Ice thickness and strength - moving targets. Fresh absolutely translucent ("black") ice that has never seen an above freezing day can be very strong. I've fallen hard on black ice not much thicker than a 1/2". It gives nicely on impact. In fact, you can watch the depression under a skater. Warming days and freezing nights destroys the wonderfully strong structure of pure black ice and its strength falls a lot. Later in winter, the ice basically "rots" and many inches are needed to be safe.

In general, the best way to judge ice strength is to watch for hockey players. They love to play and will push the boundaries but they do fall hard. Good thing is that when they do go through, everybody else is equipped with a long stick to retrieve them and it's rarely an issue beyond that wet person getting mighty cold. So hockey players? Ice is safe (except perhaps the edges and stream inlets). No players (on a pond they regularly play)? You're on your own. Be careful.