My plan was to secure my own control markers, and initially send just one or two units toward the river, to spread the Lannister forces thin, and then whittle them down.
So I first ordered both my green cavalry units - one onto the nearest building, and the other south. I intentionally positioned this unit within Addam's reach, to tempt him to attack it and thus leave his other units out of command range.
Lannister did not react immediately, though, but used his first turn to move his blue infantry to the right of the forest to block the cavalry on my other flank from riding straight south. That was a very clever and also in the long turn important move, as it slowed me down that flank considerably.
On his next turn, he took the bait on the left, as I had hoped. But he eliminated the unit with his first attack, and used his pursue to charge one hex back towards the action. Definitely NOT what I had hoped
In round 2, I was already in dire straits: Lannister sat in two of the buildings, and had engaged my green cavalry in the third. Rickard had sent one cavalry unit south, and tried to recapture a building.
My units did not accomplish much - the Lannister troops proved very resilient (= bad dice rolls). By round 4, all my cavalry except for Rickard's unit was eliminated, and I had not managed to regain a building, despite constant attacks by the Greatjon.
My right flank was gone except for one infantry unit, so I sent Rickard south in the hope to capture those control markers yet. Only a single-figure infantry unit was standing in his way. Unfortunately, this proved enough to slow him down, so he captured one of the markers, but did not manage to get a second one in round 5, which I would have needed to delay the outcome a bit more.
I probably dedicated too few resources to those southern targets. Also, letting Lannister block my right flank, even if only slowed my down for a round, proved fatal. If we play this again, I think sending some units south on the right will be my first-turn action.