I've heard some teachers say that using a chart like you suggest saves them time during rounds. The charts I've seen have the four choices across the top and kids down the side--kids get to make two choices. When they go to a choice, they remove that one from the chart, so the next round, they know where to go. So, they do get a bit on choice built in but not "right at the moment".
The only thing that bothers me a bit is they might not "name their strategy" before they go out, which might mean they don't have that in mind.
They are many other ways, I'm sure--I'd like to hear some, too.