Annotated game: HALSCRIB - Rest Of The World (Internet, March 2003)
|On March 7, 2003,
MSN Gaming Zone hosted the first
HALSCRIB vs. the Rest Of The World
match. Hal Mueller took one side of the table, using a prototype of
HALSCRIB 5 to play the cards dealt him by the Zone. A team of human players,
which included myself, Lois Fosdal, Paul Gregson and many others, took the
other side and played by consultation, discussing our discarding and pegging
choices on the chat lines. 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.
The following game is taken from that session. Grab 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 on to see what the actual players did, and why.
The Rest Of The World (ROTW) deals first, and has an easy discard of 2-K from 2-7-8-9-9-K. When HALSCRIB leads a 9, pairing it is clearly right. The bot would need the fourth 9 to retaliate, and at any rate there is no good alternative. When HALSCRIB gets a go with a J, the humans have a difficult lead to make. The 9 is the percentage play mathematically, with only three losers (since the bot is obviously out of 9s). But it leaves us trapped if the bot does play a 6, which led some of us to fear the sort of outcome that actually materialized in the game. The alternative is to lead the 8, which is more likely to give up two immediate points but less likely to get into deeper trouble afterwards. It was a close call, with a slight consensus favoring the 9. Many of us, myself included, expected that with a 6 cut showing, the bot would have led a 6 from 6-9.
But HALSCRIB surprised us by showing up with 6-7-9-J after all. The 9 is, in fact, the standard lead from this hand. Whenever you have 6-7-x and the fourth card is a 7, 8 or 9, it's usually right to lead the fourth card, hoping to catch dealer with 5-5-x-x:
In this case the bot's stealth 6 let it peg eight points in all, compared to our three. Chalk one up for the bot.
HALSCRIB's keep of 6-7-9-J from 3-6-7-9-J-Q returns both the highest average hand and the highest expected average. Some players might be tempted to keep 3-6-7-9 instead, on the theory that low cards are "better" than high cards. But this hand actually fetches ¼ point less. Remember, a J is worth roughly ¼ point on the possibility of His Nobs alone, and adding in the potential for a run on a 10 cut, this more than offsets the two extra points that 3-6-7-9 scores on a 3 or 6 cut.
Another try is 3-6-9-J, safer in the crib and pegging (and
therefore best when defense is indicated), but retaining too little
offensive potential to appeal to the bot in this position.
The humans receive A-2-4-5-7-8. At +15 to the bot's -4,
defense is called for, so we toss the relatively safe A-7.
Other reasonable plays would be to toss 4-7 or 4-8.
No serious consideration was given to tossing A-4, which
would be the optimal play at most scores.
The 4 is the best defensive lead. If it's paired, we can get the count over 15 with our 8. The 4 also forms a magic eleven with the 2 and 5, allowing us to peg a 31-2 if dealer's first two cards are ten-cards. Remember that as dealer you can thwart opponent's ten-cards with either a two-card magic eleven like 5-6 or 2-9 or — if you're looking for more offense — a three-card magic eleven that includes a couple of low cards (A-A-9 or 2-2-7). As pone, however, only a three-card magic eleven is effective against ten-cards, since you're the one who has to make the first play.
HALSCRIB starts with 4-7-10-10-K-K and tosses the 4-7, a choice it would only make playing on. 10-10-K-K is a horrible defensive pegging hand, but HALSCRIB reckons it's only a little worse on offense than 4-7-10-10 or 4-7-K-K. Since 10-10-K-K returns the most combined points between hand and crib, and since the bot is mainly concerned with offense at this score, it gets the nod. Note how a pair gains relatively little added value when you send it to your crib (the exception being a pair of 5s).
The bot leads a 10, saving its run-proof Ks
for later. On our 2 reply it continues with the second
10, saving its K-K for last in case we started with
four low cards or with a stray K, which the bot could triple
on the second play series.
As pone HALSCRIB gets dealt 4-6-7-10-Q-Q, and must choose between 4-6-Q-Q, 6-7-Q-Q or the super-aggressive 4-10-Q-Q. Going into the deal the bot is -5 to our +11, a position that normally calls for playing on. But HALSCRIB's initial six cards aren't terribly promising, so it's loathe to give up on defense entirely. This rules out 4-10-Q-Q, which averages ¼ point more in the hand but pegs worse than the alternatives (according to Mueller's statistics anyway) and gives up two points more in the crib. The choice is thus narrowed down to 4-6-Q-Q or 6-7-Q-Q. This is pretty much a tossup, but since the bot has to pick something, it picks 4-6-Q-Q.
