Fix typo

content/research/SPIRAL - Letting LLMs Teach Themselves Through Self-Play.md

@@ -27,7 +27,7 @@ This blog post introduces the first result of that collaboration: SPIRAL, a fram
 
 The [SPIRAL paper](https://arxiv.org/abs/2506.24119) demonstrates that self-play on simple games can develop generalizable reasoning skills without any domain-specific training data. The experiments consisted of training Qwen3-4B-Base on Kuhn Poker—a minimal three-card poker variant—for just 400 training steps. Despite the game containing no mathematical content whatsoever, this training improved the model's performance on math benchmarks by 8.6% and general reasoning by 8.4%. Perhaps most surprisingly, the self-play approach outperformed a baseline trained using supervised fine-tuning on 25,000 expert game trajectories, suggesting that the competitive dynamics of self-play provide a more effective learning signal than imitation learning.
 
-Self-play creates fundamentally different training dynamics than conventional approaches. When a model plays against continuously updating copies of itself, it faces an opponent that evolves in lockstep with its own improvements. This prevents 3the static exploitation patterns that emerge when training against fixed opponents: in the paper, we find that models trained against unchanging opponents like Mistral or Gemini initially struggle, then plateau once they discover winning exploits. Furthermore, given the zero-sum nature of the games, self-play forces models to develop genuine strategic reasoning that remains robust against an ever-adapting adversary.
+Self-play creates fundamentally different training dynamics than conventional approaches. When a model plays against continuously updating copies of itself, it faces an opponent that evolves in lockstep with its own improvements. This prevents the static exploitation patterns that emerge when training against fixed opponents: in the paper, we find that models trained against unchanging opponents like Mistral or Gemini initially struggle, then plateau once they discover winning exploits. Furthermore, given the zero-sum nature of the games, self-play forces models to develop genuine strategic reasoning that remains robust against an ever-adapting adversary.
 
 What makes it possible for the skills learned through SPIRAL to generalize beyond poker? Careful analysis of the resulting model’s playing style uncovered that it had developed three major strategies that were not used by the base model. As opposed to simple game heuristics, these strategies have broader applicability, enabling the model to perform better at math and reasoning tasks. The strategies are: