Halma
Despite the enduring regard in which Halma is held by game players as the classic game of its type, Halma has received scant attention from serious players, at least in terms of organized competitive play. In part this may be due to the low proportion of occupied squares (38) on the large board of 256 cells. The result is a lower interaction between opposing forces than might be the case if the game had a different format. The start can be slow, and later play that involves enemy stragglers and the attempt to block them (a salient aspect of play in the smaller versions) only puts in a limited appearance. The one "advantage" of the large board is that the game's distinctive novelty—jumps over both friendly and enemy pieces—can be performed far more dramatically than on a smaller board.
          The two smaller "grasshopper" versions of the game (8x8 with 10 pieces per side, and 10x10 with 15 pieces per side), also Victorian, were more or less successful attempts to make play more interesting at the cost of losing the prospect of constructing the very long ladders that are the hallmark of the standard game. Since these play significantly better than the 16x16 version, we can treat the issue of the right format for regular Halma as closed. Another issue, however, that of spoiling, has been exercising minds much more recently.
          In the late 19th. century it would not have appeared immediately significant that a player could simply leave pieces in his home camp indefinitely, in order to block his opponent's progress—surely no one would dare to be that unsporting!—but in latter days several attempts have been made to prevent a player thus spoiling the game.
          The best known anti-spoiling rule was formulated by David Parlett as follows: "[A] a player wins when all the opposing base points are occupied, at least one of them by a piece of his own colour" (Parlett, 1999, p. 133). This is the most logical interpretation of the more ambiguously stated rule: "A corner camp is considered full even if one or more pieces in it belong to the player who started there" (Probably attributable to Sid Sackson, 1991, although Klutz Press could not confirm this).
          Focusing on the rule as formulated by Parlett, we can see that it has a degree of effectiveness. If both players set out to win, and, at a latter stage one of them sees the game slipping away, then that player cannot bail himself out by leaving a piece or two in his home camp. Against a predetermined spoiling strategy, however, this rule is not effective, since a player can position pieces in his own camp in such a way that certain squares in it cannot be reached by the opposing player. The diagram shows White's camp with pieces left in it in the form of the most basic fortress. Black cannot make progress since the corner cannot be reached either by a step or jump move. Even today, some commentators describe such a strategy as "devious" or "pathetic," but this misses the point. It should rather be considered pathetic if I won the first game in a match but failed to avail myself of the opportunity to win by maintaining my early lead.