HALSCRIB leads a Q, hoping we'll be trapped with four ten-cards and feel compelled to pair it (the 4 would have been a more defensive lead). We play the 9 from our 2-9 magic eleven. Dropping the 2 instead is an interesting ploy when you have a 4 to cover a 3 reply. But that's more of an offensive play, and at this score with a decent (if sub-average) hand and good prospects in the crib, a little more discretion is called for. Naturally, pairing the Q was not given serious consideration.
The bot makes an interesting play on the second play series. Instead of
leading the 4, which is matched by the starter, it leads the
6, wary that our last two cards might be 6-6
At the start of this deal we humans were feeling pretty good about our prospects, up +12 to the bot's -11. But cribbage is a fickle game, and this would be the deal where HALSCRIB, aided by a perfect cut, starts its comeback.
Both side have discarding decisions to make. HALSCRIB starts with
2-2-6-6-8-Q. There are three reasonable alternatives, from which the
bot selects 2-2-6-6 for its offensive pegging potential. It
surprises me a little to see the bot commit to offense with such a weak
looking hand (6-6-8-Q would have been its choice for balanced
play). Lest you harbor any suspicions, keep in mind that the Zone, not
HALSCRIB, is dealing out the cards, so no one can accuse the bot of knowing
that a 7 cut is coming up!
|The ROTW starts with 2-4-9-Q-K-K and chooses
to keep 2-4-K-K, which saves ½ a
point in the crib over 2-Q-K-K and 4-Q-K-K
at a cost of only point in the
hand. A potential double-run combo like Q-K-K is less
powerful than it looks because it is one-sided and converts only on a
J cut. Combos like this are worth
about ½ point in added value (whereas a
two-sided potential double-run combo like J-Q-Q would
contribute about 1 point in added value). By keeping both the 2
and the 4 in our hand, we improve on any low card cut, and
have the option of leading a low card without having to worry about the bot
making the count 11 with its reply.
If HALSCRIB 4.90 was in our shoes, it would keep 2-4-9-K due to a perceived advantage in pegging. I don't know why Mueller's numbers rate 2-4-9-K so much higher than 2-4-K-K, particularly when Schempp's pegging numbers show no real difference between them. Perhaps I'm missing something, or perhaps this a glitch in the version 4.90 pegging averages. In general, I think that the current generation of bots does a more accurate job of estimating the pegging potential of dealer hands, since pone's pegging performance is heavily dependent on making the right opening lead, a skill that the bots are still learning. One reason I cite two different sources of pegging averages is to show whether there is a convergence of opinion. If so, then the bots are probably pretty close to the truth. If not, you will have to use your judgment interpreting the results. Either way, what matters is how each bot rates the hands relative to one another, not how high or low they rate in absolute numbers, since the latter quantity is more subject to statistical and systematic distortions. Mueller's numbers, for example, are consistently lower than Schempp's due to differences in how the averages are calculated.
The ROTW leads the 4. If it's paired we can then get the
count over 15 with a K. HALSCRIB replies with a 2,
preferring the risk of a 9-3 to that of a 15-5. We refuse to pair it, but do
pair the bot's second 2, since the chance of HALSCRIB
having the fourth 2 is statistically rather small, and was
deemed worth the risk when we were starting with such a weak hand ourselves.
Now we're +6, and HALSCRIB is -6. The bot keeps 2-2-5-10, eschewing the aggressive alternative of tossing 5-K to keep A-2-2-10 (with a shot at fourteen points). That might have been appropriate playing on, but the fact that HALSCRIB's positional deficit is the same as the humans' positional surplus indicates that its front-end and back-end winning chances are roughly the same. It doesn't make sense to give up on the possibility of winning through defense just to grab a 4-in-46 chance of cutting a 3.
