What are the odds of win streaks?

I just noticed I'm on a win streak (11-0).

Based on the elo formula, the odds of winning against someone of equal rating is 50%.

A coin flip is 50%. Apparently the odds of 10 coin flips landing on the same side, in a row, is 1 in 1024.

Does this mean statistically, assuming the elo of both players is both the same and stable, that a 10 game win streak is also a 1 in 1000 occurence?
This is specifically in relation to opponents of equal strength, not bashing lower rated players for a 20-0 streak.

Just found it interesting!
What's your longest streak?

Getting the forum message achievement

My best win streak in Blitz was 16 games, but that may have been playing against a friend. Over the past year 9 was my best (which was mostly Arena games).

Part of my streak is probably a recovery from a low point after a series of losses last week.
I lost something like 7 out of 10 games. So this is perhaps more of a rebound.

Nevertheless, on the flip side, I assume whenever I lose 10 in a row, that's also a 1 in 1000 occurence LOL.

@5
"I assume whenever I lose 10 in a row, that's also a 1 in 1000 occurence"
++ No. On a bad day your odds are worse than 50% to lose against an equal.
After each lost game, your odds become worse because of being mentally groggy.

Elo is a case of spherical cows on a frictionless plane. People are much messier than their elo implies, so winning and losing streaks happen way more than elo implies they do. 

This is true only if draws are not included. Elo rating alone is insufficient to describe this.

If you can draw 10 successive games against players of similar strength, however...

@Bettyuk, the chances would actually not be around1/1024. due to there being a 33% win rate, 33% draw rate, and 33% loss rate. This would mean that a 10-0 streak against a person of equal strength would actually be around (1/59049) or 0.00001693508! Pretty insane right! To find the probability of winning/losing/drawing 100% in x games you can find its likelihood by solving 1/3^x. Also, there are also set psychological factors to account for so you still can't assume that it is actually 1/59049

But also, if you have been studying or improving your game, then you might have higher odds of winning because you are actually better than your rating! Just like when you come back to chess after a long break and are likely to find yourself in a big losing streak. But yes, exceptionally low odds against people of similar strength, especially around your rating above 2000 I would assume. I would bet on the reason for the win steak being you have improved your game.

meow