diff --git a/docs/sources/reference/run.md b/docs/sources/reference/run.md
index f06ca968..7529b848 100644
--- a/docs/sources/reference/run.md
+++ b/docs/sources/reference/run.md
@@ -651,10 +651,11 @@ developer, the operator has three choices: start the server container
 with `-P` or `-p,` or start the client container with `--link`.
 
 If the operator uses `-P` or `-p` then Docker will make the exposed port
-accessible on the host and the ports will be available to any client
-that can reach the host. When using `-P`, Docker will bind the exposed 
-ports to a random port on the host between 49153 and 65535. To find the
-mapping between the host ports and the exposed ports, use `docker port`.
+accessible on the host and the ports will be available to any client that can
+reach the host. When using `-P`, Docker will bind the exposed port to a random
+port on the host within an *ephemeral port range* defined by
+`/proc/sys/net/ipv4/ip_local_port_range`. To find the mapping between the host
+ports and the exposed ports, use `docker port`.
 
 If the operator uses `--link` when starting the new client container,
 then the client container can access the exposed port via a private