A set $X\subseteq\omega^\omega$ is **unravelable** iff there is a possibly larger set $A$ and a clopen set $Y\subseteq A^\omega$ (with respect to the product topology coming from the discrete topology on $A$) such that winning strategies for the game on $A$ with payoff set $Y$ can be converted to winning strategies for the game on $\omega$ with payoff set $X$ in a particularly simple way (see Martin's paper *A purely inductive proof of Borel determinacy* for the precise definition). By Gale–Stewart, unravelability implies determinacy; however, it is not the only route to proving the determinacy of a pointclass.

My question is whether there is a known upper bound on the complexity of an unravelable pointclass. To make this somewhat precise:

Is it consistent with $\mathsf{ZFC}$ that every set in $\mathcal{P}(\mathbb{R})^{L(\mathbb{R})}$ is unravelable?

The strongest results I can find are *vastly* weaker than this, namely that under large cardinal assumptions $\Pi^1_1$ sets are unravelable *(Neeman 1,2; I remember seeing the same result for Borel-on-$\Pi^1_1$ sets, but I can't find a reference for it at the moment)*. On the other hand, I don't see an easy proof that this is anywhere close to the most unravelability we can expect, nor can I find this stated in the literature.