Groundbreaking work on 11-man ballot

[chipschap]

In this week's edition of Checker Maven (checkermaven.com) which will appear at 00:02 HST Saturday 14 September (about 2 1/2 hours from when I'm writing this), you can read about Ed Gilbert's groundbreaking work on 11-man ballot openings. This is sure to revolutionize 11-man ballot play.

If 11-man ballot interests you, you'll want to read about Ed's work and download his material, all of which he offers for free.

[Richard Pask]

Dear all,

What a fascinating piece of research by Ed Gilbert!: I commend it thoroughly to everyone. Interestingly, some of its findings relate to both 11-man ballot and 3-move - and checkers in general.

In the research Ed makes several references to the 3-move ratings I assigned in Complete Checkers and I would like to make a few related points:

First, I'm flattered that he referenced these and attributed a certain amount of weight to them.

Secondly, he interprets these ratings in the precise way I intended and, importantly, highlights the limitations of using a mere number when attempting to fully describe a 3-move ballot. (An aside: although I have striven to ensure internal consistency - for example, both 9-14 22-17; 11-16 and 11-16 21-17; 9-14 are rated [47/53] - my numbers have no strict mathematical basis but are simply a form of shorthand to avoid clumsy terminology: for example, 'Every so slightly in favour of White' or 'Incredibly strongly in favour of Black'.)

Thirdly, and most importantly, the far stronger correlation to these ratings when using the 8-piece database and the 10-piece database is telling. As Jonathan Schaeffer suggested in one of his papers, a world-class program containing the 10-piece database moves into a different realm - in a very real sense beyond human comprehension. (It was possession of this database which allowed Chinook to escape with a draw v Tinsley in the 1994 US Nat Ty.) Because it is seeing so far ahead, it is in effect too good. This was readily apparent when I was recently sent some lines analysed by KingsRow. I was hardly in a position to question their soundness, but I do know that they were not human-friendly and that, when I eventually get around to downloading the program, I can have a friendly chat with it and work something better out together! The tension between the theoretical and the practical will feature in the 36th and final chapter of Logical Checkers Book 5, which has as its main focus the extent to which our great game is open to the successful application of general principles and strategy. For a program with the 24-piece database the question is redundant and everything is just a brute fact. (And hence, so is checkers.) But for human beings, for whom the game is an eternal joy and challenge, the question will always be relevant. An interesting contradiction.

Well done again Ed.

[Richard Pask]

Further thoughts:

It would be fascinating, though no doubt very time consuming, to see how the program's ratings compared with mine using the 6-piece, 7-piece, 8-piece (already done), 9-piece and 10-piece (already done) databases respectively. Namely, would a definite pattern emerge?

it would seem likely, as has already been suggested, that from the human standpoint, the computer ratings made using the 8-piece db are the most useful and relevant.

Certainly, as databases of increasing size were used (11, 12, 13, 14, 15, 16 etc...) the program would eventually evaluate all 156 of the 3-move ballots equally: all demonstrable draws from the start and therefore dead even!

All of this ties in very nicely with a section of Derek Oldbury's Complete Ency. Namely, Volume 3, Page 269: 'Playing a rigged game'. Here he argues that when preparing an attack, you have to give your proposed opponent sufficient respect, but not too much. Too little, and you'll conclude that a dud of an attack, which is actually easily met with logical, natural moves, is strong when it's not. Too much, and you'll conclude that your opponent is bound so see everything and that every possible attack is pointless.

That our great game is sound - which we have always 'known' but has now essentially been proved - is one of the things we have to thank the programmers for: it can NEVER be shaken from its foundations.

[chipschap]

I too found it fascinating--- although in retrospect not surprising--- that the 8-piece database combined with relatively short compute times of 0.1 seconds per move, gave the best results in evaluating difficulty.

