Annotated game: Ultimate Cribbage - Schell (Seattle, 2000)

This article features an annotated game between myself and a cribbage playing bot. It's a format I plan to return to periodically, since it helps illustrate the general concepts of skilful play as well as some specific considerations that can arise when competing against silicon players. Although cribbage software has progressed substantially in recent years, computers are only just beginning to play at expert level. Their main strengths are the ability to perfectly calculate discards and scoring, and the fact that as machines, they never suffer mental lapses. On the other hand, they tend to exhibit short-sightedness in the pegging game (especially on Fourth Street), and to play predictably. A sharp human player can take advantage of both these latter traits.

For this game, I'm going to take on Ultimate Cribbage 5.52. If you have this program, I invite you to follow along. Or, you could run through the game on your own first, then compare your plays to mine afterwards. Either way, you should start by going to the Options, Play screen, and ensuring that your settings match the following:

In particular, make sure that Skill Level is set to Hardest, and that Style is set to Optimal. Select Local Human Player Deals under First Game Dealer. We're playing with 6 Cards to 121 points.

Next go to the Options, Scoring screen, and turn off all the options.

Once the program is properly configured, click OK, then go to Game, New and select game 963196409.1886313957. Click OK to start playing.

Deal 1

My first hand is A 4 9 10 J J. Since it's my crib, I toss A-4. The cut is the 2, and the computer leads the 6. I decide to take a 15-2 with my 9. On a better cut, I'd have played off with a J, something I also would have done on a 4 through 9 cut, since any of those starters could combine with pone's lead to form a high scoring hand.

PONE  (0):
Ultimate Cribbage
 
 

3-6-6-6  (J-Q)

 play:
   6  9 (15-2)  3  J (28-1)    6  J  6 (22-1)    10 (10-1)   
  crib:   J Q
A 4
cut:  2           
9-10-J-J  (A-4)
 
   
DEALER  (0*):

Schell
 
 

The computer breaks with the 3, and I play my J (which keeps a flush fake alive). By saving J-Q for last, I have a bit of added flexibility on the second play series. If I get a go here, I can play the 10 if pone leads a Q or K, but the J if he leads an 8 or 9. Against another opponent, I might have dropped the 10 instead, so that I could run the two Js if pone's last two cards were A-A or A-2. But based on my experience with Ultimate Cribbage, I'm pretty sure it would have led a low card, and not the 6, from either A-A-3-6 or A-2-3-6.

As it turns out, my J does get a go. Ultimate Cribbage now leads a 6, I play my second J, and the computer gets a go with a third 6. My 10 is last card. The computer's twelve point hand gets it to 13 — not bad, but still five points short of the First Street positional hole (18). The computer had tossed me J-Q, giving me a four point crib to go with my nine point hand, making the score 17-13*.
 

Deal 2

DEALER  (13*):
Ultimate Cribbage
 
 

4-J-Q-K  (6-8)
  crib:   6 8
10 K
cut:  K          
play:
   A  K  8  Q  2 (31-2)    4  A  J (15-3)   
A-A-2-8  (10-K)
 
   
PONE  (17):

Schell
 
 

The computer deals me A A 2 8 10 K — not much to work with. Fortunately, the A-A guarantees I'll get at least two points, enough to beat the computer to the positional hole as long as it pegs fewer than five points. I toss 10-K, the optimal combination to send to your opponent's crib.

The cut is the K, leaving me with the two points I started with. Despite that, I'm still going to play conservatively. The computer is only five points behind the positional hole, and could seize the advantage here with unusually high scoring. Thus I lead the A, which is not only covered by my other A, but also forms a three-card magic eleven in combination with the 2-8. By leading the A instead of the A, I can fake a spade flush if I play my 8 next. Of course, the A could combine with the 2 to fake a club flush, but it's less likely that I would want to play the 2 next.

The magic eleven works, as I peg two points for a 31-2. Perhaps the computer saw that my first two cards were spades, and made the count 30 figuring that if I did have a flush, I wouldn't have a second A. The computer pegs three, and has a nine point hand, but my 10-K toss holds it to a two point crib.
 

