Can you figure out how much RL will actually buy you before you commit a month of GPU time？
This paper says you can predict it based on the checkpoint you start from. The authors recreate the entire LLM pipeline in chess -- pretraining 5M-1B models on Lichess games ， SFT on synthetic reasoning traces， then GRPO on puzzles with verifiable rewards -- and sweep 36 pretraining-RL combinations.
Signal is mostly carried by two pretraining properties. The pretraining validation loss predicts the post-RL pass@1， with the fit tightening from |ρ|=0.93 to 0.99 as the reference RL compute increases； and the reward gained per 10× of RL compute increases with log pretraining tokens （Pearson r=+0.84）. The same two patterns are seen in a 1B model trained on math text.
The fitted frontier puts RL's compute-optimal share at around 20% at 50M parameters， and 28% at 680M. With budget， the share increases but remains a minority.
The mechanism is the part worth noticing. RL is not uniform sharpening： on the hardest puzzles it generates correct moves to almost non-existent levels after SFT， but makes already-preferred wrong moves many times more often.
That is why they get pass@1 gains but not pass@16 gains， and it leads the work in a different direction： suppress wrong-mode amplification， rather than sharpen harder.
- arxiv. org/abs/2607.16097
Title： "Understanding Reasoning from Pretraining to Post-Training"