You are probably not going to like my answer but hopefully I can give you sound reasoning for it.  

My number is three months of home expenses, whatever that may be.

Here's the why.  We like to think that when we put our money in a bank, its still our money.  If you learn one thing in life, lean this.  Its not.  It becomes their money and they are only indebted to you.  They can withhold it and they do on people all the time. Most people think bank closures but honestly, I've known anyone or been involved with one.  You would not even believe the stupid things they can for too.  I've seen $10,000 plus frozen for $500 credit card dispute.  God knows how many accounts I've seen frozen over divorces and back child support disputes. In today's stolen identity world, this is even more critical, The point is, you don't have to do a thing wrong.  All it takes is someone else claiming you do, a dispute.  Getting them unfrozen then becomes resolving the dispute.   In disputes, time cost money especially lawyers, while if time is not as much a factor most disputes we can resolve without lawyers.  

Here's the kicker, you still need to eat and pay your bills.  

Three months is a good number.  That's pay your mortgage, utilities,  car payments, credit card payments, food, gas, etc.  If you don't know what this number is, then you shouldn't be asking this question.  That means you are not budgeting.  The idea is to not have to change any of your lifestyle while giving you time to resolve whatever has your funds tied up.  

That's a much bigger number than the power went out but its not EOTWAWKI sell my precious metals and lose potential profit either.  For many of us, its enough to buy a used car and many more enough to buy a gun.  For most of us, its enough to cover most household emergencies where paying cash can save you 20%-30%.  The later, I've used it for many times and saving money is never a bad thing.  I can even say this, I've saved more money paying cash for some household emergency than I could have made having the money in a savings account.  In fact, way more.  

The how depends on your circumstance.  The most popular is a hidden safe while in the past when I didn't have as much I've used a book in a book rack or a boot in a pile of boots even.  

One time years ago, I was broken in on.  I had just cashed my paycheck and that night put the bulk of my cash in a book.  A cat burglar broke into my house and the next morning I woke to find my billfold torn in pieces at the foot of my bed.  The cash was safe the book.  BTW, I always had a mouthy dog after that night.

Tj