According to the same formulas (and even other formulas from other websites) the probabilities of a 7 loss streak or run at this chance to win is extremely low, which I took and interpreted as, the 6th roll in these two sequences are most probably the last to lose, the next one (the 7th) will most likely win.
That was true with the first time. On this second time, I still don't know yet if it will win since I have not yet made the 7th roll. However, since the average number of loss runs until the next greater than 6 run of losses in a row is about 2.4 million, and I've only rolled 1.3 million times, I think I'm not going to lose the next roll.
I also understand that, they keep saying all rolls are independent and dice have no memory, and assuming that, I still have an 87.7779% chance the next roll will win.
They do keep saying that and it is true. I absolutely guarantee you that as long as the site is fair you will have an 87.7779% chance to win every time you play the 87.7779% game. I also think you wont lose the next roll, in fact I'm 87.7779% sure you won't lose. More info on memoryless probability distributions:
http://en.wikipedia.org/wiki/MemorylessnessInteresting article. Now the question is :
Is just-dice a Markov chain characterized as memoryless or not ? How can you verify it ?