Super Halma
As already mentioned, the low proportion of occupied squares in standard 16x16 Halma means that the interaction of opposing forces is both delayed and retarded throughout the game. Super Halma also works surprisingly badly in this format. In the standard game itself some interest occurs via blocking along the main diagonal pathways between the two camps; in Super Halma even this interest is lessened.
          It can be demonstrated that the interaction of pieces is affected considerably, not just by the board area but by its dimensions, too. This is illustrated by an extreme case: change the dimensions of standard Halma from 16x16 to 8x32. Now the opposing forces have such an impact on each other that neither player has the slightest chance of traversing the board! (Somewhere between these two, about 12x21, are versions that would work quite well, although game would be protracted.)
          On any rectangular board, a rough guide to indicate the number of pieces per side that could perhaps produce a playable game would be one less than twice the number of squares along a shorter side, so that a player is unable to form a solid barrier two ranks deep across the board. On this basis, it can be asserted that the highest playable proportion of pieces to squares will be found on square boards. On the other hand, rectangular boards have a funneling effect that increases the blocking opportunities.
          After much experimentation, the two formats that I felt were worthy of further testing were 8x11 with 15 pieces per player and 10x10 with 19 pieces per player, from now on referred to simply as 10x10 Super Halma. My tentative conclusion regarding 8x11 is that the funneling effect is too great. The game has a puzzle-like interest, and it enabled me to be clearer about the requirements of an anti-spoiling rule in these versions where the density of pieces is higher. Suffice it to say, for now, that the issue of whether or not one player can block off the progress of another is too dominant in the rectangular version, and not easy to solve.
          10x10 Super Halma has several points of interest that depend not just upon super movement, but also on the higher density of pieces it allows. Interestingly, the use of this format with normal Halma rules produces a more or less unplayable game. This is because a player can construct a two-rank or two-file deep side-to-side barrier with which—even though it may be incomplete—he can slowly advance. In Super Halma, however, this strategy allows the opponent too many opportunities to make progress by jumping over the barrier while it is under construction.
          An interesting diversion is the following conjecture about this version. Since the number of pieces is so neat (2x10 - 1 = 19), and they fit around the corner so conveniently, exactly as in standard Halma, it seems feasible that the standard game may have existed in this format at some point during its evolution. Although the exact origins of Halma are shrouded in transatlantic fog, it is generally accepted that in 1883 Howard Monks returned to the U.S. from England and that during the visit he had either devised Halma or developed it from a pre-existing game. Since I am in the middle of research concerning the genesis of Halma, I prefer, at this stage, not to make any guesses as to whether or not Monks did pick up on an earlier game, and, if so, how much of an inventive leap his input gave.
          However, suppose that one were to start from scratch, experimenting with the basic idea of Halma, using a 10x10 board. At first you might try it with each side having 20 pieces arranged on their two home ranks. Of course, no progress can be made. A logical next step would be to remove one piece per side, to make a totally impenetrable side-to-side band impossible, and to shift the home camps to opposite corners, to make forming such a band more difficult. Hey presto! Nineteen pieces fit neatly around the corner, and the arrangement begins to feel right.
          Now, as Monks sails back to the U.S. with the game of Halma having reached this stage, we can sail further into the realms of my conjecture. According to this reconstruction, having returned from his vacation, Monks would have had little time to experiment further. He may have found that each player could form and advance with a side-to-side barrier, making the game unattractive and inconclusive. Now, it is just about conceivable that if he had had more time to develop the game he could have solved this problem by introducing super jumps—and thus he would have arrived at the game I am presenting here!
          Instead, the game was transposed to the 16x16 board, on which longer ladders can be constructed (but on which, from scratch, 21 pieces per side would be a more logical choice). Thus, enchained hops over pieces of either color, the number one novel feature of the game, later described by Bruce Whitehill as "the first American classic strategy game" (Whitehill, 1992), could be more attractively shown off. Not only that, but all the unused space of the otherwise empty corners could be utilized in alternative versions for three or four players.
          To return to where we got to: the rules of 10x10 Super Halma, without the necessary small print rules, can be stated quite briefly, as follows. The small print rules I propose are given afterwards.

Rules of 10x10 Super Halma
Super Halma is a game for two players. The board and starting position is shown below. Each player starts off with 19 pieces in his "home camp," the boundary of which is marked by a bold line. A 10 x 10 International Checkers board and pieces is ideal. Colored masking tape can be used to mark off the two home camps.

Small print rules for 10x10 Super Halma
Winning conditions
1. A player wins when, after making a move, the position is such that all of the following are satisfied:
(a) None of his pieces could be moved, in a single turn, closer to the corner of the enemy camp;
(b) None of his pieces that are outside the enemy camp could be moved, in a single turn, closer to a vacant square within it;
(c) None of his pieces that are outside the enemy camp would require more than three step moves to reach that camp if the intervening squares were empty.
(Note that "closeness" here is measured by the number of step moves that would be required to get from one square to another if the intervening squares were vacant.)
2. If these conditions are met, the win is still not valid if all the attacking player's pieces are connected into one group (via step-move adjacencies) and yet there is still a vacant and accessible square in the enemy camp. "Accessible" here means not protected by an enemy fortress.
(The " normal" win, when a player occupies all the squares of the enemy camp, is an example of a win under these conditions.)