At the limit, should there be a 24-piece database, all non-lost ballots would be equally difficult, at least for the computer, since they would all draw all the time. As Ed said, too much heuristic information is lost when the computer plays a superhuman game beyond any possible human understanding. Moves are made based on concrete analysis rather than application of principle. This is well demonstrated in Ed's other work on machine learning; the computer eventually plays a recognizably stronger game when it 'trains' knowing nothing more than the rules.

So in the end what Richard says, that our great game is sound, rings true in the following sense. The game is, ultimately, balanced. It is a draw for 156 of the 3-move ballots and 2,253 of the 11 move ballots. The computer will always find the draw.

But over the board, the challenge will always remain. The draw is there, but we have to earn it. We are mere humans, and we should be glad of that.

[Chexhero]

Do we know if the 11-man opening list that was analyzed as either win, loss, or draw actually proven or is it just program best guess? For example, many of the 3-move openings were considered losses until it was proven otherwise. We know for 100% certain that white doctor will draw if the weak side makes no mistakes. Because if proven, we may want to think about modifying the current 11-man deck to take out the openings that don’t draw. Or, maybe is worth doing that anyway, if the program is at least 99% sure.

[Ed Gilbert]

Do we know if the 11-man opening list that was analyzed as either win, loss, or draw actually proven or is it just program best guess?

The only way to prove it is to do what Schaeffer did to prove that GAYP is a draw, except that you would have to do that 2500 times. However, just because the 11-man analysis is not guaranteed, that does not mean that it is not useful. It is very close to being 100% correct. I think it's unlikely that more than one or two of the 2500 ballots are incorrectly classified, it any.

-- Ed

[chipschap]

I don't want to try to interpret Ed's work on my own (I'm far from qualified for that), but I think that if there are any openings incorrectly classified, they will be in the nature of losses that are actually super difficult draws, rather than draws that are losses. I base this on the trends we've seen in the past. We (or our computers) learn how to draw "impossible" positions rather than learning how to win what was believed to be a difficult draw.

So if there is a move to eliminate lost ballots, and one or two are eliminated that really might be draws, those ballots would be so unbalanced as to be undesirable in any event.

And even if the current rules are continued, there is now a very sound practical basis for players to utilize in deciding whether or not to play a given ballot. Who would play a ballot that the computer thinks is a loss, even if there is a very remote chance that the ballot actually can draw?

[okrunjoe]

I have often wondered why the red piece on square 4 and the white piece on square 29 were not removed in the balloting. Removing either of these two men would result in many playable openings. Don't know how many but it would probably be several hundred. Another way to do 11-man would be to remove any two pieces and not have the two-move opening. This would also add many more openings. Would appreciate any comments.

Joe McDaniel
Tulsa, Okla.

[Edgar C. Atkinson]

In 1952, when I was a lad of 14, the Philadelphia PA experts were playing 11 man ballot with the pieces squares 4 and 29 removed. They would write the names of these squares on the cards that were in use at that time. They felt that it was less weakening to have these pieces removed than to remove pieces from squares 6,7, 26 or 27. Of course provision in the rules would have to be made for openiings such as Off: 12 and 29, Move: 11-15 22-18 giving up two pieces.

As can be seen, there is precedent for the suggestion.

If memory serves, Newell Banks, the inventor of 11 man ballot, in his book, Blindfold Checker Masterpieces, that one way to play was to ballot off a piece from any of the three rows.

[JR Smith]

I agree Joe, over 15 years ago Don Brattin introduces me to “Roll Your Own” a variation of checker openings created by rolling a set of dice. You could play RYO, RYO-11 Man, or Simple 11. He was correct in stating that RYO-11 Man generated more openings (331,776) than Newell Banks 11-Man Ballot, just by adding the extra rolls of a 12 side dice to select which checker to remove. He gave me a set of dice and instructions. Our group of NC players played with dice, and I gave away several sets. RYO never took off in North Carolina, probably because most of the players owned their Newell Banks deck, and they felt it was plenty enough new openings. I remember Bill McClintock asking me, “Why are you always trying to change the rules when you can’t even beat me at GAYP?” I do think RYO with the 3 variations adds excitement and merit to checkers. The nature of checkers contributes itself to cause a proficient player to enjoy the advantage of being familiar with openings and positions; therefore, he wants to keep it that way.

