three times the same card drawn at the start of a match - randomizer issue?

naabaldan

This issue was discussed but left unchanged a long time a ago but brought it back to my attention as it happens way to often over the last coalition event (HOD). Drawing the same card three times at the beginning of a match should result into a shuffle of the cards and redraw. While the chance to draw the same card three times in a row is very low, i have collected almost all of its appearences and now I am able to fill a wall with all of those screenshots.

This goes together with another "phenomenon" while we open packs and pull the same cards twice in a row feeling that should not happen that often, especialy when the duplicated draw is a mystic or even masterpiece.

jtwood

Just to add to this, hypergeometric probability indicates that the odds of drawing the same 3 cards from a 40-card deck with 4 copies of that card at 0.0404858%. So, yeah... The odds are very low. The only way to really argue that something is wrong with their randomizer, though, is to accumulate a lot of opening-hand samples until you can prove with a high degree of statistical significance that the sampled data is inconsistent with predicted distributions. That would be no small task.

Tremayne

Be careful, you are not allowed to question the randomness of MTGPQ!
Or that is at least the lesson I have learned.

Every time weird randomness is brought up it is either an anomaly or observation bias. It is never RNG that have been poorly implemented.

Foznertep

I observed this very frequently as well, though. Drawing cards in triplets during the first turns of a match happens often enough to make it really improbable to happen "naturally".

naabaldan

34 screenshots as an example of tripple card draw at turn ONE: https://imgur.com/a/tELrGbk

naabaldan

Battle-Logs available

jtwood

@naabaldan said:
34 screenshots as an example of tripple card draw at turn ONE: https://imgur.com/a/tELrGbk

You would also need to provide a count of how many total matches you had played to help with calculating a ratio.

naabaldan

As of the percentage this should happen, no.
But I have to guess. I mainly play coalition events and first match of fblthp and rising tension 4 matches up to 3 days week. lets say about 100 matches a week?
Provided screenshots are only those ones I have saved the battle-log too. I did not save every occurance.
Between 29th of March and 13th of April it happens 6 times. That was the reason to post
I also did not show or count those occurances when three cards are drawn in a row after the first card...

TheHunter

@naabaldan said:
As of the percentage this should happen, no.
But I have to guess. I mainly play coalition events and first match of fblthp and rising tension 4 matches up to 3 days week. lets say about 100 matches a week?
Provided screenshots are only those ones I have saved the battle-log too. I did not save every occurance.
Between 29th of March and 13th of April it happens 6 times. That was the reason to post
I also did not show or count those occurances when three cards are drawn in a row after the first card...

This should happen approx 5% of the time. There are 10 different cards in your deck, and with repeats allowed there are 220 possible different ways to draw 3 cards. If you think of the cards as labelled A to J, then you can draw AAA, AAB, AAC, etc. and if you wrote this out long hand you would get your 220 combinations. Now consider that there are 10 sets here (AAA, BBB, CCC, etc.) where you have drawn 3 the same, so 10/220 = 0.0454545...

Annoying when it happens, and always memorable because it seems unusual, but not so statistically unlikely as you may think.

If you're feeling hardcore, keep a diary of your draws for a few weeks and count the number of times you get three different cards, two the same and three the same.

naabaldan

Your calculation is WRONG, we had this discussion in an earlier post. The correct maths goes like this:
First draw: 4/40, second draw 3/39, third draw 2/38, equals 4/40 * 3/39 * 2/38 = 0,000404858.
This may happen ten times --> x10 = 0,00404858 or 0,4% or every 250 games one time. Still frequent, but not that frequent as it happens. There is german page you may like to test: https://www.mathepower.com/kugelnziehen.php
in case you don't trust me.

Feden

NOPE. First is not 4/40, it's 1/1. It doesn't matter what the first card is, just that the next two march whatever it was.
Your probability is that a specific card is drawn 3 times; not that any card is drawn 3 times.

TheHunter

Hi @naabaldan I'm afraid your maths are right but for a completely different situation.

First, as @Feden points out the first draw is statistically 'free'. You have calculated the odds of drawing a specific card three times rather than the odds of drawing ANY card three times at the start of a game

Second, where did you get 4/40 from? Are you getting confused with paper magic? In MTGPQ your deck is ten different cards effectively infinitely generated.

With n = ten different cards to choose from, and r = three draws being made, the number of different ways they can be drawn (with repetition possible and order not important) is (r + n -1)!/r!(n-1)! which is 220, and ten of those 220 will be three the same (AAA, BBB, etc.) so your odds of getting three the same at the start are 10/220 or 0.04545 recurring, roughly 5%.

naabaldan

A math professor around? 5%?
I give up. Check the link...
or try this one:
https://math.stackexchange.com/questions/294850/3-balls-drawn-from-1-urn-probability-all-same-color-with-without-replacement

TheHunter

OK rule one for a happy life - never be afraid to admit you were wrong!

I under counted. The perms/combs approach I took treated ABA the same as AAB (say, Connive, Demolish, Connive and Connive, Connive, Demolish). You'll end up with the same three cards in hand, but they came in a different order.

So there are still 220 different combinations of 3 cards you can have on your first go, but there are exactly 1000 different ways these can be drawn (my formula above becomes n to the power r = 10 to the 3 = 1000)

There are still only 10 ways you can get 3 the same, so 10/1000 = 1%

That feels a lot better than 5%, and explains why I only scraped a B in Maths!!

jtwood

@Xucachris said:

Second, where did you get 4/40 from? Are you getting confused with paper magic? In MTGPQ your deck is ten different cards effectively infinitely generated.

