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You can't use any knowledge of previous events to predict what will happen in the future if the events are independent.

For example, if you have a random walk on the integer line (every step go forward or back one number), if you repeat this an infinite number of times (may take a jiffy or two), you will visit every number you can think of at least once (in fact, an infinite number of times).

EDIT: But what is true, and I think this is what you are trying to say, is that if you add up all the numbers visited from your random walk, the sum will approach zero as the number of steps tends to infinity (assuming that moving forwards or backwards is equally likely).

That's what he's getting at I think. While you cannot predict future events on past events, you DO know that if you've been moving forward that, as you keep walking, EVENTUALLY you'll move backwards to balance it out. The difference between this and the gambler's fallacy is the timing. A statistician knows that 10 steps forward means AT SOME POINT 10 steps backwards while the gambler believes that 10 steps forward means THE NEXT 10 steps will go backwards. What they miss is that those 10 backward steps could come next, or after 50 years of walking. It's a debt with no time limit or minimum payments. The system is perfectly free to make you walk 10,000 steps forward then, long after you are broke, slowly walk you back to 0.

For those reading that and going 'wtf', I realized not long ago that we live in a world made up of quarks that seem to be better explained through Loony Toons logic than Physics. The basic forces of mathematics and science is the source of all that which is Troll.

I think that's what he means too but his additional explanations (after a run you are likely to see a regression towards the mean) are incorrect.

All that is guaranteed is that a streak will end at some point but that does not mean future events will balance it out in any reasonable amount of time (which is the point you are making as well). Assuming independent events, each event has no memory of what happened previously, so you could immediately go on a new streak of the same type (win/loss/druids/no-druids etc.) after your previous streak ended. It's also just as likely to have a streak of the opposite type (or in fact no streak at all).

In short, once you collect the data it has no bearing on future results. The only thing you can say is that after a large number of events, they will even each other out eventually.

Note this only applies to independent events. For example, I notice I go first more often than going second when I play arena, and was wondering whether it would get back to a 50% rate at some point. But the answer is that it will most likely not do that, because my win rate is higher when going first, so the correlation between going first and win rate improvement means I will play more games going first than going second. So winning and going first are not independent, they have a slight correlation.

EDIT: That's because my arena total win rate is above 50% at the moment. If it was lower than 50% I would probably see the opposite result, i.e. more games going second than first.

I think that's what he means too but his additional explanations (after a run you are likely to see a regression towards the mean) are incorrect.

You've either misunderstood what I wrote or you don't get the underlying principle.

Yes, you can immediately go on a new streak of the same type, but the fact that these independent events have a mean that is somewhere else makes it more likely that you will not, over timeframes short or long. For independent events, they're always most likely to be closest to the average (which is why the Gaussian distribution's peak is at its mean.) Sure you don't KNOW what the result will be but the mean is always the most likely result*

* for a continuous parameter. When looking at something discrete like coin flips or die rolls or what class you're playing against in your next Hearthstone game, the question is over the next N games how well the resulting distribution approximates the underlying distribution of those discrete possibilities.

So, in my hypothetical where one swaps in Skulking Geist after a few games against Jade Druid, you're still most likely to get a rogue or a priest on the next game. Why? Because Rogue and Priest are best represented on the ladder. You were more likely to get Rogue and Priest before, you just didn't. More games are likely to represent the underlying distribution, just as the earlier games were (even though they didn't turn out that way.)

Yes, you CAN have three more Jade Druid games, but it's unlikely because at 8.52% ladder representation, the chance of that happening on the three successive games is 0.06%. The chance of three games against rogue or priest are 5.2%.

(Using numbers from today's Vicious Syndicate Class/Archetype Distribution here.)

The timeframe where it evens out is unknown though - and definitely not short term. It only evens eventually due to the law of large numbers in statistics. With the emphasis on "large".

EDIT:

For example, a fair coin toss is a Bernoulli trial. When a fair coin is flipped once, the theoretical probability that the outcome will be heads is equal to 1/2. Therefore, according to the law of large numbers, the proportion of heads in a "large" number of coin flips "should be" roughly 1/2. In particular, the proportion of heads after n flips will almost surelyconverge to 1/2 as n approaches infinity.

Though the proportion of heads (and tails) approaches 1/2, almost surely the absolute difference in the number of heads and tails will become large as the number of flips becomes large. That is, the probability that the absolute difference is a small number, approaches zero as the number of flips becomes large. Also, almost surely the ratio of the absolute difference to the number of flips will approach zero. Intuitively, expected absolute difference grows, but at a slower rate than the number of flips, as the number of flips grows.

That's all true but nothing I've said conflicts with that.

Edit: To proceed with the coin flip example, let's say that I have had six flips that are all heads. I predict that over the next two flips, my streak will be broken.