Deal 3

Ultimate Cribbage has moved ahead of me, but I'm still a favorite to win. I'm three points past the First Street positional hole, and have my three counts to get to the Second Street positional hole (44). Since average scoring for a two-deal cycle is 26 points (25 on Fourth Street), this means I have a three point positional surplus. In other words, I can score three points below average between this deal and next, and still beat my opponent to the next positional hole, assuming my opponent gets average scoring.

PONE  (27):
Ultimate Cribbage
 
 

3-5-5-7  (3-10)

 play:
   3  10  5  2  7 (27-1)    9  5  8 (22-1)   
  crib:   3 10
A 4
cut:  5           
2-8-9-10  (A-4)
 
   
DEALER  (21*):

Schell
 
 

The computer, on the other hand, is seventeen points behind the Second Street positional hole, with only one count to get to it. Since average scoring for one deal as pone is ten points (a bit less than that on Fourth Street), the computer has a seven point positional deficit. If Ultimate Cribbage outperforms the averages by seven points on this deal, it will beat me to the next positional hole.

Since I'm +3 while pone is -7, I will be playing cautious offense, trying to maintain my position without taking any undue risks. I'll pay particular attention to pone's lead. If it matches the cut, I may have to switch to defense to hold down pone's scoring. I certainly don't want the computer to leap into position with help from my careless pegging.

I toss A-4 from A-2-4-8-9-10. The cut is a 5, giving me a seven point hand. The computer leads a 3, and alarm bells go off immediately, since this lead could combine with the starter for a high scoring hand. I have three statistically-equivalent replies available: the 8, 9 or 10. Each of these has six possible losers. I choose the 10 for two reasons:

  • If pone takes a 15-2, I can retaliate with my 2 for a pair. I can also take a 31-2 with my 8 if the computer pairs my 10. I cannot retaliate if pone scores off my 8 or 9
  • Given that the cut is a 5, I'd rather see a 2 in pone's hand than another 3 or a 4

As it turns out, my play doesn't matter. The computer and I each peg one point. Unfortunately, Ultimate Cribbage has a fourteen point hand, getting it to 42, while I only reach 36. I notice that the computer kept the 3, tossing me the 3 in combination with the 10. If it had kept the 3 instead, it could have faked a spade flush with its first two cards.
 

Deal 4

DEALER  (42*):
Ultimate Cribbage
 
 

5-10-J-K  (4-7)
  crib:   4 7
Q K
cut:  9          
play:
   4  K  2  J  5 (31-2)    7  10  7 (24-1)   
2-4-7-7  (Q-K)
 
   
PONE  (36):

Schell
 
 

At 36-42*, I still have the advantage, but I'm running out of leverage. I must score at least eight points to reach the positional hole, while trying to prevent the computer from overcoming its two hole positional deficit. This might be difficult given what I'm dealt: 2 4 7 7 Q K.

I toss Q-K. This is almost as safe as 4-Q, and even a bit safer than 2-Q, while maximizing my hand potential. The cut is a 9, giving me a mere four points.

I lead the 4, hoping to catch a 2, 3, 4, 7 or 9 in reply. A 2 lead scores on as many replies, but leaves me trapped if dealer plays a 5 or 6. In the event, the computer is holding 5-x-x-x, and the play proceeds without any contact. I manage to peg a point by stealing last card, but I still fall short at 41 points. Ultimate Cribbage gets to 53 on a nine point hand and a bust crib.
 

Deal 5

I start this deal with a three hole positional deficit. The computer has a nineteen hole positional surplus, and is now the favorite. I must try to make up my deficit through aggressive play. If I can reach 60 points this deal, without letting pone get close to the Third Street positional hole (70), then I'll become the favorite again.

PONE  (53):
Ultimate Cribbage
 
 

4-5-5-6  (8-J)

 play:
   5  Q (15-2)  5  A  6  4 (31-2)    4  A (5-1)   
  crib:   8 J
8 10
cut:  Q           
A-A-4-Q  (8-10)
 
   
DEALER  (41*):

Schell
 
 

I toss 8-10 from A-A-4-8-10-Q. The cut is another Q. Ultimate Cribbage leads a 5, then plays a second 5 on my Q reply. Taking advantage of the predictability of silicon players, I decide to make the count 21 with my A. My experience with Ultimate Cribbage makes me suspect that it is holding four cards in the 3 to 7 range, and has led from a pair (Ultimate Cribbage tends to lead from a pair whenever possible, even a pair of 5s, and will also typically lead a ten-card if its hands consist exclusively of 5s and ten-cards). Besides, risking a 31-2 on a ten-card is better than playing a 4 and risking a run if the computer has a 3 or 6.

