Heartstone analysis - rigged or not from physics point
Hello everyone.
First i wish to apologies for my english 
Let us start from my background so you can have a insight in who is typing this and then you may, maybe, give it a bit more weight. I am physicist and 42 years old mean who enjoys playing games. I am saying this because my analysis will provide a insight in faulty RNG system that is in use in this game.
First of all let us talk about “distribution”. As you all know distribution is a number of times event is happening in one array of events. We express that in “sigma distribution” aka standard deviation. In standard deviation events tend to distribute as: (rounded) 32%, 13%, 2%, 0,1% etc… named as sigma 1, sigma 2, sigma 3 etc. in the same order.
Now lets get technical:
We have population (your deck), events (one card from that deck), success (you have gotten card that you want), sample size (your starting hand or “draw 3 cards” etc, everything that is MORE THAN ONE draw of card). We are getting at something called Hypergeometric distribution.
Let us calculate chance to have 1 card that you want in a opening hand when you play first: deck 30 cards, number of copies in a deck 2, opening hand first player 3, number of success - getting the one card: 1 (we do not want two of the same card in a opening hand). Withput going in to math Hypergeometric chance is: 18%. That cahnce will go up and down for a card while your deck shrinks and “in hand” grows.
What are those numbers say: It give us a average chance that in 100 events this card will be picked in average 18 times. Knowing, as we know, that average is 32% we now know that one card, stay with me now, will be picked in average of: 18% of 32% of 100 games. That is 5,76% of a time per cerd.
Now we all know that quest cards are allways in opening hand and yes that will skew a bit a math explained but NOT for a big so we will asume that every card has same chance!.
We all know that some cards do get more than others in our opening hand. So everything explained is NATURAL distribution for everything in our nature stasrting from stars and ending with quarks. But we have here not natural but weighted distribution ehere some cards has more chance to be in your opening hand. All that puts your opening hand in sigma 3 or 4 distribution meaning: not random but quasi random. Giving the fact that ONE CARD has its weight you need to have that cards in order to have them in your opening hand. So again - not random. Not pseudo random. This is simply to say rigged.
Let us go now deep into one game. We have now used more than 1/2 of our deck, we have more cards in our hand than at the beginning. Chances are now much higher to draw a card from deck then at the beginning. But we are now talking not about a chance of a one card but about a chance of THE one card that will turn the tide.
Again we need to look at the array of games. Lets have an array of 10 games where you have lost. Lets first say that you are average player with average cards, playing average games. Your win rate should be, approaching to infinity, 32% from down side. That means you will approach 32% of winnings and then you will oscillate around that number. Normal distribution says that, and that is an imperative, you NEED to oscillate around 32%, in an infinity, if things are truly random. So if you play 1 billion billion games you will win 32% of a time with every card showing in your opening hand 5,76% of a time. SInce that is not true (im not talking about quest cards) we have here sigma 8 or 9 distribution in layman terms: once in a lifetime you live to see similar opening hand over and over.
Let us go back to our moment deep in the game. Suddenly ONE of you start getting JUST RIGHT cards. They are not per se JUST RIGHT they just happen to be there in distribution…hm…yes if our wining rate is, to infinity, around 32% but it is not so something does not add up.
My conclusion here is: we have here weighted distribution destroying average natural distribution. Weighting is done, i do not know how since i do not have source code, giving some “hidden variable” to cards and letting RNG system decide on card sitribution based of that weight.
Therefore game is not rigged in the sense that game KNOWS which card to give to whom but it is rigged in a way that some cards has they weighted average adjusted so you can get that card in a “right moment” more times than you should in a natural distribution.
Have fun!