Joust is an interesting game insofar as it seems to inhabit the borderline between simple abstract games and complex strategic games like Chess. The following observations seem to be true, but if you find something different please email me.
One player has, under normal circumstances, a considerable advantage. This is the player who moves first when both players are on the same colour. The advantage consists of the ability to directly block the opponent. If the game finishes with both players a Knight's jump away from each other, the player holding this advantage will win.
Although it is not possible for you to ensure that your piece stays close to that of your opponent, your opponent's possibilities are restricted by his need to be more than one jump away at the end.
(In Chess, a somewhat analogous situation occurs when you are a pawn up in the middlegame. One little pawn hardly makes any difference to the total forces on the board. But every time a pair of pieces is swapped, the extra pawn becomes more significant. As a consequence of that extra pawn, you may sometimes drive your opponent back simply by threatening to swap pieces. If material on both sides were equal, swapping pieces would not matter to him.)
Irrespective of the above, in a symmetric Joust position on a board with an even number of squares, the player moving second (Black) can always win. Irrespective of what White does, Black responds with the mirror-image move. It works whether the board is symmetric about a point or a line. And the advantage of being on the right colour is of no consequence.
This symmetric winning strategy is typical of simple abstract games, and is not usually found in the classic strategy games like Chess. If it did exist, the rules would have to be changed to prevent it. In my computer version of Joust, the computer always plays second, but is quite unaware of the symmetric strategy - and it does not analyse deeply enough to find it 'over the board'. If you are playing a two-player game, however, you should avoid symmetric starting positions, or make some other rule to prevent this strategy.
Finally, Joust is complex enough that an overall strategy can exist. By this I mean that many tactical complexities are 'lumped' into one overall parameter. In Joust, it is good to maintain control of the centre. Ultimately, a piece closer to the centre of the board tends to have more moves available. In the nature of things, there is a statistically increased likelihood of having a winning move, if you have more possible moves.
By the same token, it is good to keep your opponent close to the edge or corners. But the operative word is 'keep'. It's no use pushing him back only to have him leap out past you in his next turn. The computer player (from Peasant up) tries to maximise the ratio of moves available to him compared to those available to you, but does not attempt specifically to control the centre. However, the importance of this factor can be gauged by the fact that, with no other rule than the above, the 'Peasant' is quite a tough opponent.
The Knight and the Baron carry out an analysis of their moves and your possible responses so as to maximise the ratio (of the moves available to them compared to the moves available to you) several moves ahead. Thus they are capable of 'reculer pour mieux sauter' as the Chess phrase puts it - temporarily retreating in order to jump all the farther.
With version 1.1, the King was added, and the
evaluation function was change to include a tendency towards staying
in the centre of the board. I think a little more is needed,
though, to make the computer super-strong.
There is also a 'rule of two' in Joust, but it is hard to describe exactly. Often the board is about to be split into two large sections of squares. You want to be left in the larger section, preferably having used up some of the squares in your opponent's section. Or if you have the colour advantage, you want to be either in the larger section, or the same section as your opponent. But before the sections are split, a time will come when there are two pathways joining them. The first player to break such a path has a disadvantage, because the player breaking the second (and last) path gets to choose which side to stay on.
The above idea, which I have rather vaguely outlined, is probably the most complex tactical/strategic decision in Joust. It is, after all, a very simple game!
If you want to become a Joust 'master' (which I define as someone who can beat the computer at Baron level on an 8x8 board, starting on a square of the 'wrong' colour) you will need to consider the 'rule of two'. A very specific plan is required from the start to do this. But I will leave you the pleasure of finding it!
Anyway, if you have anything to add to the study of Joust, or indeed if you disagree with any of the above points, why not email me? I will update this page with any new insights.