2/2 hand consisting of two mid-cards and two ten-cards, or two mid-cards and 5-x, it's usually right to lead one of the mid-cards. This is one of those cases, and would be even if the bot hadn't been dealt a second 8.

The second interesting decision is the humans choice of reply to the 8 lead. This is a similar situation to the choice we had on deal 1 holding 2-5-J-K opposite the same lead (though with a different cut). In the earlier case it was pretty much a wash between playing the K to stay out of a pair now and playing the J to stay out of a run later. With A-4-J-Q instead, you might think that playing the Q would be clear, since it's less run-proof than a K and thus less valuable to retain. But it turns out that the difference between A-4 and 2-5 counts for more than the difference between a Q and a K, so in fact with A-4-J-Q, dropping the J on an 8 lead performs better than dropping the Q. The reason is that the A-4 is far more likely to get squeezed out on a go, leaving you to face the second play series with your remaining ten-card:

8  Q?  7!  4  A (30-1)    9  J  10 (29-4)

Here is how HALSCRIB 5.00 rates the choices:

 

Average pegging:
Net  (pone/dealer) 
A       -0.21 (1.82/1.61)
4 +0.01 (1.59/1.60)
J +0.20 (1.54/1.74)
Q  -0.17 (1.88/1.72)

Remember this idea the next time you are trying to decide which ten-card to play on pone's mid-card lead. Try to save your most run-proof card (a Q or K) for last.

Note that dropping the 4 is a reasonable alternative to playing a ten-card. We actually considered this play at length, the idea being to avoid disaster against pone's A-A-6-8. In the end we figured that the A cut made this too unlikely a scenario.

A subtlety occurs on the second play series after HALSCRIB leads its 9. We play our Q, but if we had a 10 or K instead of a Q, we'd have played the 4 here. Can you see why?

Deal 6

DEALER  (62*):
HALSCRIB
 
 

2-J-J-Q  (8-8)
  crib:   8-8
7-K		 cut:  K        
play:
   3  Q  2 (15-2)  2 (17-2)  A  J  3 (31-2)    J (10-1)   
A-2-3-3  (7-K)
 
   
PONE  (67):
ROTW
 		  

The humans find themselves in an almost identical situation to deal 2, holding A-2-3-3-7-K as pone. As we saw earlier, a hand like 2-3-3-K should give up roughly ½ point less in the pegging than A-2-3-3, assuming you play defensively. That's about the same amount as you'll save throwing 7-K to the crib instead of A-7, so with no reason to do otherwise, the ROTW just keeps the double run. Note that the World team is +7 to the bot's -9. When your positional surplus is about the same as your opponent's positional deficit (or vice versa), it's usually best to play cautious offense rather than play off.

Before the cut, things look bad for HALSCRIB, but the K improves its hand to nine points, with its 8-8 still to be heard from in the crib. The bot doesn't want to commit to all-out offense quite yet — the humans could have weak cards, and HALSCRIB doesn't want to blow its back-end chances with reckless pegging — so after we lead a 3 it eschews the play of the desperation 2 which would have enabled it to score on a J or Q reply. Instead it has to decide between playing its lone Q or one of its two Js. Both options are equally likely to be paired by pone (see Card frequency in cribbage), so the question is: which combo is best to save for later pegging, the touching J-Q or the J-J pair? This is one of the most common, and difficult, tactical dilemmas in cribbage.

What would you do in HALSCRIB's shoes? Saving J-Q for later preserves the most potent available high-card combo. If pone started with 2-3-x-x for instance, you'll be able to score by trapping a lone 10, Q or K:

3  J  2 (15-2)  2 (17-2)  10 (27-1)    J  10  Q (30-4)

You'll also have more flexibility if you have to face a second lead:

3  J  J (23-2)  2 (25-1)    9  Q  10 (30-1)    J (10-1)

However, if you wind up with a two-on-none at the end, you'll be much happier if you saved your pair for last:

3  Q  2 (15-2)  2 (17-2)  9  A (30-1)    J  J (20-3)

3  Q  2 (15-2)  2 (17-2)  6  4 (27-1)    J  J (20-3)

3  Q  2 (15-2)  2 (17-2)  10  4 (31-2)    J  J (20-3)

Saving the pair will also hit the occasional jackpot:

3  Q  Q (23-2)  2  5 (30-1)    J  J (20-2)  J (30-7)

Keep in mind that tripling pone is far more likely with a pair of Js than with another ten-card pair, due to pone's discarding bias.

