Mathematical proof of Hearthstone manipulation, found!

Community Discussion
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Simple, Arena, I’m playing against yet another opponent with $20,000 skins, he inserts 5 bombs into my deck, I have 25 HP, next turn I draw 5 bombs in a row… I lose. So I ask Gemini to calculate the mathematical probabilities of drawing 5 bombs in a row… result?
The calculation is based on the conditional probability for draws without replacement. You have to multiply the probability of drawing the first correct card by the probability of drawing the second correct card from the remaining deck, and so on. First card 1/25, second 1/24, and so on, multiplying everything. Result

The probability is 1 in 6,375,600.

As a percentage, this equals approximately 0.00001568%.

Now, for those who don’t understand, let’s assume we’re calculating the probability of a meteorite hitting Blizzard’s headquarters, with obvious consequences. I asked Gemini about this too. Result:

Our probability of drawing exactly those 5 cards in a row is 1 in 6,375,600.

:comet: Comparison to Meteorite Impact
The probability of a meteorite hitting a specific building, destroying it, is such a localized and specific event that it’s virtually impossible to calculate precisely scientifically, as it depends on:

The probability of a meteorite falling to the ground (and not disintegrating in the atmosphere).

The probability of that meteorite falling in a populated area.

The probability of it falling on a single building.

However, we can make a comparison based on more general estimates:

The probability of dying from a meteorite strike in a lifetime has been estimated (by Alan Harris) at around 1 in 700,000.

An estimate of the probability of a local extreme event (not defined as “a specific building,” but of similar size) has been given as around 1 in 5,700,000 (as cited in one study).

:bar_chart: The Comparison
Your probability of 1 in 6,375,600 is therefore:

Much lower than the estimated probability of dying from a meteorite strike (1 in 700,000).

Comparable to or slightly lower than the probability of a local destructive meteorite impact event (1 in 5,700,000).

In short, the drawing of your 5 cards in a row is as rare, if not rarer, an event as a meteorite hitting a specific, limited area on Earth.

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Expecting the forum defense brigade in 3 .. 2 .. 1 ..

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It’s impossible to defend the forum from mathematics. They’ll say that since it’s within the realm of possibility, things just happen. It’s a shame that anyone who isn’t ignorant and fully understands mathematics knows perfectly well that a possibility tending toward zero is impossible.

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Excellent post. The math sounds solid.

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They seldom use actual logic, or, god forbid, math. Anyone who understand statistics can see that very improbable things happen way more often than they should.

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Don´t get me wrong, I am not saying hearthstone isn´t rigged. But unfortunately your calculation isn´t proof of anything.

Lets take the lottery as an example. Where I live it´s 6 out of 45. The chance to get 6 numbers right is 1 in 8,145,060 (lower probability then your calculation)

According to your logic it would be impossible to ever win, yet it happens again and again.

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There’s a problem. In your lottery scenario, there’s always someone who wins randomly, and it’s the same as everyone else. However, here on the forum, I’ve experienced countless situations like this against opponents who pay Blizzard a lot, all with impossible statistical calculations. Today’s situation is just one example, which, as Gemini also stated, considering that I’m a free-to-play player and on the other side there was a “I pay a lot of money to play,” adds a very important variable to the equation that certainly raises at least a serious doubt about Blizzard’s good faith. On the other hand, with thousands of Arena games, I’ve never won thanks to a totally impossible stroke of luck on the order of 1 in 10 million, and I’ve played at least 10,000 Arena games in 10 years.

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A wise man once said “Real stupidity beats artificial intelligence every time”

Idon´t give much about what gemini has to say. It´s a usefull tool, but I prefer to think for myself :wink:

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Pay attention, and I’ll give you another proof: in the public rankings of the top 100 positions, there are ONLY normal accounts; there are no disposable accounts with nicknames like “skjfbsnf.” None of these PROs has ever demonstrated that by opening a new account, they remain PRO and finish with a 12-0 record and the favor of the public by scoring a dozen runs. How is it possible that out of thousands of players who use disposable accounts, or as we call them “barcode accounts,” no one ever makes the rankings? Unfortunately, today’s world forces us to ignore everything and accept everything in silence, but I’m not like that. There’s something rotten here, and I’m saying it openly.

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Is this another thing gemini said?

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I used Gemini to do some mathematical calculations, and if there is a human being who does them faster, introduce him to me and I will take him to the Guinness World Record, mathematics proves things then everyone reading this post can make their own evaluations and understand if it is worth giving money to play in the arena

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I calculated the probability for 6 in 46 myself and checked the result with google.

