O.k. now things get really really small. About 0.0000013% of other customers would share fate in this case. It's so small that because we have fewer than a million customers per cell anyway, there can be zero full overlap.pic.twitter.com/xmZHjKMIy0
You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
The bracket notation is short for "choose" and since x choose x is 1, and x choose 0 is 1, we can replace everything above the line with 1.pic.twitter.com/X6evtSZMsv
Now let's expand the choose operator into its factorials ...pic.twitter.com/f0L2ZBGZYw
When you were about 10 you probably learned the reciprocal of a reciprocal is just to turn it upside down. That's still true. That gives us our final form ...pic.twitter.com/KfL5vELMxy
In that form it's pretty easy to see that the smaller S is relative to N, that Shuffle Sharding gets dramatically more and more effective! Convinced? I hope so!
That was my whole talk and it took me longer to tweet it than it did to give it on stage! Go figure. Feel free to AMA. And thanks for reading and making it to the end. Now use Shuffle Sharding anywhere that you can!
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.