That's a reasonable prediction because the chances of one or more tails are 75% and the chance of two more heads is 25%. Furthermore, if one switches the situation to be a streak of six flips that result in tails, the chances that that streak will be broken in two more flips also is 75%.

Even flipping coins over very short horizons like two flips, one can follow up a streak with a prediction of reversion to the mean and be more right than wrong.

Yes, you can immediately go on a new streak of the same type, but the fact that these independent events have a mean that is somewhere else makes it more likely that you will not, over timeframes short or long.

Which is incorrect. Especially if you consider short timeframes.

Yes, you can immediately go on a new streak of the same type, but the fact that these independent events have a mean that is somewhere else makes it more likely that you will not, over timeframes short or long.

Which is incorrect. Especially if you consider short timeframes.

I posted a specific counterexample of coin flips over a two flip timeframe (which we can both agree is very short), so I'm not sure why you're saying that.

That's all true but nothing I've said conflicts with that.

Edit: To proceed with the coin flip example, let's say that I have had six flips that are all heads. I predict that over the next two flips, my streak will be broken.

That's a reasonable prediction because the chances of one or more tails are 75% and the chance of two more heads is 25%. Furthermore, if one switches the situation to be a streak of six flips that result in tails, the chances that that streak will be broken in two more flips also is 75%.

Even flipping coins over very short horizons like two flips, one can follow up a streak with a prediction of reversion to the mean and be more right than wrong.

You are like me with your ninja edits.

You are correct that you can predict an end to a streak within a set amount of flips according to probability.

But the next streak is just as likely to be a run of heads or tails, since the coin has no memory of previous events. In the long run, streaks of heads and tails should be of equal likelihood. In the short term, all bets are off.

But the next streak is just as likely to be a run of heads or tails, since the coin has no memory of previous events. In the long run, streaks of heads and tails should be of equal likelihood. In the short term, all bets are off.

Yes, absolutely! The point of all of my statements about reversion to the mean isn't that I'm saying a streak of heads should be followed by a streak of tails. It's that a streak of heads is far more likely to be followed by anything but a further streak of heads, over any timeframe over a single coin flip.

Edit: This is relevant to my Jade Druid hypothetical because in that case something unlikely happened, the player swaps something to respond mistaking the unlikely events for a pattern, and the unlikely thing doesn't continue. Then, the player guesses that swapping the card made it stop, when in fact it was just that it was unlikely to begin with.

My point is, it's not. Define a streak as two or more results the same. Once one streak ends, the probability that the next one is of the same type is the same: 50% for the coin case.

Unless you are just saying that a streak will come to an end at some point, which is true (and obviously so). EDIT: It seems that is what you are trying to say. In which case I agree.

Unless you are just saying that a streak will come to an end at some point, which is true (and obviously so).

Yes, that is exactly what I am saying, nothing more.

Particularly in Hearthstone match-ups, people in this thread say things like "I had three games against X, I teched against that, and suddenly got three games where my tech didn't help." Their fallacy is that they assume switching cards caused the change, when in fact they were responding to something unlikely enough that it would have stopped on its own.

Well the important thing about tech cards is they are there for when you need them in various matchups, assuming you draw them of course ;) And you should only add them if it significantly improves your winrate against the deck you tech for (so I only run Skulking Geist in my N'Zoth Paladin deck and no others because it is a very slow deck and has no chance against Jade Druid otherwise, other decks have a fighting chance). Only other tech cards I used (apart from various flavours of crabs depending on whether murlocs or pirates are abound) have been Flare in my midrange hunter when burn/freeze mage was everywhere and an Eater of Secrets in my water rogue for the same reason. I certainly never noticed any decrease in numbers of mages faced when I decided to include them (I did notice my win rate improve a lot against them though).

The worgen OTK thread just opened up made me remember how I used to have to add a Sunfury Protector to my resurrect priest deck because it had no taunts otherwise.

Particularly in Hearthstone match-ups, people in this thread say things like "I had three games against X, I teched against that, and suddenly got three games where my tech didn't help." Their fallacy is that they assume switching cards caused the change, when in fact they were responding to something unlikely enough that it would have stopped on its own.

No no no. The fallacy here is that you believe something which you mistake to be true and then argue as though it is. You have no way of knowing what code Blizzard is really running here - that code could be doing anything. The only way to argue your case as being actual fact is to have Blizzard open source the matching making code, which would prove beyond doubt that either match making really is random/fair/etc or is somehow rigged/skewed/responsive. If you can see the difference between discussions on coin tosses and other real theoretical random events... and software... then you have to acknowledge the possibility is there and take this more seriously. As a software engineer, in the programs I create, I can control the randomness so that the very next number thats generated is exactly what I want it to be (through something called a seed) - that makes probabilistic analysis a moot point. If I can do these things, so can Blizzard's engineers, and that's just a quick example.

