Wondering how the random algorithm takes into account champs owned.

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I don't think we can know how it actually works, but here's one possibility:

For each player in the game, an algorithm randomly shuffles all owned champions and places them in an ordered list. Starting at the top, each player gets the first champion in their list. If there are any ties, both players could move on to the next champion in their list. Or one of them could get the champion tied, and the other player could move to the next in the list.

There are a million different ways the champions could be randomized, and this is just one. But it would work, I think.

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The funny thing about random things is that its only random when you look across a HUGE pool. Like all selections ever made for every game. But when you look at a single persons "random" selections you will find champs that get picked more, less, ect. Anomaly's always pop up in random selection generations.