Schell's mailbag, January 2002

It's our second anniversary at Cribbage Forum. To mark the occasion, here's a new installment of Schell's mailbag, which features some of the most interesting comments and questions from Forum readers. Several players wrote in with pegging questions, and we also hear from two programmers — Max Kassler and Hal Mueller — who released new cribbage software during the past year.

Handling 2-3-5-x as pone

We begin with a question from Pat Hayslett, a pegger from Potsdam, NY who can be frequently found playing at MSN Gaming Zone:

"I have recently been trying to raise the level of my game and I think I have succeeded quite a bit thanks to your Forum and your suggested reading, like Colvert's and Chambers' books. However, I have one little pegging tidbit I wonder about that is not addressed. Let's say I have 2-3-5-J as pone, and the pegging starts:

3  x  2 (15-2)  x

I am now forced to play my 5 and get my J caught in a two-on-one, most likely for a run or a pair. How do you suggest dealing with such a pegging hand?"

Pat, thanks for the nice comments, and congratulations on having improved your game through study and thoughtful analysis. As for your question, no pegging hand is risk-free, especially if you're pone. With 2-3-5-x, there's really no substitute for playing the hand the way you describe. True, you give up a two-on-one on the second play series if dealer is holding four ten-cards, but the alternatives are no better. If you eschew the 15-2 and drop your 5 second, you're still vulnerable against x-x-x-x:

3  K  5  10  2 (30-1)    Q  J  J (30-3)

Dropping your J second gives up a three-on-none on the second play series, which is even worse than giving up a two-on-one. Nor does leading the 2 (instead of the 3) gain you anything against x-x-x-x. Fortunately, Craig Hessel's research on four-card hand frequency suggests that dealer will be holding four ten-cards just 5% of the time. So don't fret too much. Just lead a 3 from 2-3-5-x, take the 15-2 if offered, and hope for the best. The only times I wouldn't do this are in defensive situations where the 2 is matched by the starter or a discard (in which case I'd lead it instead of the 3), or in an endgame situation where I have to peg and expect dealer will be playing off (in which case I might lead the J, hoping to keep him guessing about my hand composition).

Tournament formats

Code Clements from Prince George, BC asks:

"Is there a set of rules to hold a small company cribbage tournament? About 16 people will be playing, probably in pairs. The sites I have visited refer to two types of tournaments: Swiss or round robin. Hope you have a suggestion."

There are lots of ways to organize an over-the-board cribbage tournament. The most popular format in North America is a round robin arrangement where every entrant plays a fixed number of games, all against different opponents. Regular wins are worth two game points, skunks are worth three, and losses are worth zero. The tournament winner would be the player (or team if you're playing doubles) with the best scorecard at the end. If there is a tie, the first tiebreaker is the raw number of games won (irrespective of skunks), and the second tiebreaker is total spread points (points scored minus points given up). Grass Roots tournaments usually follow a nine-game round robin format, which can be comfortably completed in three hours. Note that in a round robin it is not necessary for each entrant to play every other entrant, just for each entrant to play the same number of games, all of them against different opponents in a predetermined (and usually random) order. This can be facilitated by seating entrants at one long row of tables, and directing everyone except a single anchor player to shift one seat counterclockwise after each game.

Single- and double-elimination tournaments are popular on the Internet, probably because they quickly free losing players to do other things. This same characteristic makes them unpopular for over-the-board tournaments, where there are fewer activities available for players who are knocked out early. Elimination rounds can be a single game, or a match of several games against the same opponent. In single-elimination, you are out when you lose a round. In double-elimination, you are out once you've lost two rounds. Double-elimination reduces the luck element somewhat, since a single batch of bad cards can't dump a player out of contention, but this format is more complicated to run, and takes longer to conclude.

Most ACC sanctioned tournaments are a hybrid between round robin and single-elimination formats. They start with a round robin qualifying round, in which each entrant plays several games (most commonly 22) against different, randomly-drawn opponents. The player with the highest scorecard at the end of the round is anointed top qualifier, and usually receives a trophy and an extra cash prize. All entrants who finish in the top 25% advance to the playoffs, which are a series of single-elimination matches — typically best-of-three or best-of-five with skunks disregarded — that determine the tournament champion. In major tournaments, the qualifying round is usually held on a Saturday, with playoffs taking place on Sunday. A consolation event is also held on Sunday for players who do not qualify in the main event or get eliminated early in the playoffs. Consolations usually follow the same basic format as the main event (i.e., a qualifying round followed by single-elimination playoffs), but fewer games are played in each stage, allowing the action to conclude in a single day.

