I need to simulate the game of bingo, to determine the average number of balls required to achieve 1, 2, 3...12 lines. the ultimate deliverable for this job is simply 12 data points (how many balls on average have to be called, before a single player achieves 1 line).
1. in my game of bingo, there are 25 numbers to collect, which are randomly selected from 1-50., and randomly placed. So a sample grid might look like on the attachment.
2. There's a bucket of 50 numbered balls, and they're called out one at a time, at random, until all 50 have been called out. The player strikes off the numbers that they need.
3. there are 12 possible lines (5 x horizontal, 5 x vertical, 2 x diagonal).
My question is: on average how many balls need to be removed from the bucket before a player has 1 line. How many til they have 2 lines...and so on.