The eleven men above certainly aren't playing 11-man ballot or any other variety of checkers, though we'll bet many of them did surely play checkers in a slightly less risky environment.

But today, our subject is indeed the 11-man variant of checkers. Created around 1907 by champion player Newell W. Banks, it provided an inventive alternative to the common "go as you please" (GAYP) style, in the hopes of lending the game fresh variety and reducing the number of draws.

In GAYP, of course, there are no restrictions on opening moves. Players indeed go where and as they please. The relatively short-lived "2 move restriction" style, in which the first move for both Black and White is chosen by lot, was played for a while in the early 20th century; and "3-move restriction" in which the 3-move opening sequence Black-White-Black is randomly selected, came just a bit later and is current today. (GAYP is also still played at the highest levels of the game.)

The 11-move ballot variant got some play and some attention but never really caught on, at least not until recently, and while 3-move restriction has been extensively analyzed, 11-move ballot has remained mostly new territory.

For a full description of 11-man ballot, you can see this link, but the basic idea is that one piece chosen at random is taken off the board on each side, and then the first Black and first White move are also chosen at random. There are some further rules and limitations, but that's the main idea. There are 2,500 independent ballots in this variation! Some are known to be dead lost (and are not played), many are clearly playable, and some are open to speculation.

Until now. For Ed Gilbert and his mighty KingsRow computer engine have been very busy, and Mr. Gilbert has made yet another contribution to the game: he has analyzed and classified every last one of the 2,500 ballots, labeling each as won, lost or drawn for Black or White, and further, calculating a difficulty factor for all of them. This information is handily summarized in a series of tables (see links at the end of this article).

Ed has also prepared a special 11-man ballot computer opening book containing 1.1 million positions, which is now distributed with the latest download of KingsRow. He has made all of this material available free of charge on his website (again please see links at the end of this article).

11-man ballot will never be the same again.

What follows is a fairly detailed discussion of Ed's work. But first, to illustrate the depth of Ed's discoveries, take a look at the following position.

This, gentle reader, is a draw. Yes, it is, requiring no less than 20 star moves on the part of Black. Ed ranks this as the toughest of all the 11-man ballots and we call it the toughest checker problem ever published.

Care to try it? You can access our no-spoilers animation here. Try to guess each Black star move and the strongest reply by White before you click the arrow to show the next move. If you can solve it, you're superhuman, but it's fun to try and will give you a real workout. If you'd rather just play through on a board or on your computer, you can click on Read More to see the list of moves.

And now let's let Ed describe his work in his own words, through a series of emails sent to us over the past few months. A bit earlier on in the process, Ed said this:

"I have finished the analysis work I've been doing on 11-man ballots.

"I have found a few more 11-man lost ballots. There are now 248 lost ballots identified by the opening book generator. This may be the exact right number, or perhaps I'm off by 1, I can't be absolutely sure, but it's been over a month of book expansion since the last lost ballot was identified, so I feel that the analysis is quite solid now. I read on the NC Checkers site that when they play an 11-man championship match, after selecting a ballot at random, the 2 players sometimes spend some time trying to determine if the ballot is playable or perhaps a loss. Maybe this analysis will at least be useful to simplify that part of the matches."

---

A little later on, Ed sent this update, wherein an additional ballot (the one diagrammed above) was found to be a draw rather than a white win, reducing the number of lost ballots to 247:

"Using a combination of engine matches and additional book expansion, I found that one of the 11-man openings that I had classified as a white win is actually a draw. It is ballot #2493, and a very difficult draw to be sure. When I updated the rating tables, this ballot went to the very top of the difficulty table with the highest difficulty figure of all the drawn ballots. It appears that for the first 20 moves, there is only one drawing move for black (when white plays the strongest attack)."

Finally, here are the details about how Ed computed difficulty rankings. To determine a reference for relative difficulty, Ed first re-analyzed the 3-move ballots and correlated various measures with the difficulty ratings assigned by Grandmaster Richard Pask and published on the ACF website (see link at bottom of article).