Finally, there is Swiss System, a complex format often used for chess tournaments. In this format, pairings are not pre-determined, but are calculated anew after each round, with the goal of matching players with similar scores in the tournament. The idea is to arrive at a single clear winner after a fixed number of rounds, and to allow entrants to play similarly-performing opponents. Swiss System has not been used much in cribbage, mainly because of the time and effort required to generate pairings after each round, but I think it has merit for tournaments that feature match play rather than single games. I would nevertheless avoid using this format in a small casual tournament.

It sounds like your best bet is a round robin format, perhaps the nine-game version used in Grass Roots play. If you like, you can send the top two or four finishers to playoffs to determine the winner. To give players with weak scorecards a chance to win something, you might offer small prizes for novelty hands like crib flushes, Raggedy Anns and the last 24-point hand of the evening. For some local advice, I recommend contacting your Prince George Grass Roots club. You can also find specific instructions for running this type of tournament in the ACC Grass Roots Manual.

Rules questions

A few readers wrote in asking about pegging runs, one of the greatest sources of confusion for new players. This message from Darryl Wiebe of Alberta is typical:

"I was in an argument a couple of weeks back, where a person missed an opportunity to score on a run for 31:

2  8  6  4  5 (25-3)  6 (31-?)

He actually played the 6 but only took two points (for the 31). When I asked him why he didn't take his extra three points, they (himself and the girl he was playing) said it was because the run was already being played (the 6-4-5 for 25-3) and to continue the run for four points, he would have had to play a 3. I tried to explain my point of view on the situation, and they both looked at me like I was from Mars. Could you please clarify this situation, as it's driving me totally nuts, and it would also mean I've been playing this game wrong for the last 30 years, which would devastate me, LOL."

Darryl, you are right and the people you were watching are wrong. To score a pegging run, the cards in the run need not be played in any particular order — they need only be played contiguously. The 6 played for 31 clearly forms a three-card run with the preceding 4 and 5, so the fellow should have pegged five points, not two points. It doesn't matter that the 4 and 5 were part of another pegging run previously claimed.

Here's another rules question from Gail Cullen:

"I have played crib all my life, but recently started playing with a group. I was taught that if a J was cut and as dealer you were within five holes of the finish line, you could not take your two points. Some at the group say this is not so. Can I have your ruling on this please?"

Any group of people that plays together is certainly free to make up their own rules, and the one you describe seems to be especially popular in Canada. But the internationally accepted rule is that a J starter is worth two points for dealer regardless of board position. If you're dealing from one or two points out, and pone cuts a J, you win immediately. This is how the game is played in American Cribbage Congress tournaments, and on all the Internet gaming sites.

5-x-x-x as dealer

Pat Hayslett asks about a common pegging dilemma:

"There is a situation that doesn't happen frequently but when it does I am always left wondering what the better move is. It happens when as dealer I have all ten-cards and 5s. Pone leads a 3 at me. I can't dump off my 5, so I get the count up and they make 15-2. My policy has been to dump the 5 at this point, which is obviously superior if pone has face cards left. However, you really get nipped if they have low cards like 3-4. I seem to break even so far when I make this move. Do you think it is best to dump the 5 or get the count up again? Does board strategy factor in? It almost seems to me dumping the 5 could be useful playing on to fish for a high card run or a pair royal at the end."

Unfortunately this is one of the many tactical situations in cribbage that has no easy answer. Usually, if I'm holding 5-x-x-x and pone scores a 15-2 with a magic five, I'll drop a ten-card next instead of the 5. This is particularly true if my last ten-card is a K, since if I do get trapped into an early go followed by a two-on-one, I'll at least be holding the most run-proof possible ten-card. Doing this has two advantages relative to dropping the 5. First, it performs better against hands like 2-3-3-4, 2-3-5-5, 2-3-5-x and 2-3-4-6, and second, if pone's last two cards total six or less, the 5-x will score a 15-3 at the end (what Dan Barlow calls a big finish). Nevertheless, dumping the 5 first certainly has merit. As you mention, it keeps you from getting trapped into a two-on-one if pone's last two cards are both ten-cards (i.e., if pone started with A-4-x-x or 2-3-x-x). This is more of an issue if you have no K to hang on to, since a lone 10, J or even a Q is more likely to get trapped into a run or triple.