Read about "RYO" http://www.nccheckers.org/NCCA/Newell ... board.htm

“Roll Your Own”... Perfect for generating a random number between 1 and 12 or a random number between 1 and 4. Roll the 12 sided dice to remove one of the checkers from each side, then roll the 4 sided dice to replace the removed checker. Count squares from double corner just like the numbered board for red side. Use the white corresponding square that represents the red numbers on the white side, now replace the checker by placing it on square 1 though 4 counting from DC. Example: square 13 is 1, square 14 is 2 and so forth. Using the same corresponding squares on the white side. Example: square 20 is 1. This method creates thousands of checker starting positions was designed by William "Bill" Scott from Bowie, Texas who publish the Texas Longhorn Checker Magazine, the official organ of Texas Checker Association. He introduced the system in the early 60’s. He made a deck of cards, a set of 4 cards and a set of 12 cards. Don Brattin from Berea, KY realized he could do the same thing with 2 dice from a set of Dungeons & Dragons dice, and coined the catchy phrase. Use the top number after the roll, the triangular base pyramid dice has 4 faces and the dodecahedron has 12 faces for 1-12 selection for removing one of the 12 checkers, and the 4 face dice replacing it. This system produces 2,304 starting positions (12x12x4x4=2,304) and no transpositions. It generates more losses than Eleven Man because it may remove a piece from the king row, second row, or an initial man-down opening, but you play with 12 pieces, red moves 1st, play both sides, and you roll your own! You can play "ROY-11 Man" by rolling the 12 sided dice again to select which checker to remove, if it is already gone just roll again. RYO-11 Man has 331,776 starting positions (12x12x4x4x12x12 = 331,776). You can also just play "Simple-11" by removing a checker from each side. Simple-11 has 1008 starting positions (7x12x12 = 1008).

GAYP has 7 starting position
2-Move Ballot has 46 starting positions
3-Move Ballot has 156 starting positions
Roll Your Own has 2,304 starting positions (12x12x4x4 = 2304) No Transposition = 2,304
11-Man Ballot has 3,136 starting positions (8x8x7x7 = 3136) Less 20.3% Transposition = 2,500

[chipschap]

This all reminds me of Chess960 (also known as Fischer Random and previously Shuffle Chess). Chess960 distorts the initial setup to a much greater degree than 11-man or Roll Your Own.

All of them are interesting variants with their own merits and possible shortcomings.

But JR touched on something interesting: vested interests. Does a top level player want to stay with (say) 3-move because of the immense effort already invested in developing expertise in that variant? Does a lesser player wish to play a variant to short-cut certain aspects of learning checkers (to wit, mastering the complex 3-move literature)?

I think we've all seen the latter from time to time, and there are examples around the internet that go along the lines of, "Here's a new way to play checkers that's way more interesting than the boring old game we played as kids" --- this something of a substitute phrase for "Let's play my new game because I was never any good at the old one."

Of course things are not that simple; time invested in 3-move expertise surely translates into pure over-the-board skill as well. But as we increase the changes made in variants, we get further and further from the original (GAYP) game. At some point, it's virtually a new world, just as Chess960 is (in my view at least) a new world. And that's neither good nor bad per se; it's just, well, different.

Oh, and just as a corrective footnote: Roll Your Own 11-man actually has (12x4x11x12x4x11)/(2x2) starting positions, or 69,696.[1] Simple 11 has 12x12 or 144. And GAYP has just 1.

[1] Thanks to Russ Rader for pointing out I had originally (incorrectly) calculated permutations rather than combinations.

[JR Smith]

Thanks for reply and correction! JR