I'm attempting to create a Hash table in hardware and I would like to calculate the optimal table size and chain length (for collisions). Unlike in software, I can't easily (and don't want to) grow my table, and I'd like to set a fixed chain length per bucket. So having some probability equations would be excellent--I'm particularly interested in calculating the probability of exceeding the chain length for any bucket.
For example, say I have 4000 random values I'm inserting, my table size is 64K buckets, and each bucket has a chain length of 4 for collisions. What is the probability that I will exceed the chain length of any bucket? The number of values I will be inserting is fixed, but their contents is unknown, so I can't necessarily simulate the exact behavior.
I've done a bunch of google searching, but can't seem to find this even though it seems like an interesting problem. I've found equations to calculate the probability of a single collision, but I need to go further.