Warning: The following material is not for the faint of heart or the non-mathematical!

"Each position along the PV is visited, and a 5-second KingsRow search is done with KingsRow configured to use only an 8-piece endgame database. The sum of those search scores is the value used.

"By the way, I found that if I did the searches with a 10-piece database, the results did not correlate nearly as well as they do with 8-piece. Too many searches return 'database draw' using the 10-piece database, so too much heuristic information is lost that way. I should also mention that database draw search scores of +/-1 and repetition draw scores of +/-3 were given the value 0 during the PV sum process.

"'Match score difficulty' is the second rating value that is an independent input into the model. To get this value, a number of engine match games were played for each 11-man ballot. To be specific, each ballot was played for 96 games, KingsRow vs KingsRow, opening books off, 8-piece database, and blitz time controls of 0.1 seconds/move."

"This component of the model is based on a suggestion from Martin Fierz. I will paste exactly what he wrote to me, because I liked his reasoning and found it slightly amusing. He wrote, 'My feeling is that at 0.1s the engines are playing very well according to human standards, but not yet inhumanly well, so that this metric kind of approaches what strong human players would do when playing these ballots.'

"To turn the Black wins ('bwins'), White wins ('wwins'), and games into a ranking score, I used this logic:

if (bwins >= wwins) 

    rank = bwins / games 

else     

    rank = -wwins / games

"I had previously tried other logic, like 'rank = (bwins + wwins) / games', but that metric by itself did not correlate as well with Richard Pask's ratings (for 3-move ballots). To put this into words, it seems that the Pask ratings are based primarily on his perception of how difficult it is for the weak side to play these ballots, and does not take into account that perhaps there are significant opportunities for the weak side to actually score a win. It didn't happen often, but you can see there are a few ballots where the weak side scored almost as many wins as the strong side.

"So we have these two rating values, PV sum and match score, and these were combined and a best fit to Pask's scaled ratings was found through linear regression. If you plot a best fit of each of these ratings to Pask's separately, you find that PV sum by itself has an R-squared value of 0.608.

"When PV sum is used by itself to predict Pask's ratings, the R-squared value was much lower, something like 0.2. I also did this with the 'match score' ratings. So by themselves they would not provide a good model, but when combined it does increase the adjusted R-squared by nearly 0.1.

"The output of the linear regression module for the full model is the scaled ACF difficulty, and these coefficients are used directly to generate the 11-man difficulty ratings."

So there you have it. 11-man ballot has at long last been put on a solid footing based on detailed calculation and computer analysis. Is this the very last word on the topic? Ed himself would likely say that in checkers, the last word is never really in, but have we ever come a long way!

And some people think checkers is simple? After hundreds of years, we're still finding new ideas and exciting discoveries!

---

The Checker Maven thanks Ed Gilbert for the enormous privilege of presenting his work in this column. We hope Mr. Gilbert's ground-breaking efforts will serve to increase interest in 11-man ballot checkers, leading to more competition and even more analysis and publication.

Main link to Ed's work:

11-man ballot, descriptive page

The following links can also be reached from Ed's website but are given here for convenience.

Latest KingsRow which includes the 11-man ballot opening book

PDN for all 11-man ballots

PDN for 11-man drawn ballots

PDN for 11-man lost ballots

11-man ballot difficulty ratings in order of difficulty

11-man ballot difficult ratings in ballot number order

Reference rankings of 3-move opening difficulty (Richard Pask/ACF)

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Exchanging gifts--- sometimes small, sometimes not so small--- is a long-standing tradition. Among family and friends, it makes no difference if we give a little more than we get, or get a little more than we give.

Not so, however, in our game of checkers. If we give, we'd better get back at least as much, if not more. and that leads us to this month's easy problem--- perhaps it isn't completely easy, but we've already given such a large hint that it should be simple enough. The position was provided by regular contributors Lloyd and Josh Gordon of Toronto.

Will you be able to resolve the interesting give and take? Give it a try, then take your mouse over to Read More to see the solution.

