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:
The following links can also be reached from Ed's website but are given here for convenience.
At our Checker Maven location we're already seeing preliminary effects of Hurricane Lane and we anticipate heavy rain and high winds tonight (August 23, 2018) and tomorrow and into the weekend. If the storm doesn't make its anticipated westward turn it could track right over us.
Our offices will be closed and we could be out of touch for anything from a short while to a longer while. Publication will continue for at least a few weeks as that's all automated, and our server is on the mainland.
We're hoping for the best but we're prepared to be indoors for a while with our checker books!
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A Guest Column by Kookaburra
I live in Adelaide which is the capital city of the state of South Australia and I play checkers / draughts. South Australia is quite remote as it is in the middle of Australia, and within a short distance of Adelaide is total wilderness: The Outback.
Here we have extremely hot summers with stretches over 40 degrees Celsius and winters that are mild by world standards--- no snow but a little frost. The wildlife is wonderful and unique.
I started playing chess about four years ago after a health problem and also tried a stack of other games: Backgammon, Scrabble, Four in a Row, etc., and also Checkers. Thanks to a nice and skilled checker player I met online, I became a devotee of the game.
The reality of being a checker enthusiast today is that many of us are isolated. I play checkers (or draughts) in a country where checker players are as thin as kookaburraís teeth. This however should not stop any of us from enjoying this great and beautiful game. The fact you are reading this from far away from where I live is evidence that the tyranny of distance can be overcome.
Indeed, there arenít many serious checker players here in Australia at all. I have made contact with a couple and hope to play them crossboard at some point. For the most part, I play online, and have met some amazing people that way. Checkers is unique in that it offers a friendly, accepting fraternity who have embraced my presence as a new player.
It is difficult being isolated but checker players are not so common any longer, even in more populated parts of the world, and so all of us are becoming more isolated. My goal is to be the best I can at this beautiful game and not worry about other people or the isolation but to focus on the game and my skills in it. Then it doesnít matter.
One of my role models in checkers is the late Jan Mortimer, from New Zealand, who overcame the isolation of living in this part of the world to be a world class Checker player. I donít think enough women play this game and wish more did although I think checkers needs more players; more women, more men and definitely more beginners as it is tough when you first start and it takes a big leap to go from a recreational player who knows very little to a serious player who studies the game. And I am grateful to those who have and are currently helping me leap across this great divide.
I am hoping to promote the game whenever and wherever I can and help others learn about this beautiful underrated game even from this isolated area of Australia. I play online under the name Kookaburra.
Here is my advice for any modern checker player who may not have anyone around close by to play against.
Obviously the internet is extremely useful. Play turn based and speed games both to gain as much variety and experience of playing. Turn based sites are great for the social aspects of meeting and chatting to other players from around the world. Checker players are friendly and ask them about checkers and they chat and advise and online Iíve met some amazing players Also play speed games as thatís the way proper games are played. Start to end. Makes you think about strategy and think on your feet.
Start a checker book collection. There are great books out there. Start with beginner books and work your way up. There is enough out there to last a lifetime.
Research checker history. Some of the books I have now are from the 19th Century. The oldest is 1886. Reading them gives a fascinating incite into how the World was back then.
Join a checker association. The newsletters are great and it is worth it to hear news and make contacts from around the world and get to know who are the current and past checker champions.
Use social networking tools. Make a connection with other players.
If you want to play crossboard and canít find any checker players, join a club for another game with a similar board and use it to practice playing face to face.
Here is an exerpt from an old checker book dated 1911: Draughts Praxis or Modern Match Games, by Frank Dunne.
Check the last rule proposed to players over 100 years ago:
LOSE WITH GOOD TEMPER, AND WIN WITH SILENCE AND MODESTY
Amazing advice, I think!
And now I'd like to share my favourite problem. I like the fact Dr Marion Tinsley almost got stung with it, making for a connection to checker history.