Ultimately, I think the two plays are very close. Not surprisingly then, board position, as well as the cut and even the two cards you tossed to your own crib, can tip the balance one way or another. What it basically comes down to is: Which type of hand do you most need to defend against, something like A-4-x-x or 2-3-x-x, or something like 2-3-3-4 or 2-3-4-6?

Suppose pone scores a 15-2 with a 2-3 combo. The starter is a 2, and the score is tied 77*-77. In this case you should be most concerned about pone having two more low cards, and thus a possible 16- or 18-point hand. That, in combination with a couple more pegs, would give your opponent good standing on Fourth Street. Therefore you should play a ten-card on pone's 15-2. This might give up a couple extra pegs to a hand like 2-3-x-x, but it would still leave pone short of the Fourth Street positional hole (96). Giving up a couple extra pegs to 2-3-3-4 could end up costing you the game.

Now suppose the score is tied 83*-83. Here there's little point in defending against 2-3-3-4, since that hand would already ensure pone excellent Fourth Street position. Better, I think, to drop the 5 first, hoping that if pone does have 2-3-x-x, she'll peg only one more point, leaving her at 94 or 96 points, a scenario that still gives you plenty of winning chances.

Board position might also factor in on offense. As you mention, dropping the 5 first can give you a shot at pegging four points (if you trap pone in a run) or seven (if you triple pone) on the second play series. As dealer it's unusual to know so precisely what you need to peg to make a difference, since you can't know for sure how much your crib will be worth (the exception, of course, being when you're within pegging range of home). But if you have somehow decided that you really need to peg four or more points — and that pegging three points at the end with an uncontested 5-x won't matter — then by all means drop the 5, and save your pair or near cards for last.

Incidentally, HALSCRIB and the other bots tend to favor playing a ten-card instead of the 5, even if they don't have a spare K.

One thing that I hope comes out from all this is that the time to think about which play to make is when pone first leads her 3 or 4. That's because the plan you select dictates which ten-card to play first. Suppose you're holding 5-J-Q-K when pone leads a 3. If you're planning to drop the 5 if pone takes a 15-2, then you should play your K now, saving your J-Q for last. This maximizes your chances of scoring a run or pair on the second play series. If you're planning to play a ten-card on pone's 15-2, then you should play your Q now. Pone is slightly more likely to be able to pair this card than your K — assuming no other ten-cards have been seen — but by playing the Q now, you can then drop your J after the 15-2, leaving the less vulnerable K for last.

Of course, if pone leads a 2 instead of a 3 or 4, you would play your 5, not a ten-card. You knew that. If you play your 5 on an A lead, however, you'll be screwed if pone pairs it, so in that case I prefer to drop my least pairable ten-card.

6-7-8-8 as pone

Another pegging question comes in from niner1, a Yahoo! Games pegger:

"Say I have 6-7-8-8, and I lead an 8 and my opponent plays a K down. What card would you play next? If you play the other 8, most likely opponent has a 5 or a low pair. If you play the 7, opponent could have a low pair or a run. Your 6 could be paired, along with the other risks, but I figure it's the best play, since if the other guy has a low card run to finish the play series for four points, I can then play my 7-8 for a 15-3. Still, what would you play?"

With 6-7-8-8, I would ordinarily lead an 8, then play the 7 if dealer replies with a ten-card. This allows dealer to peg two points only with a 6, whereas if I play my 6 instead, dealer could peg two points with a 7 or three points with a 6. If I need more offense, I might play the 6 anyway, for the reason you mention (i.e., if dealer started with A-2-3-x, A-A-4-x or similar, my 7-8 scores a 15-3 at the end). On the other hand, if I really need offense, I might lead the 7 instead of the 8. The idea here is to entice dealer to reply with an 8, which you can then pair relatively safely. If you're especially lucky, dealer will be holding 8-9-9-10 or similar, in which case you'll be able to play your second 8 for a 31-8. If dealer plays a ten-card on your 7 lead, you can then dump the 6, keeping 8-8 for a big finish if dealer has three low cards.

Cribbage variants

George Rasmussen forwarded this question from Austrian pegger Peter Ebner:

"As I am living in Vienna, cribbage is a totally unknown game over here, and sometimes I think that I must be the only person who is able to play that game. Therefore I prefer to play cribbage mainly against my PC. I have tested a few cribbage games and I must say that I really love them all. Unfortunately I have never seen a version for five-card cribbage. Is a five-card cribbage program for PCs available?"