Trapped pieces

In our correspondence earlier this year Dan Troyka proposed that a player should simply forfeit the game if he has not cleared out his camp within a prescribed number of moves (probably 50 or thereabouts in standard Halma).
          Putting the application of these ideas to standard Halma aside (except to say that they both look promising), let me demonstrate what I see as their shortcomings when applied to Super Halma.

The crux of the matter concerns how, or whether, we are to distinguish between Position A, above, and Position B, below. In both, Black cannot make further progress since his straggling piece can be held back permanently. After a lot of testing, I have concluded that if a player attempts from the outset to build a side-to-side barrier—and advance it with the precise intention of preventing his opponent winning—then, against reasonably competent play, the most he will achieve will be a position comparable to Position A (rather than position B). In Position A, David Ploog's proposal seems appropriate. Black cannot advance further due to the blocking pieces and should be awarded the win.

Position B, however, is very different. The black piece that is held back forms, together with the white pieces that curb its progress, a mixed group of contiguous pieces that are totally detached from the main black group. Since Black could easily have prevented such a position from occurring (if White had directed his play towards this from the start), then this cannot be justified as a Black win. Note, however, that under Ploog's proposal Black would have a win here even if only the marked white pieces were placed as they are. As will be seen below, there are occasions when a position like this will emerge as a possible saving resource, rather than from a spoiling attempt. This corroborates the justice in not allowing a win here.
          (Note the relevance of Condition 1(c) in the anti-spoiling rules. If the straggling piece is at three or fewer step moves distance from the enemy camp—as in Position A—then it and the pieces detaining it cannot possibly form a group detached from the main body of black pieces.)
          Finally, regarding a 50-move type of rule, it is evident that this would neither prevent these positions occurring, nor be of any aid in judging their values.

Clarifications
For the purposes of clarification, here are some positions with their values plus any relevant comments.

1. Standard win.

2.

The position above shows a flaw in David Ploog's attractively simple formulation, according to which this is a win for Black. Condition 1(b) comes into play here. Black must get the last piece into the enemy camp to win. (This takes away nothing of the promise of Ploog's proposal with regard to standard 16x16 Halma. If a short supplement prevented a player claiming a win, as here, then his rule becomes, as he intended, sufficient for competitive play outside of organized competitions. The chance of anything coming up that it does not cover is very small.)

3. Win with mixed pieces.

4. Standard win against "holey fortress."

5. The position below is not a win since the since the piece at i5 can move closer to the corner. This seems to be an unnecessary technicality. However, add white pieces to the marked squares and it makes a difference; White to play could draw.

6. The position below is not yet a win as the piece at f4 can move towards f2. Once at f2, a winning position has been reached. As with the previous example, similar positions are possible where these extra moves could be critical. Again, this would be if White were chasing a draw by means of trapping a black straggler.

7. Finally here is an example of one type of impasse among the many that could possibly occur.

White, having a piece trapped in his home camp, can no longer win and has pursued a draw by trapping. By playing h9j9 he can effectively draw even though the piece on j8 is not technically trapped. If Black were ever to move the backstop at h6, White would play g5h6 and claim a draw. With regard to this and all similar impasse situations, it seems much better to rely on the intelligence of players than on specific rulings that could be added to the rule set at this stage.
          Having seen these dynamics, one might ask, "Isn't there a simpler way?" My first response to this would be that equivalent rules are also required in any truly thorough rule set for Halma itself. It may well be that a competitive form of Halma, and 8x8 or 10x10 Grasshopper would be suitable candidates, has never got off the ground precisely because no one has ever taken the trouble to promote any particular complete rule set sufficiently. On the other hand, people have enjoyed playing Halma for nearly 120 years, and for the vast majority of recreational players no fine print rules have been necessary. Similarly, one can enjoy Super Halma, outside of organized competitions, without any reference to most of these rules.