Can you solve Kookaburra's favorite (or should we say favourite) problem, one that gave pause to Marion Tinsley? It's not as hard as you might suspect. Don't be left out (back); give it your best and then click on Read More to see the solution.[Read More]
Checker history is about to be made starting April 20, 2018, when an all-star team of American players travels to Rome, Italy to face top Italian players. While US vs. Great Britain matches have taken place numerous times over the last century, with the US largely dominating, this US-Italy match-up is a first, and the Italians are very strong indeed.
The US team faces significant costs, and you can help by following this link to the American Checker Federation on-line store, and donating whatever you wish.
Of course, The Checker Maven is US-based, so we're behind our US team, but we wish the best of luck to all in what we're sure will be a spectacular event.
Some of our board diagrams, notably those published between 2005 and 2011, have started to display incorrectly on the Chrome browser as of Chrome version 64. There are no problems with Chrome version 63 or earlier, and we don't yet know why only some diagrams are affected.
There's little we can do about this, and we can only hope that Google fixes their browser as soon as possible.
If you run into this issue, we suggest using a different browser (such as Firefox). Please accept our apologies for this inconvenience, which is outside our control.
Update as of March 8, 2018: We reported the problem to Google and it's fixed in Chrome 65.
The Checker Maven site was down for more than nine hours yesterday (Saturday, January 21, 2018), in what was probably the longest outage in our more than thirteen years of publication. Of course, it would have to take place on a Saturday, which is our weekly publication day, and when offices are closed and tech support staff are few and far between.
After 70 minutes on the phone with hosting provider GoDaddy, we were told that the server had gone down (we knew that) and it could take as long as three days to move us to a new server. Fortunately, that got done in about six more hours, and then we were up again.
Well, not quite. The new shared hosting server had some configuration differences, and we were here in the office well into Saturday evening getting things squared away. Doing this kind of work "au pied levť" isn't anyone's idea of fun, but we have to do what we have to do.
Fortunately, all is well once again, and our headache is receding. Our apologies for the inconvenience and our thanks for staying with us.
When we launched The Checker Maven years back, web hosting costs were a lot lower. But with the passage of time, costs have risen and now our web hosting alone runs well above $200 a year, and we haven't even begun to tally other costs, nor do we wish to.
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However, we will advertise our books, as print versions do generate a small profit. And we are considering a change in our policy on accepting donations. Right now we won't accept them even if offered, but at some point we might.
Thank you for being a reader of The Checker Maven and for your understanding.
Checker Cruncher is a new website under development by Brooks Thomas, and it's the first online checker tactics trainer to make an appearance.
While there's still some work to do, the site is eminently usable right now, and we found it rather impressive. We've made many repeat visits. A subscription model is contemplated for the future, but at the moment the site is completely free.
We asked Mr. Thomas to answer a few questions for us, and he graciously took the time to provide detailed responses.
1. So what's Checker Cruncher (CC) and what can we expect to find there?
Checker Cruncher is a web application designed to help people improve all aspects of their game and have fun doing it. The heart of the site is a large number of automatically generated tactics puzzles. Both players and puzzles get Elo ratings so beginners will be given easier problems while experts will be given more severe challenges. Other learning tools are also available such as a searchable database of expert games and an opening explorer to look at win rates and best moves. The puzzles are better for tactics and end games while the database is more for openings and strategy. Lastly, there is a forum for giving feedback and asking questions. More is coming as it's built.
All the puzzles come from real games where one player had the opportunity to win. Maybe that player found it and maybe they didn't but the engine claims the opportunity was there. Your task is to exploit said opportunity to the fullest. Some puzzles are as simple as promoting a king or choosing the better capture. Others are 20+ moves deep with zero margin for error. Each is a bite sized piece of practice for both the speed and accuracy of your calculation which is critical to avoid blunders and pounce on your opponent's mistakes. After each attempt you can check out the game the puzzle came from or look to the computer analysis for the answer. As of September, 2016, the puzzles are selected randomly because the ratings have not yet stabilized. As the player and puzzle count grows and the puzzles get sorted by difficulty I'll implement the smarter problem selection.
