Colonel Blotto game with varied castles

In an earlier post we have seen basic framework behind the Colonel Blotto game. We have assumed that castles are identical and of equal value. In this post let us consider one of the simplest ways to generalize Colonel Blotto game is to assume that castles are heterogeneous. Can you still find a winning strategy?

Interactive app

This app is mostly similar to the app from the earlier post, but with an important difference is that now castles are not equal - each castle is worth as much prestige points as the number of flags raised above its battlements. So, if you look carefully the left most castle is worth 3 points, the next two are worth 2 points each, and the last two castles are worth 1 point each. As there are 9 points to collect in total, collecting 5 points is sufficient to win the game. But can you do that?

Random strategy used by the computer was slightly updated to provide better competition. Can you find a fixed strategy to beat computer? My best fixed strategy gives roughly 50% win rate (against 44% win rate by the computer).