[kgwgk]

Not necessarily "more likely" but "better" in some "loss" sense.

It could be "more likely" in the jars example where estimates may convey some relevant information for each other. But consider this example from wikipedia:

"Suppose we are to estimate three unrelated parameters, such as the US wheat yield for 1993, the number of spectators at the Wimbledon tennis tournament in 2001, and the weight of a randomly chosen candy bar from the supermarket. Suppose we have independent Gaussian measurements of each of these quantities. Stein's example now tells us that we can get a better estimate (on average) for the vector of three parameters by simultaneously using the three unrelated measurements."

https://en.wikipedia.org/wiki/Stein%27s_example#Example