Schell's mailbag, January 2005

Another year, and another edition of the Mailbag. Once again, here's a selection of the most interesting reader letters from the past twelve months, with some editorial comments from Yours Truly. When you write to me, please remember to include your full name and home town. If you want my opinion on a specific play, be sure to indicate the score and who is dealing, in addition to all the known cards. I'll publish as many of your questions and comments as I can, after editing for length and clarity. And please be patient awaiting a reply. Thanks!

Printing Cribbage Forum articles

"I like your site, but have one slight problem with it: when I try to print some of the articles, I only get about half the wording on the page."

- Jim Baukner

That's the result of the wide columns required to accommodate the statistical tables and play diagrams in some of the articles. If you find that the text is cut off at the right margin, then changing the print orientation from Portrait to Landscape should work. I also suggest going to Print Preview before you send the job to your printer. That way, you can spot potential formatting problems before committing yourself to paper. Unfortunately at present I lack the time to craft separate print-optimized pages the way some large commercial sites do.

Cribbage software

"Which is the best Cribbage game to run on a home computer, specifically one running Windows XP Home Edition?"

-Charles Nighbor (Walnut Creek, CA)

As regular Cribbage Forum readers know, HALSCRIB has clearly established itself as the world's strongest silicon cribbage player, as well as the most useful cribbage software for human players looking to improve their game. As of this writing (December 2004), it's really not a close call, and hasn't been for at least three years.

Understand that I'm not dissing the contributions by Bowman, Hessell, Schempp and others who advanced the state of cribbage programming with their work. It's just that at present, HALSCRIB surpasses the rest of the field by a significant margin. I think all cribbage enthusiasts should support Hal Mueller's solitary and devoted efforts to further the game by buying HALSCRIB now! The money you spend will be easily repaid in tournament prizes and tavern wagers.

And yes, HALSCRIB will run under Windows XP Home Edition.

28 and 29 odds revisited

"I think I see a flaw in the calculation of 29 hand odds at 1 in 216,580. The rules of the ACC were not taken into consideration. They state that at least four cards must be left on the top of the deck and no fewer than four must be left at the bottom of the deck when the cut is made. This then removes eight cards from being available to make the cut of the ever elusive fourth 5. I was also wondering what the odds of obtaining a 28 hand are."

- Jim Duff, Director, Sweet Onion Peggers (club #274)

The cutting rules do not affect 29-hand odds: the cut card still has a 1 in 46 chance of being the last 5, whether it's drawn from the middle of the pack or toward one of the edges (and whether it's cut legally or not!). Remember, we presume to have no knowledge of where the case 5 is, and thus no reason to assume that it's in the forbidden edge of the deck, or the legal middle of the deck. Even if the rules mandated the exact card that must be cut, the odds would not change. See here for more on how 29 hand odds are calculated.

Regarding 28 hands, the generally cited figure is 1 in 15,028, which assumes that you would not toss the right J starting with 5-5-5-J-x-? or 5-5-5-J-x-x, but would keep the eligible hand in all other cases. The "pure" odds, which assume you always keep the eligible hand, are 1 in 14,484. Of course in the real world there are going to be times where a competent player deliberately eschews the eligible hand, mainly in endgame pegout situations where you don't want to be caught sitting on three or four 5s. Thus you can expect that the actual incidence of 28 hands will be slightly less than the mathematical odds predict.

By the way, Jim's Sweet Onion Peggers club meets on Thursday evenings during the Grass Roots season (September to May) in Walla Walla, WA. Drop by for an evening of cribbage if you happen to be passing through.

Stinkhole rules, with a side rant on cutting before dealing

"I am interested in reading or finding out about any restrictions that are used in international cribbage tournaments regarding the stinkhole. I have always played that if you land in the stinkhole, you may not peg to win, and can only win by counting the points in your hand. Recently I played with someone who says that if you peg into the stinkhole, you may continue to peg to win, however if the points in your hand land you in the stinkhole, you cannot peg to win but must count from your next hand. Comments?"

