We make a lot of use of probability and randomness on DelugeRPG. They decide whether the next poke you find on the map will be a legendary or not, whether it will be shiny or dark or normal etc, what reward you'll get in the raffle among other things. Many of our users misunderstand or have misconceptions about probabilities and randomness.

This page tries to help with those issues with some examples related to the game. The numbers used in the following examples are not the same as they are in the game

Shiny? or not?

Lets see how its decided whether a pokemon that shows up on the map will be a shiny or not.
We ask the computer to pick a random number from 1 to 100. But before it picks the number, we create certain conditions. Say, we decide that if the computer picks a number between 1 and 5, we will show a shiny pokemon, between 6 and 10, we show a dark pokemon, and so on. When the computer picks the random number, we check it against out conditions. If the computer picks 4, we know 1 to 5 is for shiny pokemon, so we show the shiny pokemon. If the computer picks 9, we know 6 to 10 is for dark pokemon, so a dark pokemon shows up. If it picks 97 and there are no conditions to it, it shows a normal pokemon.

This happens again on your next step on the map, and on the next and the next and so on. The computer's previous number of choice does not affect its next choice in any manner. Remember how we had 5 numbers out of 100 allotted to shiny pokemon? We can say that there was a 5% chance or probability of getting a shiny pokemon. On your next step, the chance is still the same 5%. It doesn't change. If you do not get any shiny pokemon 20 times in a row, that does not mean that you are due for a shiny. And if you get 2 shiny pokes back to back, that does not mean its impossible to get a third one on the next step. Some may call these favourable patterns lucky and the unfavourable ones unlucky, and no matter what you call it, it doesn't affect your next step.

Legend or not?

It is similar for choosing if you next poke is a legendary or not. While the poke can either be a legendary or not, the chances are not 50% each. Because we don't want legendary pokemon to be common, we set a lot probability for them. Lets say 5%. So in 100 numbers, 1 to 5 are for legendaries. and 6 to 100 are for non-legendary. We ask the computer to randomly pick a number and thats what decides whether you get a legend or not.

When you get a raffle reward such as LEGENDS++, what we do is double the probability of getting legends from 5% to 10%. so the range is 1 to 10 for legends and 11-100 for non legends. Remember, even though its doubled, legends are still rarer than non-legends. And because the computer makes these choice randomly, it is very possible that one may sometimes get more legends without LEGENDS++ than with it, but its less likely than the other way round. 
A lot more people feel they get more legends without the raffle event because they spend a lot more time on the maps without the LEGENDS++ effect than they do with it. They should simply logout and log back in again to lose the event's effects.

Useful links for further reading