Of the four egg cases I put out in the yard this year (I buy them at garden shops), one has hatched for sure, don't know about a second one, and I've plumb forgot where I stuck the other two.

I have found natural cases now and then from mantises I had in past years, but I like to make sure.

Sometimes a little hanging mass of shedded material stuck to the case gives the hatch away, but if that falls off, an empty egg case looks exactly like an unhatched one. All of them look like a little gob of brown caulking foam.

One summer when I have more time to kill I stuck one egg case in a cage and fed the hatchlings using tiny bugs vaccuumed from the grass into a modified dustbuster. Didn't take too long for this to become a big pain in the tush, and I let them go.

Surprisingly, the mantises in the cage did not eat each other much, and a number of them just starved (another reason to let them go). I have found that mantises will not attack another mantis unless there is a distinctive size advantage (mature mantis vs. one a few molts behind), or a possible ambush. With those eyes, it is not easy to sneak up on a mantis.

Young mantises are extremely good at Not Being Seen--their mortality rate is very high. It's not unusual to be unaware that you have mantises at all until they have matured (only fully mature mantises have wings) and you were lucky to spot babies.

Mature mantises are looking for mates, and then it's all about Being Seen. This is when you see them on walls, on fencetops, and other places. I used to worry about future mantis generations, and "introduce" males to females, but later heard that females can lay fertile egg cases on their own--they just have no male hatchlings.

Incidentally, the mating behavior of mantises is highly exaggerated. I have watched mantises mating, and almost always, the result is the male making a quick and safe getaway. I suspect that most of the observations of legendary mantis male-eating took place in small cages.