It's 100% rigged to some degree. Example, just recently: I made a dragon warrior deck to complete a warrior card quest. First opponent? Dragon warrior, can't remember the last time I'd seen one.

Particularly in Hearthstone match-ups, people in this thread say things like "I had three games against X, I teched against that, and suddenly got three games where my tech didn't help." Their fallacy is that they assume switching cards caused the change, when in fact they were responding to something unlikely enough that it would have stopped on its own.

No no no. The fallacy here is that you believe something which you mistake to be true and then argue as though it is. You have no way of knowing what code Blizzard is really running here - that code could be doing anything. The only way to argue your case as being actual fact is to have Blizzard open source the matching making code, which would prove beyond doubt that either match making really is random/fair/etc or is somehow rigged/skewed/responsive. If you can see the difference between discussions on coin tosses and other real theoretical random events... and software... then you have to acknowledge the possibility is there and take this more seriously. As a software engineer, in the programs I create, I can control the randomness so that the very next number thats generated is exactly what I want it to be (through something called a seed) - that makes probabilistic analysis a moot point. If I can do these things, so can Blizzard's engineers, and that's just a quick example.

Just because something is possible it doesn't make it worth taking seriously. There is infinite number of possible things. We need more reasons.

Aside from the obvious fact that what he describes works the way I've been saying and has no elements that resemble what this thread is about, I'll just point out that the design and business goals around building a matchmaking system focus on a concept that F2P game designers call engagement. Engagement is pretty much about how likely a player is to come back and play another game. These engagement goals are listed in that GDC presentation by pointing out that a designer ideal is to "put players into matches that are fun" and a business ideal is to "keep the most amount of players in our game having fun."

A matchmaking system that attempted to find the counter to your deck and match you against it would be one of the most direct ways I can think of to stomp on those ideals and jump up and down on the broken pieces.

There are further problems. From a technical standpoint, the more complex the parameters or algorithm used for matching, the slower the assessment of match quality will be, and as Dr. Menke points out in his presentations, on launch day a product may have to match millions of players into games, and keeping the time short between hitting "play" and putting players in a game matters a lot for engagement. Digging into card choices and deck archetypes to do this would be a good way to slow this process down by hundreds or thousands of times.

Finally, even if someone wanted to build a system that would kill engagement and performance, nobody's even proposed how such a system would identify deck archetypes on the fly, figure out what a "counter" deck is, or solve any of the other high-level game concept questions that otherwise wouldn't be part of the matchmaking system at all. Small deck changes can cause big changes in win conditions, and having the matchmaking system figure this out on the fly just isn't going to happen, at all.

No, I haven't looked at their code, and they're probably doing some things that would surprise me. But, I do know something about providing video games as a large-scale online service, and trying to do matchmaking based on the exact contents of a player's deck is like trying to fly to Mars in a submarine. Not only is it too complicated to ever work, it's totally unclear why you'd want to do it in the first place.

I am not raising a stupid argument like "I played yesterday with deck A and got deck B against me, thus it is rigged".

My argument and hypothesis is the following: When something really goes overboard in the sense of game balance, before release of the patch it is quite probable that company uses any measure hidden from public to overcome that issue temporarily. For example, when a certain deck is insanely strong, would it not be rational to slightly influence the matchmaking, at least sporadically , for a short time, on certain levels, or certain cases?

Sure, it's in principle possible for them to do something like that, But:

Blizzard has a major investment in matchmaking systems that are designed specifically to not need to know much about the game being played, so adding such a thing would be a huge bump in complexity and would have performance and maintenance implications as a result.

The community tends to be self-correcting, gravitating toward successful decks and away from relatively weak ones. As long as there is a good counter available for every strong deck, tweaking game systems to try to keep numbers in line probably won't be necessary.

I'd say that the Hearthstone team's behavior and statements suggest that it takes a LOT for them to characterize something as a crisis that needs immediate attention like a mid-expansion patch.

Doing this won't fix imbalances in tournaments, which are a major focus for Hearthstone's business right now.

The only way to know for sure whether something like that is going on is to collect statistics (or read the code.)

You have no way of knowing what code Blizzard is really running here - that code could be doing anything.

..

A matchmaking system that attempted to find the counter to your deck and match you against it would be one of the most direct ways I can think of to stomp on those ideals and jump up and down on the broken pieces.

...

Perhaps you should note that what I observed was the exact _opposite_. I was adding the tech cards to counter the weapon wielding classes... and they vanished... No one was countering me.

A presentation is not code. People can (and do) lie, companies can (and do) lie and sometimes people don't even know the whole truth themselves because they do not see the code that actually runs. I say again, the only way to conclusively prove it is to see the source code. All arguments being made either way (rigged, or not rigged) that are made as though truthful on here, are in fact, not from strong positions at all. The only truth is that _we do not know_.

