Why does the first ping time out? It's the router's ARP

Ping across a router with cold caches and you often get one Request timed out., then replies. Ping again and all four come back. The usual explanation is "ARP". That's true, but it skips the interesting part: two devices needed ARP for that ping, and only one of them cost you the echo.

You can prove which one. The network is PC-A (192.168.10.10), the router Edge, and PC-B (192.168.20.10). PC-A needs its gateway's MAC address, and Edge needs PC-B's. So clear one cache at a time and ping from PC-A.

Clear only the PC. Run arp -d * on PC-A. It has to ARP for its gateway all over again, yet all four replies come back.

Clear only the router. Run clear arp-cache on Edge. The timeout is back.

Why the difference? A PC that needs a MAC address holds the packet until the ARP reply arrives, so its ARP costs a moment and nothing more. Many routers don't hold it. They start ARP and drop the packet that triggered it, and the next echo finds the entry ready.

That makes the lost echo useful evidence. One timeout followed by steady replies means the path works and a router along it had to look up its next hop, so there's nothing to fix. A timeout on every echo is a different problem, and that one does need troubleshooting.

Run the experiment yourself: finish the Two LANs, one router guided build, then clear each cache in turn.