After cutting a 9, the bot stumbles a bit in the pegging. Since its hand is worth only four points, HALSCRIB should focus on defense, hoping to erode our positional surplus by limiting our pegging and perhaps sticking us with a lousy crib (the bot's A-K toss doesn't combine favorably with the starter). It should therefore lead one of the 2s. Instead it leads a 10, presumably trying to entice a pairable 5. On our K reply, HALSCRIB plays a 2 instead of dumping its 5, even though the 5 ought to be safe (since we failed to score a 15-2) and would give the bot an opportunity to either run its 2s for a pair and a go or maybe even triple a stray 2 for a big 31-8. The bot is hoping to catch us holding all ten-cards:
The humans are +5, HALSCRIB is -12. From A-2-8-9-10-K we
toss A-K, which is a little safer in the crib than 2-K
while returning the same average hand.
There was a bit of discussion about whether to lead the 2, 8 or 10. A 2 lead is least likely to give up an immediate score, but it gets us trapped on an 8, 9 or 10 reply. On an 8 lead, we'd be willing to take a 24-3 after a 7 reply, whereas leading the 9 or 10 we'd have no opportunity to retaliate if dealer scores. So we lead the 8. We play low on HALSCRIB's Q reply, hoping to trap a 10 or J on the second play series. Dumping the 2 also keeps it from getting trapped into a run or triple after a go, and if it's paired we can retaliate with our 9.
HALSCRIB has its own decision to make on card one holding 5-x-x-x. When I hold this hand, I'll usually play the 5 when pone leads an 8 or 9. This keeps it from getting trapped into a 30-4 or 31-5 if pone also has 3-4. If my ten-cards include a pair or touching cards, I'll often get lucky on the second play series: pone gets an early go with a high card, then has one or two more cards squeezed out leaving me with a three-on-one or three-on-none. However, dumping the 5 early does give up two points to a 2 or 5, so playing desperation defense I'll just drop a ten-card and hope for the best.
In this position the bot is understandably reluctant to give up any
score, even a two-pointer, so it forgoes dumping the 5 early.
The question then is which ten-card to play. Clearly a Q
would be the safest choice. Pone is ordinarily more likely to have retained
a J than a Q, especially given the 8
lead (a J can form a four-card run with the 8,
but a Q cannot). And since HALSCRIB has two Qs,
it's even less likely that we'll have the third one lurking in our hand. So
at this score, it's a pretty easy choice. Even playing on, however, it's
probably still right to play a Q now, saving the J-Q
combo for last. After pone's go, you can lead the Q and
hopefully trap a 10 or K into a 30-4, or a
J into a 30-3. This seems a tad more promising than saving
the Q-Q and hoping to end up either running the pair for a
20-3 (if pone has A-A-6-8 and plays the 6
second, for example) or, on a lucky day, tripling a stray Q
for a 30-7. In general when you're playing on as dealer and have three
ten-cards, try to keep 10-J or J-Q together
even if it means breaking up a pair. J-Q is especially
powerful if pone has ten-cards, while 10-J is attractive if
pone opened with a mid-card and may have a 9 to trap. If
neither of these combos is an option, try to save a pair for last,
particularly a pair of Js. Of course, if your position
requires you to specifically peg four points, always keep your touching
cards together. If you need to peg six or seven points, always keep a pair
together and hope to triple your opponent.
HALSCRIB's big hand and crib propel it into marginal position, right at par (0). We are technically -22, but effectively +4 if we can hold down the bot's scoring.
Obviously we need defense, and fortunately we're dealt a powerful enough
scoring hand that we can afford to play off in the pegging without worry.
There's no way we're pairing the bot's 2 lead! Instead we
break with our "out" card, the K, and end up pegging a 31-5.
The bot runs two of its Qs at the end for three precious
points. When the dust settles, the bot's position has slipped slightly to
At a critical score we are dealt 2-3-4-5-10-Q. Since there
is no combination of four cards available that could possibly get us near
the game hole this deal, our discarding strategy will emphasize defense. An
ideal toss in this position would be something like 10-K,
9-Q or 6-10. We lack those, but we can
throw 2-Q or 4-Q, either of which gives up
less in the crib than the average 4
points. We choose 2-Q, since it leaves us with
3-4-5-10, worth five points, instead of 2-3-5-10,
worth only four. The fact that we have a 3 in our hand makes
the 2-Q toss a little safer than usual. In fact here it's
just as safe as 4-Q even though 4-Q normally
gives up .1 point less.
Note that in a more offensive position, 2-3-4-5 would be our clear choice. It gets the highest average hand — despite being worth only four points going in — and is an unusually strong offensive pegging hand, racking up five points against dealer's x-x-x-x. Unfortunately it also gives up a lot of pegging points, since there is no way to disengage if dealer has matching cards. As a result there was little interest expressed in holding it here.