-Coni Rozema (Edmonton, AB)

For the uninitiated: stinkhole is universal cribbage slang for the next to last hole (120 in the standard two-player game). There are no special rules in tournament play governing the stinkhole or any other hole on Fourth Street leading up to the game hole. If you land in the stinkhole, you may advance from it by pegging, counting your hand or crib, scoring His Heels, or by a penalty assessed against your opponent, just as you can from any other hole.

There are lots of local rules variants that you'll encounter in cribbage playing countries. Some of the more common ones include:

  • Requiring players to reach the game hole by exact count
  • Forbidding players from winning on a cut J
  • Counting four-card flushes in the crib
  • Forbidding pone from cutting the deck before the cards are dealt

At least as late as the 17th Century, crib flushes were counted even if they didn't match the starter suit. But otherwise none of these rules variants has ever been a part of traditional cribbage. In Suckling's original five-card game (which ended at 61 points), there were no special rules concerning the last few holes. And this business of forbidding pone from cutting the cards before they're dealt is a particularly misguided bit of nonsense that crept into printed rules included with cribbage boards during the last century, and has been uncritically recirculated ever since by irresponsible manufacturers and ignorant players. In addition to being inauthentic, this practice also encourages cheating and confuses casual players when they first encounter club or tournament cribbage. Simply put, there is no legitimate reason not to cut before dealing, as is done in every other card game, and as is required by the ACC in their official rules, which, incidentally, are available online here.

Domino cribbage

"I love your forum. It is unbeatable and wonderful. Would you have any comments about domino cribbage? It was very popular in the Royal Canadian Air Force for years, as widely played as acey ducey was in the US Navy."

- Earl K. Dille, St. Louis County, NJ

Thanks for the kind words! I've never played domino cribbage. From the descriptions I've read, I gather it is basically standard cribbage played with double-six dominoes instead of playing cards. The total number of pips on each tile comprises its "rank", and tiles of the same rank are equivalent for all purposes. Since there is a double-blank tile, the number of ranks runs from 0 to 12, equaling the thirteen ranks in a conventional 52-card deck. However the rank distribution is not flat, but follows a bell curve with 6 being the most frequent (four different tiles) and 0, 1, 11 and 12 the least frequent (one tile each). There is no concept of "ten-cards": the 11 and 12 tiles have a face value of eleven and twelve respectively (at least this is in the British descriptions coming from the game's popularity in the Royal Air Force going back to World War II — I'd be interested to know if they handle this differently in Canada). Thus there is no premium on 5s as in regular cribbage. Also there are no suits, and thus no flushes and no Nobs. I assume the double blank tile would form a three-card run with 1 and 2 pip tiles, and that it would add nothing to the running count if played during the pegging. Discarding and pegging tactics would presumably revolve around maximizing the potential of your mid-cards (in this case 4, 5, 6, 7 and 8), as these are the ranks most likely to be matched by the starter and by the cards held by your opponent. Joe Celko has a commentary on domino cribbage at the Card Games Web Page.

Readers might be interested to know that Mr. Dille's talents extend beyond cribbage, having been a Navy pilot and a Virginia state chess champion in the 1950s.

Leading a 5 (again)

"I read and enjoyed your article on leading a 5. I lead 5s perhaps more than any other tournament player that I have seen. One of my favorite defensive leads is to lead the 5 from 5-7-8-9. On perhaps ten occasions I have had the pleasure of the following sequence:

5  9  9 (23-2)

Not to mention, what would otherwise be the safe lead from 5-7-8-9?"

- Laurence Samet, Wellesley, MA

Thanks for the tip Larry! Among other things, Dr. Samet is a Life Master - One Star, a two-time All-American, winner of the 2004 ACC Tournament of Champions, and is currently ranked 13th overall in lifetime IRPs. It's always nice to get a tip from a player with those kind of credentials.

Board strategy questions

We'll close with a couple of questions about board strategy, one general, the other more specific.