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In the United States (and elsewhere, of course), work and working have always been held in high esteem. Earning your own way, making a living, providing for a family; these things have always been respected and valued. So each year, on Labor Day, we recognize the value of work and the worker. We agree with the concept that all work is worthy and all workers deserve respect.

It seems that work, the worker, and checkers have traditionally gone together. Most of the greats of the game were working people, and many, many working people have enjoyed checkers throughout the years. Although the game has been in a long and steady decline, the connection with work and the worker still stands. Today's players come from all walks of life and work in all manner of occupations.

To celebrate Labor Day, let's look at a problem by an American checkerist who was an outstanding player back in the day, Harold M. Freyer. Serving America as a medic in World War II, Mr. Freyer gave much to his country. His profession afterwards? He was a house painter!

Is Black painted into a corner, or is it just a close brush with a loss? Black is man up, shouldn't that be enough? The solution is relatively long and precise. It's just like painting trimwork: you need patience and determination. See how you do and then brush your mouse on Read More to see the solution and notes.

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August was in its latter half, and it was time for all the teams in the National Checker League to go to training camp prior to the start of the new season in September.

The Detroit Doublejumpers, the reigning American champions, held their camp in Michigan's Upper Peninsula, at the Bois-du-Nord Resort near the town of (most appropriately) Au Train. There was plenty of room for the team's 15 person compliment of players and coaches, and there were many recreational options available after a hard day of training.

Beer, however, was strictly forbidden, as was any sort of alcoholic beverage. And that annoyed the Doublejumper's team captain, Marvin J. Mavin.

After a summer vacation that featured beer-at-will, Marvin was out of shape, and Head Coach Clyde Ronaldson made a point of insisting that his players be in top mental and physical condition. He well understood that professional checkers requires endurance and stamina.

Marvin didn't like the physical training at all. But there was no doubt that Coach Ronaldson ran the team. When Marvin checked in to camp, Coach took one look at him and immediately assigned him extra jogging and weight-lifting sessions. Marvin, who was always just on the edge of getting into trouble, kept quiet in front of the Coach, but grumbled to himself.

"How am I supposed to work on my game when I'm running laps up and down the lake?" he said. "And how can I relax and cool down without a tall cool one?"

It got worse. One day when Marvin lagged behind the rest of the team in the daily group run--- held at 5:30 in the morning--- he was assigned to play a simul against the rest of the team. That meant facing off against 9 other high-level professional players. He would have to run one half-mile lap for each draw and two for each loss; and to top it all off he would be playing White on each board.

Marvin was already exhausted from the morning run. He was further allowed only a salad and a glass of water for lunch as Coach said he was overweight and restricted his diet.

He was just beside himself. He was pretty sure he could beat the lower six players, but the next three were going to be trouble, and he didn't look forward to running still more laps in the afternoon heat.

At one o'clock on the dot, the players assembled on the canopy covered outdoor patio. Coach blew his whistle, looked Marvin straight in the eye, and said, "Play Checkers!"

It must be said that Marvin put in a great effort, and things went very well for him. He quickly won his games on the lower four boards, won the next three soon thereafter, and after another twenty minutes won on Board Two.

But Board One didn't look so good. He was playing against his Associate Captain, Pete Butterworth, a highly skilled player. In one-on-one competition, Marvin generally held a slight edge, but in a simul, Pete often had something of the upper hand.

If Marvin could win, he wouldn't have to run any laps, and at the moment, the thought of even a single lap was more than he could bear. Unless it was a lap into town to pick up a six-pack, but that would get him suspended from the team for sure.

However Marvin, with White, found himself in a man-down position. He was pretty sure he could draw, but he needed to find a win. That was asking for a lot.

"Sorry, Marv," Pete said. "Hate to have you run those laps, but ..."

Marvin, fidgeting in his chair as he so often did, replied, "Yeah ... me too. Maybe there's something here ..."

He thought for a while longer, and then gave Pete a little smile. "Watch this!" he said, and made his move.

