The rule we'll be testing in London is as such: When you mulligan for the Nth time, you draw seven cards, then put N cards on the bottom of your library in any order.
So, for example, let's say you're taking your second mulligan of a game, what we often call a mulligan to five. You would draw seven cards, select two, and place those two on the bottom of your library in any order. Then you would decide whether to keep or mulligan again.