Ultimately, the right choice in these situations depends on the exact distribution of your hand, your strategic goals (offense, defense or balanced), and the exact card led by your opponent. Occasionally the cut and your own discard also factor in. In this particular case, the human's lead of a 3 enhances the chance that they're holding a 3/1 hand that will set HALSCRIB up for a two-on-none at the end of the pegging (as in the above examples). For this reason, the percentage play is for the bot to save its J pair for last. The slim but potentially lucrative opportunity for a triple is just icing on the cake.

I should note that this case is somewhat exceptional. Usually if you have a 10-J or J-Q combo available, it's better to save that for last even if it means breaking up a pair. For example, suppose you have 8-J-J-Q instead of 2-J-J-Q, and the play starts:

3  8  5  ?

This time it's improbable that you'll get a two-on-none at the end of the pegging. Pone apparently lacks a 4, and so would need to have started with A-2-3-5, 2-3-3-5 or a handful of other relatively uncommon hands whose remaining low cards will be squeezed out after you play a ten-card. More likely, pone has a 7 or a ten-card, and thus will have something left for the second play series. In that case you're much more likely to score with the flexible J-Q than with the inflexible J-J:

3  8  5  J  5 (31-2)    J  ?

...and again, you'll score if pone's last card is a 10, Q or K.

Deal 7

PONE  (82):
HALSCRIB
 
 

A-2-3-10  (7-K)

 play:
   10  2  3 (15-2)  9  2  4  A (31-2)    4 (4-1)   
  crib:   7-K
5-J		 cut:  7        
2-4-4-9  (5-J)
 
   
DEALER  (83*):
ROTW
 		  

HALSCRIB has managed to improve its position from -8 to -4, and a powerful hand here will let it climb back into position. Unfortunately the cut refuses to cooperate. From A-2-3-10 the standard lead is the 3, which is solid enough, but rarely pegs more than two or three holes:

3  K  2 (15-2)  K  A  4  A (31-2)    10 (10-1)

The bot needs more than that to get into position, so it leads its 10, hoping for something a bit more dramatic:

10  K  3  A  2 (26-3)  4 (30-4)  A (31-2)    K (10-1)

Not a bad ploy in this position, but the humans are ready. We start by playing the 2 from our 2-9 magic eleven. Then, when the bot takes a 15-2 with its 3, we break with the 9. Since the cut doesn't match the bot's first two cards, we can see that we'll be in good shape if we just peg defensively. HALSCRIB ends up at 91*, five tough points short of the positional hole.

Deal 8

At 98-91* the World team is again thinking defensively. We're dealt 4-7-8-9-K-K and must choose whether to keep the natural 7-8-9-K or the super-safe 4-7-8-K. Our first priority, of course, is to hold down the bot's crib and pegging. 9-K in the crib is about .4 points safer than 4-K, and by keeping the 4, we'll have a covered low card available to lead with only three immediate losers (half as many as we'd have leading the 7 or 8) and only one really awkward reply to worry about (a 7). How much does this really buy us on defense? Well, again the computer-generated pegging averages are of limited help, since they're based on balanced play (e.g., from 4-7-8-K the simulators will usually pair a 7 or 8 response to the 4 lead). A reasonable guess is that having a low lead available will reduce dealer's average pegging by point if you play defensively. This makes 4-7-8-K about ¾ points safer than 7-8-9-K, though it comes at a cost of three points from the hand. Is it worth the sacrifice?