---

Can you come up with a White win in this situation? If not, you'll be running laps! (On a volunteer basis, of course.) See if you can win it with White and then click on Read More to see the solution and the conclusion to our story.

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Trap Tales is a self-help book that purports to help you overcome seven traps that might derail your life. A Tale of Traps, perhaps, rather than A Trap With A Tale. We haven't read this book so we can't say much about it, but it's received high marks from readers and reviewers.

Are there seven traps to avoid in the game of checkers? Willie Ryan has already shown us dozens, and there are countless more. One book would never be enough to tell the tale of all of them.

As we continue to move toward a conclusion of our Tricks Traps & Shots of the Checkerboard series, which has run for many years now, we have one more position to present from Willie's A Trap With A Tale section.

Here's the run-up, with brief commentary by your Editor, using KingsRow with the 10-piece endgame database.

1.	11-16	24-19
2.	8-11	22-18
3.	16-20	25-22
4.	9-13	29-25
5.	11-15	18x11
6.	7x16	22-18

Out of book, inferior, and might lose. 21-17 or 28-24 would have been fine.

7.	20-24	27x11
8.	10-15	19x10
9.	6x29	28-24
10.	29-25	32-27
11.	1-6	24-19

Worse yet. 24-20 was better but White is definitely lost.

12.

6-9

...

Maintains a slight advantage but throws away the win. 25-29 was indicated, believe it or not.

12.	...	19-15
13.	3-8	...

25-29 was still indicated. The game is now a probable draw.

13.	...	23-18
14.	12-16	21-17
15.	13x22	26x17
16.	25-22	17-13
17.	9-14	18x9
18.	5x14	13-9
19.	16-19	9-5
20.	14-18	5-1
21.	19-23	27-24
22.	23-27	24-20
23.	27-32	1-5?

White has blundered and Black now can win. First, can you find the win? Second, can you go back and correct White's losing move? It's actually not all that difficult. Work it out and then click on Read More to turn a long Tale into a short one, by revealing the solution.

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With over 200 cumulative changes from the first edition, Richard Pask's Complete Checkers (3rd edition) is now available as a free download. Just click on the Richard Pask link in the right-hand column and scroll down.

While the paperback version on Amazon has likewise been updated, there is no real need to buy a replacement book unless you wish to do so. The electronic copy will always be free of charge. It's one of Mr. Pask's many gifts to the worldwide checker playing community.

Regrettably we cannot produce an errata sheet as the changes are just too numerous and in some cases too extensive and complex.

We sincerely hope everyone enjoys and benefits from this new edition of what has already become a classic work.

Our Checker School series has recently featured 'gem' problems from noted problemist William Veal. Today we conclude the series and "reVEAL' a photo of Mr. Veal in his later days. The photo appeared in a 1952 edition of Elam's Checker Board while noting Mr. Veal's passing. The Checker Maven thanks correspondent (and himself a champion problemist) Ed Atkinson for the photo.

Now let's look at today's problem.

White is a man down but is about to even the count. Yet Black, through clever play, can still win it. The problem is about 'medium' in difficulty and reVEALs a nice little tactical trick. Can you find it? You know what we're going to say--- clicking on Read More will reVEAL the solution.

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Man overboard! It's an emergency situation and we'd best hope someone trained and experienced in water rescue is on hand.

Something similar occurs in our game of checkers. One of our men goes overboard, we're down a piece, and we're looking to find a way to get a draw.

That's the situation for White in the diagram below. But there is a way to pull off a draw, if you can see it. We'd call this a "not quite" speed problem. It isn't too difficult but you can easily go wrong.

Are you trained and experienced in man down (man overboard) situations? You won't have to go too far overboard to solve this one; but a life preserver is always at hand. Just click on Read More to see the solution.

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Tommy Wagner was pretty nervous, uncharacteristically pacing up and down and wringing his hands. "It's my big chance, Uncle Ben, but he's so good!"