My A ploy keeps the computer from pegging any points, but unfortunately the bot has drawn another excellent hand, moving all the way to 69. I have a twelve point hand myself, though. And after counting my five point crib, the score is 63-69*.
 

Deal 6

The good news is that I made up my positional deficit. The bad news is that Ultimate Cribbage is at 69, one point short of the Third Street positional hole. I'm a slight favorite to win, but now I must try to keep the computer from consolidating its position. Although the computer is almost certain to get to 70 before me (as dealer it's guaranteed to peg at least one for a go or last card), I still have a good chance of beating it to the next positional hole (96) if I can slow it down here.

DEALER  (69*):
Ultimate Cribbage
 
 

6-7-9-9  (3-3)
  crib:   3 3
A K
cut:  4          
play:
   J  6  10  5 (31-2)    9  Q  9 (28-1)    7 (7-1)   
5-10-J-Q  (A-K)
 
   
PONE  (63):

Schell
 
 

I start with A 5 10 J Q K, giving me an obvious, safe, toss in the A-K. The cut is a 4, giving the computer at least a two point crib.

If dealer was a few points further back, I would lead the 5 here to avoid the "pair or don't pair" dilemma that ensues if dealer plays a 5 on my ten-card lead (see the article Leading a 5). But with dealer at 69 points, I don't feel I can afford to risk giving up an easy 15-2. That makes the J the safest lead, since it saves the relatively run-proof Q for the second play series, when dealer might try to trap it.

As it turns out, leading the Q would have left me stuck playing my J on dealer's 9 lead on the second playing series, risking a run if dealer had a 10.

My luck holds. Not only do I easily get past 70, I've held the computer to two pegging points and a four point crib.
 

Deal 7

At 75*-81 I am +5 while the computer is -5. Despite being behind, things are looking in my favor.

I get dealt the following: 2 3 6 6 8 K. This is the kind of hand that's not in the cribbage textbooks. Should I keep four points (3-6-6-8) and toss 2-K, or keep only two points (6-6-8-K or 2-3-8-K) and make a strong toss (2-3 or 6-6)?

Keep:  Toss: 

 Average 
hand:

 Chambers 
average:

Average crib:

   Expected average:   

 Hessel   Colvert      Ras      Hessel   Colvert      Ras    
2-3-8-K     6-6 4.78 7.43 5.74 5.8 5.76 10.52 10.58 10.54
3-6-6-8 2-K 6.30 6.87 3.55 3.5 3.57 9.85 9.80 9.87
6-8-8-K 2-3 4.13 5.57 6.97 6.9 7.14 11.10 11.03 11.27

The addition method favors tossing 2-3, and this is borne out by the expected averages. But 6-6-8-K is a weak pegging hand against anything but mid-cards. And the 2-3 toss is a bit of an all-or-nothing shot. I'll take my chances here on 2-3-8-K, which returns to points less than 6-6-8-K, but gets the highest Chambers average and retains a magic eleven, which generally adds about point in pegging value to a hand that doesn't contain a 5. It's also a more flexible pegging hand, capable of playing either offense or defense, depending on how strong pone's hand appears to be. Given the board position, it seems prudent to sacrifice a small amount of offense for this flexibility.

The cut is a 10, and Ultimate Cribbage leads another 10. I play my 8. Against a human opponent I would have played my 3, figuring that if pone had started with 5-x-x-x, he would reply with a second ten-card rather than risk a run with the 5. My 8 would then get a 31-2. In my experience, however, when Ultimate Cribbage leads a ten-card from 5-x-x-x or 5-5-x-x, it will play another ten-card on an 8 reply, but a 5 on a 3 reply. This would result in Ultimate Cribbage stealing last card:

10  3   K  2 (30-1)    J  8  5 (23-1)

That makes the 8 the percentage play here, despite the risk that the computer will have a 9.