Keep  Toss 

  Average  
hand

Opponent's crib:

   

   Expected   
average

    

Pegging (Schempp): 

    

Pegging (Mueller): 
  Static    Delta   Dynamic  Net (pone/dealer) Net (pone/dealer)
4-7-8-9 K-K   7.20 5.65 +0.01 5.66    1.54 -0.9 (2.3/3.2) -1.6 (1.6/3.2)
4-7-8-K     9-K 3.85 4.03 -0.00 4.03   -0.18 -0.6 (2.5/3.1) -1.5 (1.5/2.9)
7-8-9-K 4-K 6.85 4.36 +0.04 4.40    2.45 -1.9 (1.5/3.4) -1.7 (1.3/3.0)

To find the answer it helps to consider something that I call the yellow zone: the nine point range beyond the positional hole (in this case, from 96 to about 105). If you deal from the yellow zone, you are a favorite to go out in three counts, but not in two counts. If your opponent's first count as pone puts her within pegging range of home, she will probably have an opportunity to peg out as dealer on the following hand before you get to count as pone. If you deal from beyond the yellow zone, however, you will be a favorite to go out before this can happen. If your opponent has reasonably good starting position, you'll win a few extra games out of a hundred by finding enough offense to propel you past the yellow zone.

DEALER  (91*):
HALSCRIB
 
 

2 5 Q Q  (7 7)
  crib:   7-7
4-K		 cut:  10          
play:
   8  2  7  Q (27-1)    9  Q  K (29-1)    5 (20-1)   
7 8 9 K  (4 K)
 
   
PONE  (98):
ROTW
 		  

Ironically, then, if you are pone early on Fourth Street, and are faced with the prospect of landing in the yellow zone, it may be worth taking a slight risk to increase your chance of passing the zone. If doing so denies your opponent an opportunity to peg out two deals hence, then it is worth giving up an extra couple of points on defense. Finding the right balance is tricky, but my own analysis and praxis suggests that when you and your opponent are both near the positional hole, the breakeven ratio is approximately four-to-one, meaning that for each extra point you expect to give up on defense, you must be able to average four extra points on offense to justify the risk. In making this calculation I factor in my estimate of the average hand, average crib and pegging defense. I usually ignore offensive pegging potential, since I expect to peg conservatively.

Now it appears that, based on our estimates, 7-8-9-K would just barely qualify under the four-to-one rule, and if both sides were near the positional hole (say at 98-96*) it would be a very close call. But in this case HALSCRIB is back at 91*, which gives the humans considerably more leeway. Given that, I think it is no longer a borderline decision, and that keeping the points is the clear choice.

Next we need to decide what to lead. Experts disagree about 7-8-9-x: some lead the 7, others the 8. With a K for a ten-card, and defense the strategy at hand, I slightly prefer the 8. It's thematic to lead from the middle of a three-card run in defensive situations, and if the 8 is paired, you can either reply with your 9, which gives up a 31-2 to a 6 but leaves you with the reasonably safe 7-K for the second play series, or else dump the K, which may well get a go at 26 though it leaves you with the awkward 7-9. Your choice would depend on the cut, and on which scenario you most need to defend against. The downside to leading the 8 comes if dealer plays a 5. Your 9 can then get trapped into a run:

8  5  K  7 (30-1)    J  9  10 (29-4)    Q (10-1)

Leading the 7 forestalls this scenario by keeping dealer's 5 off the table. But if it is paired, or if dealer plays an 8 for 15-2, you must then play the K, leaving you with vulnerable mid-cards and a potential disaster like this:

7  8 (15-2)  K  6 (31-2)    8  7 (15-2)  9 (24-3)  6 (30-5)

So we lead our 8. The bot plays a 2. Does it have nothing but low cards? Actually it is hoping to entice a 5 which it can then pair! Since we're sure that the bot would have scored on our lead if it could, we play our 7 next, confident that it won't be paired or trapped into a 31-5 by an 8-6.