A short note on play
I define an "open" game in Super Halma to be a game in which, from the first, players allow opportunities for mutual invasion of their camps. A typical example would be a game that began thus: 1.i3g5 c9e7, 2.g1e3 e9e5e1g1i3, 3.i5e5e9c9 c7e9e5e1g1, 4.g3i5e5e9c7, reaching the position below.
          If a game continues in this fashion, each player might be in danger of having a piece trapped in his home camp. This can be an extremely interesting phase of the game. Although it is easy in itself to avoid being thus trapped, there is a fine balance between playing safe and making quick progress.

Also, one may take calculated risks in one's own camp while engaged in threatening a piece or group of pieces in the enemy camp. This sudden death element is the most salient and exciting additional feature that super movement and a more crowded board bring to the game.
          Curiously, aggressively played open games give a greater likelihood of draws, either by both players trapping a piece in the enemy's camp or by repetition of position in such trapping situations. Nevertheless, with a little experience, it does not seem to be too difficult to avoid draws of this kind. On the other hand, as a potential saving resource for a player in trouble, the threat of a draw can even add an exciting finale to the game. In the example below, White (myself in a game against Dan Troyka) seems to have a hopeless position.

The piece at i2 looks like it is inevitably going to be trapped, whereas the black piece at c10 is about to escape. 1.e6g6e8 might give White some slight chance of holding back, or even of trapping, a black piece, but an even better chance is 1.h3j5h7, which threatens i2h3, escaping. Now 1....f7f5h3 looks good since it prevents White usefully placing a piece at e8. However, the next White move both restores this possibility and threatens to escape via i2h3: 2.h5f5f7! After 2....j7h5j3, 3.f7e8 puts pressure on those backward black pieces. Although it turns out that, with best play, Black can worm his way through—as is usual in these types of positions—he does need to exercise a degree of care to do so.
          Closed games—where one or both players advance pieces in a more airtight way—tend to be more placid through the early and middle game, but are almost bound to end with a decisive result rather than a draw. Games of great theoretical interest result when only one of the players advances in such a methodically solid way. For example, in the following position Black is, albeit patchily, more advanced, but White, to play, will be able to progress towards the enemy camp more directly. It is not easy to ascertain who has the better position.

It is mostly in terms of strategic depth that 10x10 Super Halma should provoke enduring interest—though simply seeing the immediate possibilities is a pretty good first step towards playing well. The central 16 squares, and those close to them, are important. Being able to advance swiftly through these and/or hold up your opponent's progress is likely to be a key issue through the game. Inevitably players need to take less central routes, too. Various blockings can take place on different patches of the board, and players may sacrifice (in the sense of allowing a piece or two to penetrate into their home camp) in order to block elsewhere.
          A final word is necessary about draws. The anti-spoiling ruling is not intended to eradicate all draws. The nature of 10x10 Super Halma is that draws are a possibility, though unlikely to occur more than seldom. To my mind, there is only a "drawing problem" if (a) a drawing strategy exists that cannot be countered, or (b) a sizeable portion of well-played games end in a draw. Neither of these is the case here. Rather, it could be said that the game is enhanced by the inherent possibility of draws occurring.

References
Halma. Retrieved July 7, 2003 from http://www.di.fc.ul.pt/~jpn/gv/halma.htm.
Machatchek, H. (1990). Zug um zug: Zauberwelt der Brettspiele. Berlin: Verlag neues Leben. (Original work published 1972).
Parlett, D. (1992). The Oxford history of board games. Oxford: Oxford University Press.
Sackson, S. (1991). The book of classic board games. Palo alto, CA: Klutz Press.
Schmittberger, R. W. (1992). New rules for classic games. New York: John Wiley & Sons, Inc.
Whitehill, B. (1992). American boxed games and their makers: 1822-1992. Radnor, PA: Wallace-Homestead.

Andrew wishes to thank Dan Troyka, David Pritchard, and David Ploog for vital help with research, with extra thanks to Dan for his part in some enjoyable yet meticulous play testing. — Ed.