6-Piece Tic-Tac-Toe: Solvable?

My cousin may have invented this game (or maybe he found it somewhere else, but he’s brilliant enough to make it himself, shout out to Alex Leone) that’s based on Tic Tac Toe, but with one change: each player only has 3 pieces (he used red & blue poker chips) numbered either 1-3-5 or 2-4-6.

Play starts with Red placing piece 1, then Blue places 2, Red places 3, Blue places 4, Red places 5, and Blue places 6. It’s nearly impossible for a game of tic tac toe to end that early, so next, Red picks up piece one and places it in any of the three spaces that didn’t have a piece beforehand, and that continues until one player wins.

When we were playing, it felt like we got into loops where every move was forced, but neither player could win. What’s this forum’s opinion on how solvable this game is? If it is solvable, what kind of changes could be made to make it more competitive?

Do the numbers matter here or is it just a matter of having 3 pieces that you can move around each? It’s vaguely reminding me of Gobblet Gobblers which allows for ties to go on by means of covering up other smaller pieces.

I’m not sure if it’s solvable, I could certainly see how the game might be forced to an endless tie, I wonder if it’d be interesting to lock in certain pieces, or if that would just lead to normal tick tac toe again :thinking: Like, maybe you could choose to lock rather than move one, or something like that.