PONE  (81):
Ultimate Cribbage
 
 

5-5-10-J  (3-8)

 play:
   10  8  J  3 (31-2)    5  K (15-2)  5  2 (22-1)   
  crib:   3 8
6 6
cut:  10           
2-3-8-K  (6-6)
 
   
DEALER  (75*):

Schell
 
 

As a result of my 8 ploy, I outpeg the computer 5-0. But Ultimate Cribbage has landed yet another excellent hand, moving all the way to 97. My crib is worth four, getting me to 88.
 

Deal 8

Now the computer is the favorite again. It's one point past the Fourth Street positional hole, while I'm back at 88. I'll need to slow down the computer somehow, while still scoring enough to get into Fourth Street position myself — a tall order.

I draw 9 9 J Q K K, which presents an immediate dilemma. Do I toss the 9-9, keeping the double run, but substantially increasing the computer's chances of going out on its three counts? Or do I balk the crib with 9-K, leaving me with a three point hand and twelve shots (a 5, J, Q or K) at cutting enough to reach the positional hole?

It's a tough call, but I'm going to discard 9-K. This is always a safe toss, second only to 10-K in the discard tables, and in this particular case it's even safer because I have another 9 and K in my hand. With this toss I stand a very good chance of shutting out computer's crib — exactly what I need to do in this situation. I'll have about a 1-in-4 chance of cutting myself into position, and if I miss the cut, I'll at least have maximized my chances of taking my three counts, with the opportunity to get lucky and land a high scoring hand or crib. If the computer goes out first on its three counts, I will not get that opportunity.

One thing working in my favor is that Ultimate Cribbage is a habitually aggressive player, prone to taking pegging scores whenever possible, even if the board position warrants more caution. This gives me a bit more latitude to make a defensive discard, since the computer may give me a chance to peg into position later if I fall short here. Against an aggressive opponent, it can pay to play more conservatively than usual, and vice versa.

DEALER  (97*):
Ultimate Cribbage
 
 

3-7-7-8  (3-10)
  crib:   3 10
9 K
cut:  Q          
play:
   Q  7  9  3 (29-1)    K7  J (27-1)    8 (8-1)   
9-J-Q-K  (9-K)
 
   
PONE  (88):

Schell
 
 

Luck is with me as the cut is a Q. This gives me a nine point hand, enough to get into at least marginal position if the computer falls short. I lead a Q, hoping to entice computer into playing a 9. The K is also a good lead, but I'm planning to dump my J on dealer's reply, and prefer to have 9-K (rather than 9-Q) as my last two cards. This will give me a safe reply to anything but a J lead on the second play series. Holding 9-Q, I would not have a safe reply to a 10 or J lead.

Having said that, I would probably lead the K here anyway if I was playing a human. The reason is subtle: I do not want this lead to be paired, and I think most human players would be more reluctant to pair a K lead than a Q lead. Why? Because leading a K with a Q starter on the table suggests that I have two Ks, whereas a Q lead could arise because I'm simply matching the starter rank for safety. This is a psychological point that is lost on most silicon players, so in this game I prefer to make the objectively safer play.

Incidentally, leading the 9 would be a good offensive play here, hoping to pair a Q or K in reply. But by leaving me with the poorly-spaced J-Q-K, it would increase my chances of getting trapped into a run later, something I'm desperate to avoid.

As it happens, Ultimate Cribbage responds with a 7. Since it evidently has no 5, I play my 9, making the count 26. The computer manages to peg just two points, and gets a bust crib, leaving it at 105, while I come in at 98. This time, everything has gone according to plan.
 

Deal 9

PONE  (105):
Ultimate Cribbage
 
 

2-6-6-9  (J-Q)

 play:
   6  9 (15-2)  9 (24-2)  7 (31-2)    2  A  6  9 (18-1)   
  crib:   J Q
J Q
cut:  3           
A-7-9-9  (J-Q)
 
   
DEALER  (98*):

Schell
 
 

Although Ultimate Cribbage has a seven point lead, I am the positional favorite to win. The computer will need better-than-average cards to out on this deal, while I need only average cards to go out with my three counts. My starting hand, however, is weak: A 7 9 9 J Q. Following the addition method, I toss J-Q, which does considerably better than tossing A-Q, A-7 or 9-9. But the cut is a 3, matching neither my hand nor my toss. My position has gone from good to precarious.