HALSCRIB's first two cards show a possible flush, but we open the second play series by leading our 9, not our K. The bot could have (and in fact does have) the 5. And with a 10 cut showing, we do not particularly mind giving up two points to the 6 or 9.

Deal 9

PONE  (103):
HALSCRIB
 
 

2-Q-K-K  (8-9)

 play:
   K  3!  2 (15-2)  6  K (31-2)    6  Q  3 (19-1)   
  crib:   8-9
4-10		 cut:  6        
3 3 6 6  (4 10)
 
   
DEALER  (105*):
ROTW

ROTW wins 121*-109
 

  

HALSCRIB has received scant help from the cards the past two deals, and the bot's bad luck continues here. Starting with 2-8-9-Q-K-K from 18 away, the bot tosses 8-9, perhaps hoping to cut a 5 or J then triple a K in the pegging. The 6 cut gives HALSCRIB no chance of approaching the game hole this deal, so it should probably just lead the 2 and play desperation defense, clinging to the possibility that the humans' cards will die completely — a slim hope, but better than no hope at all. In the event it doesn't matter, as the humans have more than enough in their hand to go out.

There is one last detail for the ROTW to attend to. On the bot's K lead, most cribbage players holding 3-3-6-6 would plunk down a 6 without much thought. It seems the obvious play, getting the count over 15, and giving up only one immediate loser. But the following demonstrates what can happen if you get careless in the endgame:

K  6??  4  3  5 (28-4)  3 (31-2)    4 (5-1)

K  6??  6 (22-2)  6?? (28-6)  3 (31-2)    4  3  5 (12-4)

Game over. Ouch.

You can prevent either disaster simply by playing a 3 on pone's K lead. Work it out — it saves the game against both 4-4-5-K and 4-5-6-K. In fact, the only hand you can lose to is 4-5-5-K, which beats you no matter which card you play.

The way to approach this over the board is to visualize what could go wrong with the "obvious" 6 play. Start by imaging that pone pairs your 6, then calculate the worst case scenario. You may or may not find the exact variations shown above, but you should soon realize that you'll be in trouble if the cut gave your opponent any kind of 4-5-6 double run (which would make his hand worth 14 or 16 points). Once you've established that the 6 is vulnerable, the next step is to consider the alternatives, again imagining what sort of disasters might occur. Playing a 3 is the only alternative here, and the key thing to see is that if pone can score on it (with a 2 or 3), then he clearly can't have enough points to get near the game hole. It helps if you remember that the 4 is in your crib, thus making 3 4 5 K an impossible holding.

As the saying goes, keep your head up, and you may not have to keep it down...

Summary

This game was a classic case of HALSCRIB struggling to overcome the initial positional disadvantage one has as first pone. After a fast start, the bot played aggressively, and even climbed into favorable position briefly on Second Street. But then its cards faltered, and though it continued to play on — even making an unconventional lead in an effort to generate offense — it was unable to get back on track. The ROTW aided the bot's demise by playing defensively for most of the game. HALSCRIB excels at accurately weighing pegging potential against crib/hand scoring potential when making discards, but this game gave it little opportunity to exploit this strength, as most of the bot's discard decisions were obvious.

Here's a review of some of the game's main points:

Average scoring (excluding last deal)

  HALSCRIB ROTW
Pone    
     Pegging 2.25       2.00 
     Hand 8.25       8.50 
Dealer    
     Pegging 2.25       2.50 
     Hand 8.75       6.50 
     Crib       4.25        6.75 
     
Total 25.75     26.25 

Future HALSCRIB vs. the Rest Of The World matches will be announced on the Cribbage Forum main page. If you'd like to participate as a member of the World team, just show up at the scheduled time and place and join the fun!

- July 2003

Pegging averages may have arithmetic discrepancies due to rounding. Mueller pegging averages were obtained from HALSCRIB 5.00. Click here for a guide to cribbage notation and symbols.


 
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