## Rainbow tables- some questions

I already read How Rainbow Tables work and Rainbow table - Wikipedia, the free encyclopedia
and got curious about some points that weren't specified there.

The questions are:

1-The optimal method of converting a wordlist to a RT, is to make a square RT? (example: 3000000 words = 1732x1732 table, wich means table only needs to save 1732*2 words + 1732 Reduction functions).Question is how much ocuppies each Rfunction.

2- When making a RT from a wordlist, all the words need to be put there right? so reduction functions have to work in a way that all hases contained in a column are reducted to valid words(words that wordlist contains). So each R.function has to have an geral solution algoritm for all hashes in that column. Is this right? If yes, what is the method used to find the algoritm?

3- I read here How Rainbow Tables work that chance of a collision happen is 1/L (L-lenght of a chain) If we have longer chains isnt the probability of collision bigger ? Example: we are seeking a pass for hash "FGE13". We know this hash isnt on our RT, but if we hash and reduct this hash, like 100000 times(supposing our RT chain length is 150000), probably at some time it may collide and merge into one of our chains, meaning this will give a false positive in the final reduction/hash.

thats all,
don't need to give very exhaustive deep math answers. I would like just to get the idea behind this.