Nice work! This notation allows for one of my favorite stupid dice tricks, a simple Poisson distribution. These can go arbitrarily high but with a sharply decreasing chance of higher numbers. Useful for questions such as "How many arrows in the goblin's quiver?", "How many orcs in the patrol?", "What level are the spells in this spellbook?", or "How many hit dice is the monster the wizard just summoned?"
Here are three examples with representative results.
Roll 1d4 exploding, count rolls
1d4!>3>0
sample rolls: 1, 1, 1, 2, 1, 1, 1, 2, 1, 1
Roll 1d2 exploding, count rolls
1d2!>1>0
sample rolls: 1, 6, 2, 1, 2, 1, 2, 2, 1, 1
Roll 1d4 exploding on anything but 1 (i.e. roll until 1), count rolls
1d4!>1>0
sample rolls: 1, 4, 2, 9, 5, 5, 3, 12, 4, 1