After the 8 cut we lead the 4 following the defensive principle of playing from the middle of a three-card run. This spaces out our remaining cards as much as possible. Playing on, we'd do the opposite, leading the 10 to keep our touching cards together (and to entice a 5 that we could pair).
HALSCRIB plops down a 6, provoking a lively discussion over whether to take the 15-5. A few gung-ho humans wanted to go for it, but the majority felt that playing off with the 10 was the percentage play. To understand why, consider what would happen in a best-case offensive scenario. We score five points with our 5. Dealer plays a 7, and we then score another five points with our 3, making the count 25. In a perfect world this will also be a go, so we end up pegging eleven points to accompany our seven-point hand:
Unfortunately this sequence only gets us to 116*, so assuming the bot hasn't counted out first, we'll still need to peg five points as dealer next hand to win. That's probably a three-to-one shot at best, if everything has gone according to plan beforehand. These aren't very encouraging odds. The bot is starting this deal -1, and even though the bot's 6 looks pretty ominous in combination with the 8 cut, we surely have a better chance of winning by playing off. The fact that HALSCRIB is offering us a 15-5 suggests that it is either trapped or else assumes that an exchange of runs would be to its strategic advantage. We decide to play our 10, and put the pressure on the bot to get out cleanly in three counts.
In the event, HALSCRIB is holding a 5-6-7-9 flush, and is
entirely justified in trying to egg us on in the pegging. The play of the
5 on our 3
in the second play series is odd though. The bot seems to have been fooled
by our failure to play our 5 for 15-5, and is assuming we
don't have one — an apparent glitch in this version of the program. It was
the bot's only blunder of the game.
The humans did their job by holding the bot to two pegs plus two more in the crib. But fate is smiling on the bot, and it follows up its thirteen-point flush by holding a pat twelve points in 3-3-4-5 (improved to twenty by the cut). If HALSCRIB had started this deal within six points of home, it likely would have kept 3-3-5-7 instead for safer pegging.
The humans get dealt 2-4-6-8-10-J and toss 10-J. On HALSCRIB's 3 lead we considered whether to play the 6 or the 8. A measurement I call objective risk often helps in endgame pegging situations. It is calculated by multiplying the number of losers by the amount of the score given up. Our 6 has three losers (the other three 6s) which each score four points, so its objective risk is 3 · 4 = 12. The 8 has six losers (4s and 8s) that each score two points, for an objective risk of 6 · 2 = 12. Now when pone is seven, eight or nine points away from home, I like to make a special adjustment and consider a four-point peg, such as a 15-4, to be no worse than three points in my objective risk calculations (I've found that this better handles the particularities of certain hand types at these scores). This gives the 6 an adjusted objective risk of 9, which is ostensibly safer than the 8.
But objective risk shouldn't be considered in a vacuum. You must also gauge your opponent's chance of counting out based on what you know of his or her hand. Given the 5 cut and the 3 lead, how would the bot's prospects look if its second card was one of the three losers we're concerned with? Well, if it's a 6 or 8, it's not at all clear that the bot has enough points to go out, so giving up two or four extra pegs could well be fatal. But if HALSCRIB's second card is a 4, then it's likely — though not certain — that the game is already over. To fall short, the bot would need to have started with a disconnected hand like 3-4-6-9 or 3-4-10-Q (we discounted the possibility that the bot was holding hands like A-3-4-x from which it was unlikely to have led a 3). Ultimately we concluded that a 4 wasn't really much of a loser after all, and that the 8 was thus a slightly safer play. HALSCRIB 4.90, when placed in our position, agrees that the 8 is a trifle better, though our winning chances either way are only about 35%.
In the event it doesn't matter. HALSCRIB prevails 121-114*.
This was a well-played game, with both sides showing a good understanding of board strategy and how that affects pegging and discarding tactics. The ROTW's only questionable move was leading the 9 on the second play series of Deal One. HALSCRIB seemed a bit confused about its pegging strategy in Deal Five, and committed a clear misstep in Deal Eight, but otherwise played error-free cribbage.
Here are a few points worth taking away from this game:
Average scoring (excluding last deal)
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!
- April 2003
Pegging averages may have arithmetic discrepancies due to rounding. Mueller pegging averages were obtained from HALSCRIB 4.90. Click here for a guide to cribbage notation and symbols.
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