Took my a while longer, but so I am sure I got the right numbers

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Depends of what loterly you’re talking about
There are loteries where there’s no guaranteed winner, with odds of 1 out of tens of millions, and yet there are winners

“impossible” doesn’t belong in statistical calculations

That is highly incorrect
You’ve never won on specifics 1 in 10 minions scenarios. It doesn’t mean you’ve never won in some others you didn’t notice.
For example, Your opponent has no minion and they are at 30 health, You play Fyrakk and it casts 5 fireballs at their face. That’s a 0.000002% chance of happening, yet that’s not the only way Fyrakk could have got you lethal.
If you restrict your scope to very specific scenarios you can always find extremely unlikely odds
Like the simple order of the cards in a no-duplicate 30-cards deck. Each combination has only about 4^-31% chance of happening, yet you have 100% chance of getting one combination in the end

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Its interesting that you don’t include the number of cards left in your deck when describing your calculations. You need to know this to do the calculations correctly. And the calculations you describe are definitely wrong. For the record, the probability of drawing 5 bombs in a row from a deck with Y cards (including bombs) is:

(5/Y) x (4/(Y-1)) x (3/(Y-2)) x (2/(Y-3)) x (1/(Y-4)

This equals 100% if Y=5 (you have only bombs in your deck)

It equals 16.7% (1 out of 6) if you have 1 other card and six bombs

It equals 0.03% (3 out of 10,000) if you have 10 cards + 5 bombs

etc. If you have 20 cards left, its still a pretty low number, but I dislike folks saying they have mathematical proof and clearly not understanding the calculations.

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Really? People’s brains too weak or too lazy to do such elementary exercises nowadays?

I think I lamented this somewhere already, but I can’t readily find it… Ah, no matter.

Other than that (btw, didn’t read AI-generated blah blah — no desire to do that, sorry)…

For example:

If someone keeps hitting those odds, then yes, it’s… suspicious.

(Highlighted by me)
Oh, here comes the usual Gaslight Gatekeeper. :smirking_face:

Next these people (master forum telepaths, too) are gonna tell you you’re hallucinating etc, something along these lines.

Or, perhaps, you haven’t been paying attention?

Meaning there must have been 20 cards left (plus 5 bombs).

:grinning_face: The irony…

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They did, but unlike in your reply they did not count the bombs themselves
Their calculation is (1/25)x(1/24)x(1/23)x(1/22)x(1/21)
instead of (5/25)x(4/24)x(3/23)x(2/22)x(1/21), which totals to 0.00188217579% which is still a low probability but 100 times higher

So now it’s gaslighting to ask the OP to do a step back to consider the entirety of its games and not just a single event during it ? Ok
Unless you want to pretend that in 10 000 games it never happened a single time that they won thanks to a specific unlikely outcome that they simply didn’t notice or didn’t acknowledge

The irony being that they talk about calculation understanding and you compare it to paying attention, while there is indeed a calculation error in OP’s post ?

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A computer cannot generate random numbers and hence random cards. A variety of methods can be used to create a seemingly random outcome such as a hash algorithm that takes as inputs a digit from the CPU clock or location in memory or even ambient temperature. Unfortunately, as I’ve seen with many other pseudo-random number generators often times the same number or outcome disproportionately occurs many times in a row. This could very well be what you and certainly myself and many others experienced. Of course, it wouldn’t surprise me at all if Blizzard added logic to the random number generator to favor outcomes for players who spend quite a bit of money.

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Oh, I haven’t checked the arithmetic thorougly, indeed, since, as you noted yourself, it’s low probability anyway.

Speaking of which — so much for the whole artificial ‘intelligence’ shebang (should have done the calculations himself, indeed).

I dunno why some people treat it as some oracle of font of wisdom, when it often is more like a parrot or generates outright nonsense, and you’ve gotta check important stuff.

If your arithmetic is correct (I haven’t bothered with a calculator and the answer :grinning_face: , your formula is correct, though), then it ignored that bombs can be drawn in any order.

Pure demagoguery.

Lemme cut to the chase. A guy reports something very suspicious. Instead of considering the obvious and most likely culprit, you suggest, more or less, ‘Take this time to consider your past deeds.’ Yeah, maybe ‘you didn’t notice’ something.

Perhaps you’re crazy. Oh, maybe the aliens did it, have you thought of that? Or perhaps it’s all just a dream. ‘What makes something real?’ Blah blah.

Really? Anything, but not the unthinkable option of something sus?

No. It must be something wrong with your head. How is that gaslighting? :rofl:

Check, for example, this out: Is pseudo random a thing? - #43 by SparkyElf-2852 , also below in that topic: Is pseudo random a thing? - #56 by SparkyElf-2852, Is pseudo random a thing? - #58 by SparkyElf-2852 — don’t wanna repeat it all.

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Randomnes doesn’t exist anyway in the vast majority of what we call random
All is up to a lot of variables that we don’t know
If you were to have any highly capable and all-knowing entity or program, giving it all the required information would allow you to predict any outcome we call random
And even things that we currently consider to be random may not be and we’re simply lacking a key information to understand how it happens

It of course remains possible
But all the proofs that are provided so far are extremely curated pseudo-scientifical samples

It’s like they selected that one moment you flip a coin 10 times and it lands 10 times on the same side and they call it a proof of rigging, while this event happens consistently at least once when you flip a coin a thousand times but they willingly ignore the big picture

Like all these times people claim their opponents have the “perfect answer” without even knowing what other cards they could have drawn instead, and without considering every other event that happened during their game

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Ooh, boy, looks like “you ain’t seen nothing yet” (the quotation in this case is from “It’s a Miracle” by Roger Waters).

Check out quantum mechanics for starters.

Speaking of which, looks like there’re no hidden variables there (certainly no local ones, at least).

You wish the same could be said definitely about HS, by the way. :grinning_face:

(Highlighted by me)

‘All’? Truly? Have you reviewed them all? Or, perhaps, only a ‘curated pseudo-scientifical sample’ to do the old ‘straw man’ trick?