Keith Westley's free program Ultimate Cribbage supports both five-card and six-card cribbage. Although the original five-card version has been replaced by the modern six-card version in most of the cribbage-playing world, five-card cribbage is still popular in the UK. Of course, modern three- and four-player cribbage is also played with five cards, but these are variants of the two-player six-card game, rather than direct descendents of Sir John Suckling's original formulation.

I'm glad there's at least one cribbage player in Vienna. If you can't find local players, there's always the Internet.

Michael Ventura from Southern California writes:

"Thanks for your site. I really enjoy it. I have been playing for the past several months and have recently come across a four-track cribbage board. I am familiar with a four-person game playing teams — would the concept of a four-track board be to play all four players against each other? Any pros or cons besides it being a longer playing game?"

Michael, thanks for the kind words. Yes, I've heard of four-player, non-partnership cribbage, though I've never played it. It's basically the same as the three-player version. You deal five cards apiece, and everyone tosses one card to the crib. Play starts to dealer's left and proceeds as in any multiplayer version of cribbage. The counting of hands also starts to dealer's left and proceeds clockwise around the table, ending with dealer. And yes, this is presumably what you'd use a four-track cribbage board for. I've even seen old cribbage instruction sheets that described an eight-player version of the game played in four partnerships. I suspect, though, that this is the sort of thing that gets invented by a writer who needs to fill space or sell merchandise, and is then picked up by subsequent writers and repeated over and over until everyone assumes it's the truth. If there is anyone out there who has actually played eight-handed cribbage, please write in with your experiences. For that matter, has anyone played the four-handed, non-partnership variant?

Cribbage on a floppy

Gregory Perez writes:

"Here at work we cannot install games on our PCs. Do you know of a cribbage game that will fit on a floppy?"

At the risk of contributing to the recession, let me suggest Craig Hessel's program Cribbage for Windows 97. If you copy the four core files (cribbage.exe, vbrun300.dll, cribbage.hlp and cribcore.dll) to a floppy disk, you should be able to run it from diskette on most Windows systems.

Endgame count

Hal Mueller, author of HALSCRIB, writes:

"I read your recent article re leading a J with interest. I used isolated card frequencies in my first pegging algorithm, and later discarded it in favour of four-card combination frequencies. Nevertheless, my current algorithm often leads a lone J from a hand not containing a pair, supporting your explanation.

I played in John Chambers' New England Championship in Auburn, Massachusetts. I tied for Ninth Place, but was knocked out by this heartbreaker. Dealer was at 108*, and as pone at 112, I was dealt 3-4-5-7-9-10. I discarded the 9-10 and cut a 10. Led the 4, and pegged nothing. When I got back to Canada to check out this hand, HALSCRIB would have discarded the 7-9 and would have advanced to the next round. Personally, I think I should have led the 7."

I too have had heartbreaker losses in tournament playoffs (see the August 2001 Ask the Experts). Nevertheless, Ninth Place in a sanctioned tournament is no disgrace, and at any rate, in a single-elimination playoff format, everyone but the eventual tournament champion leaves the room a loser. Despite what HALSCRIB says, I think you were right to keep 3-4-5-7 at 112-108*. I've developed an endgame count to help deal with situations like this. For each candidate hand I add:

  • 1 for every cut that puts me out completely
  • for every cut that gets me to the stinkhole
  • for every cut that gets me within two points of home, and
  • for every cut that gets me within three points of home

With dealer at 108* I add nothing for cuts that don't get within three points, since I don't expect to peg four or more points, and I don't expect to survive the deal if I fall short. The fractions represent my approximate chances of pegging the difference against dealer's defensive play. Obviously, a higher endgame count is better. Applying the count to this hand produces the following:

  • 3-4-5-7 wins on a 3, 4, 5, 6, 7 or 8 cut, gets within two on a A or x cut, and within three on a 2 cut, producing an endgame count of 27
  • 3-4-5-10 wins on a 3, 4, 5 or 10 cut, gets to the stinkhole on a 2 or 6 cut, and within two on a A, 7, 8, J, Q or K cut, producing an endgame count of 23

This corresponds to roughly 8% better winning chances (dividing the count by 46, the number of possible cuts) holding 3-4-5-7. I see no reason why 3-4-5-10 would peg appreciably better if dealer is playing defense, so I'd go with the hand with the better objective chances. I also agree with you about the lead. In most cases, the 4 is the right lead from this hand. But in this situation, with dealer likely to be playing desperation defense, the 7 lead looks best. It's an effective decoy, and it keeps the touching cards together. On a ten-card reply, you can play your 5, hoping to trap your opponent with a 5 or low card. Of course, it's easier to see all this after the fact...

