"Loaded dice - rolling for dust when hatching an egg"

#PokemonGO: TLTR – The accepted assumption that the dust and candy from egg hatching follows an equal random distribution is only partly correct. Data from 97 hatched eggs shows a biased distribution with only approx. 60% of values equally distributed. The remaining values are either maximum or minimum. The data seems conclusive for 5k eggs. A similar algorithm is assumed for 2k and 10k eggs as existing data fits with such an assumption.Lets start with what we think to know about egg hatching and the amount of dust/candy you get from hatching eggs. The following table shows the accepted values for dust and candy as well as the formula.Egg typeMinimum dustMaximum dustMinimum CandyMaximum CandyFormula2K400800510floor(dust/75)5K80016001021floor(dust/75)10k160032001632floor(dust/75)The current assumption is that the server rolls a random number for the amount of dust you get and then the amount of candy is calculated from that value. This means that the amount of dust you get should be equally distributed.There is one problem with this assumption – the chance to get maximum or minimum dust should be extremely rare as you would need to roll exactly 800 or 1600 for a 5K egg. I’m currently doing an egg diary for eggs I hatch for the Silph Road Research. The researh only asks for the pokemon I hatch. But I felt I could gather additional data doing a comprehensive egg diary. The contribution how to make an egg diary is here: http://ift.tt/2hloaGK shared my original data. I have now updated the data and show all data for 106 eggs that I have collected and hatched starting on the 5th of December. The data is here: http://ift.tt/2hAtgv1 started with an empty egg storage after first flushing my inventory. I did a second flush when the babies got introduced. Thanks to the diary I was able to follow each individual egg included in the second flush and didn't have to discard this data.I collect the date, the time, and the stop of collection, the egg type, the Pokémon which hatches, time and date of the hatch as well as the amount of dust and candy that I got. Only the egg type and dust/candy received is relevant for this article. The amount of dust and candy gained stays on the screen only for 2 or 3 seconds. I therefore do a screenshot for each hatched egg. Data for 9 egg hatches are missing. In the early days I was too keen to hatch as many eggs as possible and twice forgot to turn off the app before starting work – so eggs hatched while the app was running in my pocket. In the other cases I must have missed them while being distracted.The data:Amount of dust2K5K10ktotalpercentageMinimum21211515%Random104725961%Maximum51712324%Minimum means 400 dust for 2K, 800 dust for 5K and 1600 dust for 10K.Random is a value greater minimum and smaller maximum. These values seem randomly distributedMaximum means 800 dust for 2K, 1600 dust for 5K and 3200 dust for 10KMost data collected is for 5K eggs. Rolling exactly 800 or 1600 assuming a random distribution should be a rare event with a probability of 1/801. The chance for 2K eggs should be 1/401 and for 10K eggs 1/1601. Instead 15% of all eggs hatched were minimum and 24% were maximum values.I currently assume that approx. 40% of all egg hatches yield either the maximum or the minimum amount. Taking the advice in a different thread to look at parsimonious/simplistic solution I assume that the chance for minimum and maximum candy is equal and that it is the same for 2K, 5K and 10K eggs. This would mean approx. 20% of egg hatches give mimimum dust and 20% give maximum dust.The most simplistic assumption that a random distribution exists that includes minimum or maximum values on the other hand is clearly refuted with the data shown. Seems Niantic at least sometimes plays with loaded dice.All data has been made available in case researchers here want to use the data to come to their own conclusions.edit: Minor text fixes via /r/TheSilphRoad http://ift.tt/2i0Ts2J