The economy of tempo in abstract board games.

It is tempting to say that a tempo is a move, but that is not correct. Just listen to the phrase “Gaining a tempo”. Gaining a tempo is something one does with a move. But, each player has an equal number of moves in the game, so one cannot be gaining a move.
    Typically, when one is “gaining a tempo”, one is forcing one’s opponent to take a move that is not that beneficial to themselves, while oneself has the opportunity to do something beneficial. And since it is not the move itself that is the tempo, the tempo must then be that which is beneficial.
    However, how can something beneficial be a part of chess when there is only one condition for winning? The answer here is clearly that, that which helps one towards the goal of check mating your opponent's king is beneficial. And now, I feel, we are getting somewhere.

Tempo’s then, can be defined as “that which aids towards the goal”. Now, there are many things that are known to help one towards one’s goal. I’ll list up a few; Space, material, pawn chains, maneuverability, the bishop pair, and control of the center.
    Aha. You may have spotted it too. There is a problem with the definition - an ambiguity. These separate things are clearly separate things, so they cannot be a tempo. So what is the relation of the tempo to these things? I see two separate options. Either a tempo can be to the advantages as money is to particular coins; an abstract word for a group; or, we can again relate the idea of tempo to the move, by saying that a tempo is the average amount of beneficial things one can achieve with a move. Both sides have commendable attributes to them. The first has the simplicity, and I think the second is more accurate, because the value of each beneficiality fluctuates within games and between item. To see why, we must sadly go even deeper into the nature of the game.
Abstract games have human players. These can see into the future of the game to different degrees, depending on their calculating ability and their repertoire of concepts. They are trying to move towards a future in game terms that either has more beneficialities, or mates the king. The popular thing is to envision one’s choices as branching into the future. From each branch yet more branches and more futures can be seen. A better player is a player who can imagine himself standing on a few of those future branches, see what life looks like there, and decide which is the better. That, and a second crucial trick.
    One must not underestimate one’s opponent. The most secure way forward is to envision that one’s opponent makes the best move possible, and to find the way where this strategy will make yourself as little bad off as possible. You are looking for the best least bead position; which is why this strategy is called the minmax strategy. 
    Since the goal of the check mate is fo far off however, no player can see to the end of the game. Evaluation is still centered around these concepts of benefits, of tempo.

Now how did I use the word tempo there? It was as the potential for making moves of a higher tempo. See how words twist under our grip like this? That is the power and powerlessness of words, the paradox of speaking. Yet, we are now using the Socratic method of enchelus, and then we must soldier on with fixing and unfixing our definitions.
    With the future in mind, and taking the definition of tempo involving the average benificiality of a move, we can say that the optimal strategy is to chose those moves that, on the average over the whole game, maximises your economy of tempo. And that, if your economy of tempo is consistently higher than your opponent, the strong tendency will be for your to win your games.
    This conceptual lifting is not that easy to do with the abstraction model of tempo. Yea, you have more tempos, so what? The interesting thing, is that the quality of one’s moves are better. That, is what counts.
    Still, the abstraction model has it’s benefits. As I said. It is simple.
Imagine that you are trying to evaluate your moves. In that instance, you can look for the things that your moves will accomplish, and then simply count. Will one of my moves do more? If so, that has the higher number of tempos, and is the better move. It is maybe that simple.

A note on Skakktafl.
Chess is a zero sum game. In the end, there can be only one winner, and one loser. It is also a game with a single win condition; kill the king. Therefore, every good move that you make is also a move that is bad for your opponent, and is contributing towards your own win. The game is symmetrical in this sense. You are trying to hide away his win condition, so that his end is on a branch further along than yours, and pulling your win condition closer. Your king stays in his castle, his pawn structure is broken. These two concepts are direct mirrors of that asymmetry, which, aside from the fact that one player must start, is the only asymmetry in chess.

But what happens if we try to play with some of these fundamental aspects of chess? All of this was some of my thinking when I made Skakktafl. In Skakktafl evaluation is, if not harder, then different. There are three win conditions; get one’s king to the center of the board, invade his empty castle with one of your pieces, or kill his king.
    With multiple win conditions each move may be simultaneously good and bad, depending on what win condition your are making your move in relation to. This highlights the fact that evaluation is determined by a relevancy criteria looking at a particular goal. A good Skakktafl player will then be able to cut off a win from one’s opponent, such that he must change it; and through this retroactively lowering the value of his opponents previous moves. A good move in Skakktafl then, may be one that manages to keep the most number of roads open.
    Because of this higher complexity, the actual tactical complexity has been lowered. No piece is able to cross the gameboard fully in one move. Because of this, pieces must participate in local battles, the outcome of which will only then affect the game globally.
    This has a great effect on how one should manage one’s economy of tempos. If you can foresee that you will loose one tactical battle within two moves no matter what, then you should change your focus to another part of the board, where you can restore the economic balance between you and your player, by playing two equally valuable moves there instead. 
The evaluation of the games position therefore has three layers. The first is the local tactical positions, then it is their outcomes evaluated against the board, and then at last the board position as counting towards the six possible final outcomes of the game. Normally, these six will not be relevant at the same time. At most I have experienced three to be relevant at the same time.
For inexperienced players of Skakktafl, then, a good skill is being able to set up a new goal; managing the complexity of the board. If you start by playing for development, a good early tactic, you can close of the board pretty effectively. This will limit the need for evaluation on multiple fronts. After that, it is time to formulate a simple high level plan, what we call playing prophylactically, to, for instance, relocate resources to his right flank in order to penetrate with force, and either mate his king, or take his castle. Let the fun begin.