Familiar Acquaintance

Question

Few, if any, see me coming,
Odds have it that we've met.
I can show myself as friend or foe,
As relief or as competition,
I never do the same thing a lot,
For when I do I cease to be.
I've been the downfall of wise men
And the best friend of simple ones.
I have no feelings but can be happy, so tell me,
You, who is full of wit,
Who am I?

Answer 1

You are

An accident

Few, if any, see me coming,

If it were predictable, it wouldn't be an accident, now would it?

Odds have it that we've met.

Everyone has had something happen to them by accident

I can show myself as friend or foe, As relief or as competition,

Accidents can be positive or negative, harmful or beneficial

I never do the same thing a lot, For when I do I cease to be.

The same accident happening over and over again is not an accident, but a pattern with a cause.

I've been the downfall of wise men And the best friend of simple ones.

An accident can cause the mighty to be brought low, and lift up the lowest

I have no feelings but can be happy, so tell me,

Remember, we don't have mistakes here, only happy accidents!

You, who is full of wit,

I will just point out here that on initial reading, I read: full of...well, something that rhymes with wit

Answer 2

You are:

Luck

Few, if any, see me coming,

Luck is mostly blind luck so you don't seeing it coming. But relatively few people (i.e. those in the know, people who understand the mathematical probabilities involved very well, etc) do see it coming.

Odds have it that we've met.

A play on the word odds and everybody's either lucky or unlucky at some point in their life.

I can show myself as friend or foe,

Sometimes you're lucky and sometimes you're not.

As relief or as competition,

You can be lucky if something good has happened or unlucky if something bad.

I never do the same thing a lot,

Luck entails randomness so it has to vary.

For when I do I cease to be.

Because when it's predictable it's not luck anymore.

I've been the downfall of wise men

Many tales of wise men losing it all through bad luck (i.e. going bankrupt through unlucky bets).

And the best friend of simple ones.

But some people, with no concept at all of the odds against them, win huge windfalls.

I have no feelings but can be happy...

Pure luck is based on a mathematical model, so no feelings are involved. But can be "Happy go lucky".

...,so tell me,
You, who is full of wit,
Who am I?

If I'm lucky I got it right! :) )