4 inches high sounds like plenty. I don't know if you were going with day neutrals, everbearing, or June bearers, but June bearers are the most vigorous when it comes to runners. The others are less, enthusiastic, so to speak.

I'm going to do half & half (probably Tristar and Tribute) in a 4x8-foot bed and allow for one runner from each original plant to form...

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Each square = 6", so I'll plant 2 per foot (staggered) and allow for 2 more (X) to root from parent plant. I'll root extras in small pots before cutting them off, then plant elsewhere.

Granny

Here is a link that might be useful: Annie's Kitchen Garden

My guess is that they will easily go over 4 inches but it should not be a big deal to keep them cut off.

Not sure if there are any cross pollination issues with different varieties so close.

We cleaned out our aisles 3 weeks ago as shown here.

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Today I noticed that there are 100's of plant popping up in the aisles again. I guess tilling them under did not work that well!

They are very pervasive!