It was a sunny Florida Saturday morning, and as he had done on most Saturdays for the past eight years, Tommy Wagner was on the front porch of Uncle Ben's house. Ben, a retired checker professional, wasn't really Tommy's uncle, but all of his checker students called him 'Uncle Ben' out of respect.

Tommy, a ninth grader, was talking about the upcoming intramural match between his high school Varsity Checker team and the Junior Varsity team. Tommy had already risen to Captain of the Junior Varsity, and so in the match he would have to play a senior, Reynaldo Lopez Garcia, who was the Varsity Captain and a titled Master.

"Yes, Tommy," Uncle Ben said, "he is good. There's no other way to become a Master. And we both know you haven't reached his level yet, although I'm certain you will one day."

"He's going to kill me," Tommy said. He had stopped pacing and flopped into the porch chair next to Uncle Ben.

"What's the worst thing that can happen?" Uncle Ben asked.

"I don't know ... I'll lose my game against him?" Tommy said.

"Have you lost any games before?"

"Well, sure, but ... "

"Has Reynaldo lost any games? Did I lose any games when I was playing professionally?"

"Yes, of course, but ..."

"Everyone loses games, Tommy. Even Marvin J. Mavin and the very top players. And you never know. Anything can happen. You've got to go in there and play to win. You might win, you might lose. There is no shame in losing to a Master as long as you do your best and especially if you're a good sport about it."

"I know, Uncle Ben, but I really want to show something to Coach Schann and maybe make Varsity next season."

"Of course you do, and to do that, what steps should you take?"

"Um ... practice and study?"

Uncle Ben smiled, "Right on the mark. Let's pour a couple of glasses of lemonade and get into today's lesson, then, shall we? I've got an important situation set up on the checkerboard here."

Tommy smiled back. Win or lose, everything was going to be fine ... and he'd sure do his best to try to win. He turned his attention to the position that Uncle Ben had laid out.

"White to play and draw?" Tommy asked.

"Yes," Uncle Ben said. "Very good. It's known as the McCulloch-Miller Draw, an important drawing technique."

Tommy thought for a while. "Got it, Uncle Ben! Let me show you."

Tommy was able to work this one out. Can you? You don't need to be a titled master to solve it. When you have your solution, click on Read More to see the solution, notes, and several additional examples of the theme.

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It was another Saturday afternoon at The Beacon Cafe in the Provident Life Building in Bismarck, North Dakota, and the Coffee and Cake Checker Club was in session in one of the large booths.

Sal was the leader and there were five others present today. It was cloudy, windy, and chilly outside and the coffee was flowing.

After the boys had played an hour or so of informal games, one of them, Mike, said, "Hey Sal, don't you have a coffee and cake problem today? You didn't have one last week and I've been kind of wanting to win another piece of cake off you."

Sal frowned. The last time he tried, Mike had indeed solved Sal's problem and Sal had to buy coffee and cake. But then Sal's frown turned into a smile. "Matter of fact, Ed sent me a real nice one."

"Uh-oh," Mike said. Whenever Sal had a problem from either Brian in St. Louis or Ed in Harrisburg, it was bound to be tough. Top quality for sure, but never easy.

Sal leaned back against the seat. "Are you up for it?"

Mike and the rest of the group hesitated a little, but Deana, the owner, knowing just when to jump in, said from behind her counter, "I've got fresh apple kuchen this afternoon, boys!"

Well, that did it. Deana's apple kuchen, like most of her desserts, was irresistible.

"Lay it out," Mike said to Sal, pointing to one of the checkerboards, "and pretty soon I'll be enjoying that kuchen you're going to buy me."

"There it is," Sal said after setting up the position. "Take your time. Just not too long. I don't want to have to rush the kuchen that you'll be buying me, Mike!"

Mike laughed. "We'll see about that," he said. But five minutes later, all of the boys were still scratching their heads.

"I'll give you five more minutes but that's it," Sal said. He was greeted by the usual groans.

---

Once again we're asking if you can win coffee and cake from Sal, but unlike at The Beacon, you can take all the time you wish. When you're finished, click on Read More to see the solution.

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