With a two point hand and uncertain prospects in the crib, I'm forced to peg, even at the risk of allowing counterpegs. When the computer leads a 6, I play my 9 for a 15-2. The computer pairs it, then I take a 31-2 with my 7. Now Ultimate Cribbage leads a 2, setting up a classic endgame two-on-one. I have a choice between playing my A or playing my second 9. If the computer scores on my A, it either has:

  • 2-3-6-9, worth six points (plus three for the pegging run), getting it to 116, or
  • A-2-6-9, worth seven points (plus two for the pegging pair), also getting it to 116

If scores on my 9 it either has:

  • 2-6-9-9, worth six points (plus two for the pegging pair), getting it to 115, or
  • 2-4-6-9, worth nine points (plus two for the pegging 15), getting it to 118

Although none of these alternatives would lose the game outright, the last one would get the computer to within three points of home — close enough to win with average pegging as dealer next hand. Accordingly, I play my A, not my 9.

The computer's last card is a 6, getting it to 115. I score five points for my crib, reaching 110.
 

Deal 10

Eleven points out, I'm a slight underdog. An average hand is worth eight, and pegging three points in the endgame is ordinarily a tough proposition. It's also possible that dealer will peg six points and win even if I do get a good hand. But computers are notoriously weak on Fourth Street, and their proclivity for missteps in positions like this gives me an intangible edge.

I'm dealt A 5 5 6 J Q, and toss A-6. I have an exactly 50% chance of cutting enough points to count out (a 5, ten-card or any other ), but unfortunately the cut is the 3. To win, I'll have to peg at least one point.

DEALER  (115*):
Ultimate Cribbage
 
 

A-4-J-Q  (2-K)
  crib:   2 K
A 6
cut:  3          
play:
   5  J (15-2)  J (25-2)  4  A (30-1)    Q  Q (20-2)  5 (25-1)   
5-5-J-Q  (A-6)
 
   
PONE  (110):

Schell
 
 

Mindful of Ultimate Cribbage's proclivity to take scores, I lead a 5. I'm confident the computer will play a ten-card if it has one, and in that case I'll have a 6-in-14 chance of pairing it for two points. If it's a 10 or K, I'll dump my J, hoping to steal last card if the computer has two low cards. If it has no ten-cards, it may play an 8 or 9 on my 5 lead, in which I'll play my second 5, leaving me with J-Q and, again, a good chance of stealing last card on a low go. It's even possible that the computer will play a 5 on my 5 lead, letting me triple it, although this will cost me the game immediately if computer turns out to have the fourth 5.

If you're surprised by my choice of lead, you might want to look at the article Leading a 5, which discusses this tactic in detail.

True to form, the computer plays a J on my 5 lead, which I then pair. It turns out I'd also have won on a 10 or K reply, since the computer is forced to play a 4 and an A on my go, allowing me to steal last card.

An expert human opponent would probably have played the A on my 5 lead. This is better than playing a ten-card, but it still loses:

5  A!  10  4  J (30-1)    J  5 (15-2)  Q (25-1)

This demonstrates what a lousy defensive hand A-4-x-x is for dealer. Given that the computer started with A-2-4-J-Q-K, a better keep would have been A-2-4-K, though even this wouldn't have saved the game:

5   10  A  J (28-1)    4  5  K (19-1)

In the event, the computer grabs two last points by pairing my Q. As it watches from the stinkhole, the synthesized trumpets sound through my PC speaker, announcing my victory.

Summary

Take away the following key points from this game:

  • Most computer cribbage programs play predictably. Pay attention to their tendencies, and try to exploit them during the pegging
  • Computer programs are generally weak with it comes to board strategy, so if you pay particular attention to board position when you formulate your discarding and pegging strategy, you'll often have a significant advantage
  • Against a habitually aggressive opponent, it can pay to play more conservatively than usual. Against a habitually conservative opponent try playing more aggressively than usual
  • As dealer, a hand with a two-card magic eleven or a 5 will generally peg about point better than a comparable hand with neither
  • Leading a 5 is often a good idea if you are desperate to peg a couple points

So, how would you have done with these cards?

- December 2000

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