The historic Paris Agreement aims to constrain the peak increase in global mean temperature to 1.5 °C, or at least well below 2 °C. Every country has committed to device their own “nationally determined contributions” towards this target. These contributions are only proscribed for the coming 10-15 years with a regular reassessment of them against the global target. Here we use a global climate-economy model to explore consequences of differing levels of ambition during these reanalysis. We find that without substantially increased ambition the probability of avoiding 2 °C of warming is marginal. We present several plausible future trajectories that significantly increase the probability of avoiding 2 °C, but are unable to keep global temperatures below 1.5 °C. We advocate countries engage in the reassessment process soon and with high ambitions as catastrophic climate change can effectively be ruled out by such actions