By the way, Hal has recently released HALSCRIB 4, a major upgrade to his cribbage playing program. Check out the HALSCRIB Web page for details.

Daredevil computers

Max Kassler, author of Cribbage Hand Evaluator, writes:

"I've been back on a cribbage kick, and have been playing Ultimate Cribbage quite a bit. I've noticed a weird play that the computer occasionally makes. For example, suppose I'm dealt A-4-5-9-10-Q as pone. I discard the A-9. The starter card is a 6. I lead the 4. The weird play that I've noticed several times is the computer's 6 response! I play my 5 for 15-5. Is this just a bug in the play algorithm? Is it a valid play? If so, why would you play this? At best you get a run of four as a return (which is still -1 for the play)."

As strange as it may seem, there are indeed times when it's appropriate for dealer to play a 6 on your 4 lead. It may be that dealer's hand distribution makes him a favorite to outpeg you if you take the 15-5. For example, with 3-6-7-8, dealer will outscore you ten to six this way:

4  6  5 (15-5)  7 (22-4)  8 (30-6)    Q  3  10 (22-1)

The key question to ask in pegging run situations is: Who will likely play the last card in the sequence? That usually determines who comes out on top.

Even if dealer doesn't have a tactical advantage, playing on with the 6 might be indicated if dealer is a little short of position and figures that the four points she can peg with a 3 or 7 will matter more than the five points she gives up to your 5. In DeLynn Colvert's book Play Winning Cribbage, the first annotated game in the Cribbage for Experts chapter features an example of dealer using this play to get good position early in the game.

Having said that, my impression of Ultimate Cribbage is that it doesn't play board strategy at all (which is one reason why an expert player can bat .600 against it). It uses a look-ahead routine for pegging, so when it plays a a 6 on your 4 lead, it probably figures it can outpeg you by enticing you into a run. You might want go to the Play Options screen, and make sure that you have Skill Level set to Hardest and Play Style set to Optimal. If the latter is set to Aggressive, then the program will simply try to maximize its own scoring without regard to your counterpegs.

Going back to your example, starting with A-4-5-9-10-Q, why not keep A-4-5-10 instead? This scores point more on average than 4-5-10-Q, while giving up about .3 points less in the crib. And A-4-5-10 lets you lead from a magic five (the A-4) which will score a 15-2 if dealer has ten-cards. Of course, you still have the 15-5 available if your opponent plays a 6!

19 hands and their ilk

David Cantrell from Fort Collins, CO writes:

"I am an electrical engineer who has recently been introduced to the game of cribbage. Late one night while playing, one of my opponent's children asked why there were no ways to produce 19 points during 'the show'. I am myself very intrigued at the probabilities surrounding the various point totals, and thinking back to school I can remember permutations and combinations and such. I decided to write some code to run through every possible hand and see for myself if this was the case.

The results confirmed that there are no 19 hands in cribbage, but they also indicate that there are no ways to make 25, 26, or 27 points either. Is this a bug in my code? Do you know of a combination of five cards that, when counted using the standard rules, yields 25, 26, or 27 points?"

Your code is fine. There are no hands worth 19, 25, 26 or 27 (or more than 29) in cribbage. This is true both in the international six-card, two-player version, and in the original five-card version, as well as the most popular multiplayer variants. You'd have to find an unorthodox variant played with larger hands, or with non-standard forms of scoring, to get hands worth these amounts.

Nice words

From Cory Watson:

"Just a thank you note for the informative strategies involving cribbage. This will undoubtedly prove to be extremely valuable as I am an avid player. I will in the near future most likely purchase some of the recommended reading materials you've suggested. Once again thank you and happy pegging!"

Cory, I appreciate the nice message. Rest assured there's much more to come at Cribbage Forum in the future. Good luck to you, and I hope to see you at the Tournament of Champions in Reno one day!

Thanks to all of you who have written, including those of you that I didn't get to feature this time around. Contact me here to share your questions and vignettes. Please include your name and location, and if you're asking how to play a specific hand, be sure to indicate the score and who is dealing. I'll publish as many messages as I can in the next Mailbag (after editing for length and clarity). Until then, keep on pegging!

- January 2002

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