### Math Question not Crawl related (its CRAZY tho)

Say you have a deck of 52 cards, and you have to pull n cards. On each card is a command to pull between 0 and m new cards, with each value having a given likelihood in the deck (for example 10 cards will tell you to pull two new cards).

You get a tree if you graph out a given run, but what is this cascading effect called in mathematics? I already programmed a simulater so I can play with the outcomes, so not really interested in a solutions (unless there is an explicit solution or some interesting boundary behaviors).

Reason I am curious is that I am messing around with a game I am designing and thought this might offer a means of ramping up difficulty in a natural and still somewhat randomized manner, in a way which requires zero memorization or computation (other than simple counting) from the player. You get an exponential decay curve for the total cards drawn, which you can easily tweak by altering the internal populations as well as the original number of draws.