I want to create a deck of cards where each card is a room in a dungeon. Each will have between 1-4 doors, one door per side of a card. This will create corners, T intersections, hallways, open rooms with a door on each side, and dead-ends.
How may I go about this (or what sort of math can I do) to show me how many cards of each number of exits to make (or how many of each type of intersection, preferably) so that a dungeon caps off after an average number of draws. Say I wanted a game to last 50 turns, I'd make a 50 card deck and want to know I'd draw at least 45 of them before there are no exits to connect on the board.
It wouldn't need to fit inside a grid, but limiting it's size to fit on a coffee table (instead of generating an overly horizontal or vertical bias) would be preferable. How would the math change if I were to fit it inside a grid, say 5X5 (max 25 cards), 5X9 (max 45 cards) or 10X10 (max 100 cards)? Assuming the edge of the grid would place a cap on an exit.
How do other games go about estimating this ratio?
I say cards, but the concept would be the same using square tiles or something similar.