"We cannot ever be absolutely certain of obtaining a result from randomness."
There are some reasons in logic we might disagree with this assertion, but in general this is the level of our current mathematics.
In other words, if something is random, we could technically carry on a process forever (to infinity and beyond), without ever be absolutely certain of obtaining a result. This is definitely a weird truth, and it is a reasonable thing to resist.
+ Show Spoiler +
I obviously don't want to spoil too much in the category of statistics since I think that people are encouraged to learn statistics themselves, and this is one of Blizzard's objectives with Hearthstone
Anyway, there are some weird events that were happening on the Diablo 3 hardcore ladder: players were as usual worried about "toughness" statistics. If you know what toughness is you'll see why people worry about it.
So we got to talking in general chat about random processes and probabilities and I thought of an interesting way to worry about things.
I made this Excel spreadsheet to graph a function of our chances of flipping at least one heads within 1,000 flips. Interestingly enough it is (statistically) impossible to say we absolutely will flip 1 heads in 1,000 flips (for the above arguments).
I don't know if you can see my picture, but the result is that on the 50th iteration (row 51) we obtain a probability of 1 for obtaining heads.
Now of course this Excel, professional software that most businesses use, and I've appended to the maximum possible quantity of decimal places (30).
We know the correct answer is that we can never obtain a probability 1 of obtaining at least heads (especially not within only 50 attempts). In fact, as we know, the correct answer is that we can never obtain a probability of obtaining at least heads even in 1,000 attempts (which is what I was hoping to look at graphically).
This is a fairly interesting result we look at the graph. It looks like (and would under almost most conventional resolutions) look like that we should always roll heads after fifty attempts (and of course that is what our data actually says in this case).
But as I said before, we know with certainty that outside pathological cases we can never flip heads with certainty. Therefore this result is wrong.
So now we must wonder as the Diablo players were wondering: Are we getting the right results in our games? We have no idea how Blizzard servers keep track of everything, and the chances of appending a decimal place are evidently very high. Since Excel is truncating decimals at what looks to be 15 places in calculation and 30 places in display-mode, there is a good chance something like this could be happening at Blizzard.
It's pretty important of course that we look at this because it could affect our game experience.