2. What gave you the idea for CC?
I got the idea for Checker Cruncher from a friend at the coworking space where I work. I was playing a game of checkers over lunch and lamenting the lack of a checkers version of ChessTempo when he asked, "Why don't you build it?" At the time I was making a mobile app about billiards that I didn't have much faith in. Over the next few days it become obvious to me that Checker Cruncher was going to be both more fun to build and more likely to succeed. I knew I was on to something when I started getting distracted from building the site by practicing checkers on the site. Since then I've had more ideas then time to implement them.
3. How long have you been working on it?
4. How do you see the site developing in the future?
I've got a huge list of features I want to add, I don't think I'll ever run out of ideas. I'd like to see a smarter problem generator, a larger game database, puzzle comments, tags, and share buttons, leaders boards, achievements, end game tutorials, live play, etc. I'm only one person so none of these are coming soon but if the site gets traction and enough users to pay for the hosting costs I'll keep adding features. Who knows where it might go?
In the near term I'm working on improving the site experience on mobile devices. It's not quite ready for phones but it's close. The smarter problem generator is also a big priority. I'd like the next batch of puzzles to be more consistent with where they start and end. It should also create fewer puzzles that have many winning moves. In the mean time, if you bump into a puzzle you don't like point it out on the forums. I can disable it and add it in my test cases.
5. Tell us a little about yourself (age, background, education, interest in checkers, location, profession, whatever you wish).
I'm 31 years old, living in Philadelphia. I got my degree in Computer Science at the University of Rochester in NY and have been a professional programmer since. Most of my experience is in windows desktop applications. Outside of work I've always had an interest in games and game theory. A little before I started Checker Cruncher I started playing chess more seriously and I'm now a 1700 rated player which I'm quite proud of. When I get the chance I also enjoy hiking and mountain climbing with my lovely wife Amanda.
I had no idea checkers was even an interesting game until reading about Chinook in One Jump Ahead. That was probably five years ago. I downloaded Martin Fierz's CheckerBoard and of course the engine Cake stomped on me so badly I didn't understand why. But I loved the simplicity of the rules vs the monstrous difficulty of the play. So I bought some pieces and started playing with whoever was willing. Now I play primarily with my friends and against my phone. I've thought about playing online but haven't really broken into it yet.
6. Do you think CC will become a major resource for checker training? Is that your long-term goal or hope?
Yes I hope so. I know it already works great for beginners. A few friends and I have been testing it and we've improved dramatically. Even very strong chess players have to practice tactics regularly, I think checkers must be similar. If it gets a healthy user base and good feedback I think Checker Cruncher could be a tremendous tool.
7. What do you see as the future of English checkers? Is it bright or not so bright? Do you think checkers might some day see a revival?
Lots of work needs to be done of course but I think the future of checkers is very promising. One of the major reasons I play chess and checkers instead of Counter Strike and League of Legends is accessibility. Checkers has been around for centuries, it's one of only a handful of games you can play with both your grandparents and your grand kids. It's not going anywhere. Moreover I think more people are playing checkers now than ever before. The checkers phone apps have millions of downloads. People may be playing casually, primarily against their phones, or even without forced capture. But they play and if more serious players and organizations can reach and educate them I see no reason why checkers can't be a large and thriving community.
8. Any advice for the aspiring checkerist and/or user of your site?
For the aspiring checkerist:
Play! Play with whoever is interested, kids, parents, coworkers. Checkers is the perfect game over a lunch break. But do warn your opponents about forced capture; at least where I am very few people know about that rule.
If you're playing against your phone or another computer turn the difficulty up to where you win or draw a little more than half the time. You should win often enough that you don't get frustrated but lose often enough to learn to be careful. As you improve, turn the difficulty up again.
For the tactics problems:
Like when you're playing over the board don't try to guess the answer. Take your time, spend five minutes thinking and try to see the whole solution before you make the first move.
9. Anything else you wish to say or add?
Please participate in the forums, feedback of all kinds is deeply appreciated! This is especially true for intermediate and advanced players, I'm working from my chess experience about what works, but checkers is a different game. For instance I'd love help building a list of favorite puzzles. My favorite so far is number 127.
This is definitely an entertaining problem, and it isn't all that hard if you find the correct first move. Give it a try, and then either go to the Checker Cruncher website to see this problem and thousands more, or click on Read More to verify your solution.[Read More]