"Chambers' board position par figures are the same whether you are pone or dealer. Colvert's, however, differ depending on whether you're first pone or first dealer. In Cribbage Forum analysis, when you refer to being + a certain figure as dealer or pone or - a certain figure by dealer or pone, I'm not immediately understanding the base number from which the positives or negatives are being derived.

- Scott Johnson (Fairfield, CT)

Scott, this is a good question. Let me start by summarizing the differences between Colvert's and Chambers' schemes:

  • Chambers refers to four positional holes (not counting the game hole), whereas Colvert refers to par holes
  • Colvert uses + and - to denote both players' position relative to the par holes (what I call positional standing). Chambers does not
  • As you note, Colvert has two sets of par holes, one for first dealer (the player who deals first) and one for first pone. Chambers' positional holes are the same for both players. As I explain below, this is really only a difference in nomenclature
  • Colvert's is a "pure" 26 theory. He counts back 26 holes from 121 to establish 95* as dealer's penultimate par hole. Chambers' corresponding positional hole is 96*, though his three preceding positional holes are 26 points apart

A full explanation of modern board strategy as I teach it will need to await my book, which, alas, is some years from materializing. Briefly, though, I can tell you that my system draws on both Colvert and Chambers, with adaptations designed to make it easier to use, handle skunk situations, and better reflect the realities of expert level play as well as the results of recent computer analysis.

Since one set of positional holes is easier to remember than two sets of par holes, I use the former, though I've adopted Colvert's +/- notation to denote positional standing. And although 26 points represents average scoring for a two-deal cycle on First through Third Streets (holes 1 through 90), the experience of modern expert players and programmers has established 25 points as a more realistic figure for average scoring on Fourth Street. This gives us the four positional holes of 18, 44, 70 and 96. In this regard I agree with Chambers, though accidentally so, since Chambers' rationale for placing the Fourth Street positional hole at 96 is actually based on a mathematical error.

In my terminology, pone has the positional advantage if she has reached, or is within ten points of reaching, a positional hole that dealer has not yet reached. Otherwise dealer has the advantage.

If you have the positional advantage, your positional surplus is the difference between your score (or your score plus ten if you're pone) and the last positional hole. Your opponent's positional deficit is the difference between her score and that same positional hole. If your opponent is pone, add ten points to her score. If she is now at or beyond the positional hole in question, then her deficit is the distance to the next positional hole. All this is reversed if your opponent has the positional advantage. Note that the ten-point adjustments are based on the average amount pone will score in one deal. Based on this you can see that after allowing for the one-point shift from 95 to 96, Colvert's par holes correspond exactly to the positional holes used by Chambers and myself.

You apply this information as follows:

  • If your positional surplus or deficit is greater than your opponent's positional surplus or deficit, you should generally favor defense. The greater the disparity between your and your opponent's standing, the more you should emphasize defense over offense
  • If your positional surplus/deficit is less than your opponent's positional surplus/deficit, you should generally favor offense. Again, the greater the disparity between surplus and deficit, the more aggressively you should play
  • If your positional surplus/deficit is about the same as your opponent's, try to balance offense and defense

That should give you enough guidance to follow most of the discussions of board strategy at Cribbage Forum and elsewhere.

"Your Second Place Grass Roots finish nationally couldn't happen to a more fitting player. A quite successful ACC player from the East Coast brought up an interesting scenario. The score is 65-65* and dealer deals you 2-2-J-Q-K-K. What do you toss? Is it worth it to keep 2-J-Q-K rather than throwing the pair of 2s and giving up 6.4 crib points (according to your statistics)? I would also consider tossing J-Q, giving up a 5.5 point crib while retaining 4 points in hand. I see this as a middle ground toss between the other two."

- Pat Hayslett (Potsdam, NY)

Pat, nice to hear from you again! At 65-65* I am +5 while dealer is -5. In other words, my positional surplus is exactly equal to my opponent's positional deficit, a situation that normally calls for cautious offense, a strategy in which my goal is to outscore my opponent. Some call this balanced play as distinguished from offensive or defensive play. In these cases I'll keep the hand that gets the best expected average, after factoring in card distribution and pegging potential. With that in mind, let's look at the hands.