>

@someone said:
In March of last year, @Hibernum_JC explained the way decks are supposed to work in game in mtgpq:
Four copies of each card are used to form a virtual 40 card deck. When the deck is depleted, another 40 cards are appended. Likewise, when a card fetches a fifth instance of a card (i.e. Deploy is looking for three creatures in a mono-creature deck after two have been cast) another 40 cards are appended.

https://forums.d3go.com/discussion/64326/40-card-deck

naabaldan

Sorry guys, even 1% is not true.
This is quiet easy:
You have a deck of 40 cards 10 different ones each 4 times.
The chance to pull one specific card is 1/40. As there are 4 equal cards in that deck, chance is multiplied by 4=4/40 or 1/10. Simple.
Second step. You drew one card. Now the decks has 39 cards. Our selected one from the first draw is 3 times in the deck. Chance to draw one specific card now is 1/39 and that one and only card that has three left is 3/39 or 1/13.
Third step. The deck has now 38 cards left. Drawing a specific card now is 1/38. There are still two cards left in our deck we drew the first and second time, so the chance is now 2/38 or 1/19.
Allover chances are multiplied: 4/40 * 3/39 * 2/28. And we have 10 different cards we can do the same thing with:
This leads to 4/40 * 3/39 * 2/28 * 10. Simple as it is. Equals 240/59280 or 0,00404858 or about 0,4% of each game we play. In other words: each an every 250th game I start will beginn with three times the same card.
This is realy simple probability calculation I learnd at school, even though it is like 45 years ago.

Tremayne

@naabaldan - I like your persistence. I hope you will be able to illicit a response from someone on the company side.

Sidetrack - can anyone remember any recent answer from D3 or Octagon regarding the implementation of RNG? Is it a nuclear secret or something.

jtwood

@Tremayne said:

Sidetrack - can anyone remember any recent answer from D3 or Octagon regarding the implementation of RNG? Is it a nuclear secret or something.

If I were them, I wouldn’t reply. Just like how there are some people who will never believe that this virus is real, there are some people who will never be satisfied with any explanation around randomness.

naabaldan

@Tremayne said:
@naabaldan - I like your persistence. I hope you will be able to illicit a response from someone on the company side.

My intension is to motivate the developers to check their code. They can set up a testing modul that starts a match over and over again counting the occurances of a tripple card draw and check the results against probability. I'll never expect a comment from the developers here.

On the other hand, they simply can do a redraw in case this happens.

You may have watched Nalthazars video about opening packs on youtube... he himself noticed how often the same two cards where pulled in row while opening packs in his video. Chances are more complicated to calculate but the high number off occurances speaks for itself.

Actually I am at 850+ unopend booster packs. I will record opening them when I reach 1000 packs. Lets see what happens.

Tremayne

@jtwood said:

@Tremayne said:

Sidetrack - can anyone remember any recent answer from D3 or Octagon regarding the implementation of RNG? Is it a nuclear secret or something.

If I were them, I wouldn’t reply. Just like how there are some people who will never believe that this virus is real, there are some people who will never be satisfied with any explanation around randomness.

You are probably right, that D3/Octagon will never bother replying, call it trade secrets to discuss RNG.

I don’t know if it is a snide remark at me, but I do believe randomness exists and I have been satisfied by explanations from other users on these forums. Especially @volrak have enlightened me many times. (Thanks Volrak)

What has left me quite puzzled is that in spite of the track record of the developers of this game, it seems that RNG is beyond reproach.

As I mentioned above; you are not to question RNG. If someone complains about an issue any evidence is brushed aside, typically as observation bias or a special case which is within statistical range (isn’t everything however small?). This of course does not mean RNG is flawed, but since it is beyond most users to actually come up with the proof of any RNG issue and D3/Octagon lack of response, it is never proven one way or the other.

I suppose I must just accept that RNG is never the issue and drop it. There are plenty of other issues in this app to focus on.

Tremayne

@naabaldan said:

@Tremayne said:
@naabaldan - I like your persistence. I hope you will be able to illicit a response from someone on the company side.

My intension is to motivate the developers to check their code. They can set up a testing modul that starts a match over and over again counting the occurances of a tripple card draw and check the results against probability. I'll never expect a comment from the developers here.

On the other hand, they simply can do a redraw in case this happens.

You may have watched Nalthazars video about opening packs on youtube... he himself noticed how often the same two cards where pulled in row while opening packs in his video. Chances are more complicated to calculate but the high number off occurances speaks for itself.

Actually I am at 850+ unopend booster packs. I will record opening them when I reach 1000 packs. Lets see what happens.

I hope you succeed, but I don’t think that D3/octagon has the capacity and capabilities to set up such a testing platform. I based that on the number of errors they make elsewhere. I have seen nothing in the last 4 years to indicate that they devs have implemented automatic testing, let alone using a test management tool to improve quality.

I’m looking forward to your experiment with the 1k boosters. Might I suggest you open a thread explaining the test and describing your test method and documentation strategy to get feedback in case you have missed something that would invalidate your results? Of course, you might be a world class tester/test manager, so you know your stuff, if so please disregard this suggestion.