You can run Stockfish single threaded in a deterministic manner by specifying nodes searched instead of time, so in principle it is possible to set some kind of

You can run Stockfish single threaded in a deterministic manner by specifying nodes searched instead of time, so in principle it is possible to set some kind of bounty for beating Stockfish X at Y nodes per move from the start position, but I haven't seen anyone willing to actually do so.