I really liked how the power-ups and it made the game had a fun twist! I'm very impressed with the A.I. you made also, because it actually does use the powerups to win in the game! I just wish there was some music to go along with it! Good job!
In simplest terms, given a state of the table, for every empty slot that a piece can be placed, check all 4 directions (horizontal, vertical, and both diagonals). For each direction, check 3 pieces away from the center (the empty placeable slot). If an AI piece is encountered, add points to an AI direction score sum; if a player piece is encountered, add points to a player direction score sum. Piece points can be 1, 2, or 3, being 1 furthest to the center and 3 nearest. For each pair of pieces of same type (AI or player) found consecutively, a multiplier (x2) is applied to the direction score sum of the corresponding type. Once checked all four directions, add up all direction scores of one type. Once checked all empty placeable slots, pick the highest AI score or a player score thats higher option to place the piece. If there are multiple highest score, randomly choose one.
With this, AI tries to bunch up its pieces in the same zone or breack up players piece clumps, so it moves without exclusively searching for amount-of-pieces-in-a-row slots.
And of course, the are many flaws. Biggest one is sometimes AI doesnt see 3 in a row pieces because another slot has higher score for some reason. Maybe the score system needs some tweaking, but for now, with the amount of time I dedicated in it, its good enough to play with.
As you can see, there arent branched prediction thingy like minimax algorithm and stuff, because I dont know any of those things, I couldnt find a simple plug-in implementation, and I dont have enough time to add the real stuff.
About AI using power-ups, let me reveal you the secret. It doesnt, really :D. A power-up piece is treated as a placeable empty slot, but only adds 5 points to the final AI score, where scores can be up to tens and hundreds.