The offensive choice is J-Q-K-K, worth eight points pat. The defensive choice, 2-J-Q-K, keeps only three. (In reality the average hands are 10.45 and 5.32 respectively, assuming the J suit is matched by one other card). You mentioned that 2-2 gives up 6.4 points on average, while 2-K gives up 4.5. Over the board, I'd guess that 2-2 costs an extra point or so relative to 2-K since you're not blocking any helpers for the former toss, whereas the latter toss is partially blocked by the extra 2 and K you've retained. (The exact adjustments, or delta, are +0.10 for 2-2 and -0.05 for 2-K, according to DS.EXE).

Now consider pegging. If I retain J-Q-K-K, I'll presumably be playing defense after the cut, and J-Q-K-K is a weak defensive hand, though not as bad as something like 4-5-5-6 or 6-7-8-9. 2-J-Q-K is better, since you have a low lead in the 2, and you aren't likely to get killed even if dealer scores off it, though it probably doesn't have much more offensive potential than J-Q-K-K. A good rule of thumb is that a hand with a safe low lead is point safer on defense than a comparable hand without one. That makes J-Q-K-K about 2 points more dangerous than 2-J-Q-K. Since this is significantly less than the five points of offense it costs me to hold 2-J-Q-K, I would grit my teeth and toss 2-2 here. It's the best way to handle this awkward hand.

If tossing 2-2 in this position seems reckless, consider the following:

  • Although 70 is a positional hole, it's not a life-or-death goal. If dealer makes up his five point positional deficit here, it doesn't mean he's won the game, only that he's become a favorite (perhaps 52–53%) to go out on his three Fourth Street counts. By ensuring that you don't fall behind yourself, you retain most of the 47–48% underdog equity in that proposition
  • Making a dangerous toss doesn't guarantee that dealer will move into position. He still needs a better-than-average hand, or else to get lucky in the pegging by holding something like 4-5-6-K
  • If you get a favorable cut for 16 or 17 points, you'll have pushed yourself to at least 81 or 82 points without having directly improved the 2-2 in the crib. You'll be able to play defense the rest of the way out, with little fear of falling out of position yourself. And with average cards, you'll expect to deal the last hand from 107* or 108*, well past what I call the yellow zone (the ten hole range that begins at a positional hole, in this case 96*–105* inclusive). The significance of this is that you are a favorite to go out in two counts as dealer, and probably won't need to count your hand as pone on the following deal. This denies your opponent the opportunity to peg out as dealer on the last hand, an advantage that is generally worth sacrificing a couple of points for elsewhere on the board
  • Continuing this last idea, you could get real lucky by hitting your cut here then getting better-than-average cards down the stretch, allowing you to go out early even if dealer does temporarily make up the deficit. You might even get a skunk this way. Playing safe instead would pretty much eliminate any skunk potential
  • If your opponent knows what he's doing, you risk giving him tremendous flexibility on the next deal by holding 2-J-Q-K and cutting one of the several ranks that leaves you short of the positional hole. Imagine, for example, that you get stuck at 68* or 69*, while your opponent gets average scoring (despite your 2-K toss) and reaches 81. Now depending on what you deal him, he'll have a full range of choices between playing offensively (if he has a shot at reaching 96 as pone), breaking up his hand for full defense, or sitting on the fence with middling cards. By holding J-Q-K-K you nail down your own position. You can then worry about stopping your opponent

I've given short shrift to your 2-2-K-K option, an interesting choice that I might not have found over the board. It's a better pegging hand and averages .42 more in the hand than 2-J-Q-K, though it does give up 1 point more in the crib. For the reasons cited above though, I'd still keep J-Q-K-K.

Whew. Who says cribbage is a simple game? Keep on pegging everyone, and stay in touch!

- January 2005

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