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Richard Reilly
United States
Bryan
Texas
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As my recent Geek-list (the Tic-Tac-Toe Family Reunion) shows, the N-in-a-row principle has inspired many games. Like the proverbial inventors of better mouse-traps, game designers continue trying new ways to make Tic-Tac-Toe more of a challenge. Some add movement, some the ability to capture, some the element of secrecy—-there are too many variations, really, to list here--and some, of course, try expanding the board, modifying its shape, or adding another dimension.

To the best of my knowledge, Time Vectors is the only one to try adding yet ANOTHER dimension beyond the third.

Time Vectors at first appears to be simply Qubic with another dimension: Tic-Tac-Toe on a 4x4x4x4 grid. Except that’s not quite accurate, because the fourth “temporal” dimension is not linear, as are the first three, but circular. Its fourth dimension wraps around the central column, so that a “vector”—that is, a line of four in a row—can begin in any quadrant. Thus, for instance:

x . . . | x . . .
. . . . | . . . .
. . . . | . . . .
. . . . | . . . .
-----(P)-----
x . . . | x . . .
. . . . | . . . .
. . . . | . . . .
. . . . | . . . .

Looking down from the top at a single level-—with “(P)” representing the post in the middle—-this diagram illustrates a vector in the game’s fourth dimension. Notice how the vector has no beginning or end; it is a circle or square, not a straight line. Notice also that in each quadrant of the level, the grid is oriented in the same direction; that is, the quadrants themselves do not rotate.

The vector above was not difficult to see. But now consider these:

x . . . | . . . .
. . . . | . x . .
. . . . | . . o .
. . . o | . . . .
-----(P)-----
o . . . | . . . .
. . . . | . o . .
. . . . | . . x .
. . . x | . . . .

Once again we are looking down from the top. Here two complete vectors wrap around the board. Notice that they are a bit more difficult to spot. Notice also how, although these vectors do have end-points, such vectors could begin/end in any of the four quadrants.

Now if you will imagine these vectors winding not only around a single level, but across levels as well, you will begin to understand the challenge that Time Vectors presents to its players.

And it is, indeed, a challenge. To be sure, the game has not the depth of the classics. Its decision tree (if I understand decision trees correctly) is relatively shallow. One is always, in a sense, three moves or less away from losing or winning. But as the stones begin to appear across the levels, spotting the potential vectors becomes damned difficult: there are so many directions, it seems, in which they might go! The thought processes, in other words, are not so much of an “If he goes there, then I’ll go here, and then if he goes there, I’ll go here. . .” variety, but more along the lines of “Can he create a vector that goes from that stone of his up there to this other stone of his down here? What about to that one? Is he about to create a double threat? Can I safely try to work on my own vector? Can I block his vectors in a way that will add to my own? How can I most craftily create a double threat that he won't see coming?”

Some have suggested that this game is fundamentally flawed, because a solution for Qubic has already been found and could just as easily be applied here. This, however, fails to take into account the circular nature of Time Vectors’ fourth dimension. A player who tried to win just by “playing Qubic” would, I believe, be readily defeated by an experienced Time Vectors player.

Others have noted the failure of the game’s rulebook to include a swap rule: the so-called “pie” rule, used in many connection games, that balances the game by allowing the second player to swap with the first if the first makes too strong an opening move. Point granted; but this is easy enough to fix, isn’t it? And, for the time being at least, I do not believe it needs to be any more complicated than simply allowing a first turn swap for the second player, as not all opening moves are equally strong. Although no solution to the game has yet been found, I believe a player who begins by occupying one of the central spaces of a 2nd or 3rd level quadrant, or a corner space of a 1st or 4th level quadrant, has a serious advantage. Such an opening move should probably always be swapped. Opening moves on the non-corner sides of 2nd or 3rd level quadrants, on the other hand, are quite weak. Non-corner sides of the 1st or 4th levels are probably a bit stronger. As of yet, I am not sure about the relative strength of opening moves to corners on the 2nd or 3rd levels, or to central spaces of 1st or 4th level quadrants, but I think they are probably at a happy medium between the extremes.

Is the game solvable? I suspect that it is. But it hasn’t been solved yet, and until it is there is quite a bit of play value here. And even if it does get solved, there’s something else to consider: the game can be played with three players! And a solution to that, I believe, will NOT be readily forthcoming.

Meanwhile, the physical components of the game itself are outstanding. The central columns are polished oak or cherry, the levels high quality acrylic, the stones colored glass. Unlike some independent games I’ve purchased, I see nary a flaw in the production. Indeed, it is quite a beautiful game. Mine is set up in my office at work, where I use it to study games being played on Richard’s PbeM Server. With the light shining through it makes an attractive object of desk-art.

My overall assessment is that, even if it is not a classic in the league of Go, Chess, or the games of Project GIPF, Time Vectors is well worth having. It is fast, challenging, and requires some degree of skill to play well. Moreover, there is considerable pleasure to be had in foiling an opponent's traps before they are sprung, and in the sudden revelation--through your own traps--of an opponent’s imminent doom.


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