If you know the distribution of the data (which can be imputed as part of the sorting process by sampling the data), it is possible to guess if the next number

If you know the distribution of the data (which can be imputed as part of the sorting process by sampling the data), it is possible to guess if the next number is going to be larger or smaller than the current one 75% of the time without looking at it by using Cover's pick the largest number trick [1, 2, 3]. I wonder if distributed sorting algorithms know and incorporate this, which should reduce the cost of hitting the network in distributed algorithms considerably? (Asking because I don't work in that field; this is just an idea that I had). References 1. "Playing a Trick on Uncertainty" by Thomas Bruss, page 7 of http://www.emis.de/newsletter/newsletter50.pdf http://www.emis.de/newsletter/newsletter50.pdf 2. "Tom Cover’s Number Guessing Game" by Robert Snapp, http://www.ibrarian.net/navon/paper/Tom_Cover_s_Number_Guessing_Game.pdf?paperid=15348704 http://www.ibrarian.net/navon/paper/Tom_Cover_s_Number_Guess... 3. "Who discovered this number-guessing paradox?", https://math.stackexchange.com/questions/709984/who-discovered-this-number-guessing-paradox https://math.stackexchange.com/questions/709984/who-discover...