You've either misunderstood what I wrote or you don't get the underlying principle.

Yes, you can immediately go on a new streak of the same type, but the fact that these independent events have a mean that is somewhere else makes it more likely that you will not, over timeframes short or long. For independent events, they're always most likely to be closest to the average (which is why the Gaussian distribution's peak is at its mean.) Sure you don't KNOW what the result will be but the mean is always the most likely result*

* for a continuous parameter. When looking at something discrete like coin flips or die rolls or what class you're playing against in your next Hearthstone game, the question is over the next N games how well the resulting distribution approximates the underlying distribution of those discrete possibilities.

So, in my hypothetical where one swaps in Skulking Geist after a few games against Jade Druid, you're still most likely to get a rogue or a priest on the next game. Why? Because Rogue and Priest are best represented on the ladder. You were more likely to get Rogue and Priest before, you just didn't. More games are likely to represent the underlying distribution, just as the earlier games were (even though they didn't turn out that way.)

Yes, you CAN have three more Jade Druid games, but it's unlikely because at 8.52% ladder representation, the chance of that happening on the three successive games is 0.06%. The chance of three games against rogue or priest are 5.2%.

(Using numbers from today's Vicious Syndicate Class/Archetype Distribution here.)

The timeframe where it evens out is unknown though - and definitely not short term. It only evens eventually due to the law of large numbers in statistics. With the emphasis on "large".

EDIT:

For example, a fair coin toss is a Bernoulli trial. When a fair coin is flipped once, the theoretical probability that the outcome will be heads is equal to 1/2. Therefore, according to the law of large numbers, the proportion of heads in a "large" number of coin flips "should be" roughly 1/2. In particular, the proportion of heads after

nflips will almost surely converge to 1/2 asnapproaches infinity.Though the proportion of heads (and tails) approaches 1/2,

almost surely the absolute difference in the number of heads and tails will become large as the number of flips becomes large. That is, the probability that the absolute difference is a small number, approaches zero as the number of flips becomes large. Also, almost surely the ratio of the absolute difference to the number of flips will approach zero. Intuitively, expected absolute difference grows, but at a slower rate than the number of flips, as the number of flips grows.(Bolding mine). From https://en.wikipedia.org/wiki/Law_of_large_numbers

That's all true but nothing I've said conflicts with that.

Edit: To proceed with the coin flip example, let's say that I have had six flips that are all heads. I predict that over the next two flips, my streak will be broken.

That's a reasonable prediction because the chances of one or more tails are 75% and the chance of two more heads is 25%. Furthermore, if one switches the situation to be a streak of six flips that result in tails, the chances that that streak will be broken in two more flips also is 75%.

Even flipping coins over very short horizons like two flips, one can follow up a streak with a prediction of reversion to the mean and be more right than wrong.

You said this:

Which is incorrect. Especially if you consider short timeframes.

Edit: This is relevant to my Jade Druid hypothetical because in that case something unlikely happened, the player swaps something to respond mistaking the unlikely events for a pattern, and the unlikely thing doesn't continue. Then, the player guesses that swapping the card made it stop, when in fact it was just that it was unlikely to begin with.

"Excuse me... You are on fire."

My point is, it's not. Define a streak as two or more results the same. Once one streak ends, the probability that the next one is of the same type is the same: 50% for the coin case.

Unless you are just saying that a streak will come to an end at some point, which is true (and obviously so). EDIT: It seems that is what you are trying to say. In which case I agree.

Well the important thing about tech cards is they are there for when you need them in various matchups, assuming you draw them of course ;) And you should only add them if it significantly improves your winrate against the deck you tech for (so I only run Skulking Geist in my N'Zoth Paladin deck and no others because it is a very slow deck and has no chance against Jade Druid otherwise, other decks have a fighting chance). Only other tech cards I used (apart from various flavours of crabs depending on whether murlocs or pirates are abound) have been Flare in my midrange hunter when burn/freeze mage was everywhere and an Eater of Secrets in my water rogue for the same reason. I certainly never noticed any decrease in numbers of mages faced when I decided to include them (I did notice my win rate improve a lot against them though).

The worgen OTK thread just opened up made me remember how I used to have to add a Sunfury Protector to my resurrect priest deck because it had no taunts otherwise.

No no no. The fallacy here is that you believe something which you mistake to be true and then argue as though it is. You have no way of knowing what code Blizzard is really running here - that code could be doing anything. The only way to argue your case as being actual fact is to have Blizzard open source the matching making code, which would prove beyond doubt that either match making really is random/fair/etc or is somehow rigged/skewed/responsive. If you can see the difference between discussions on coin tosses and other real theoretical random events... and software... then you have to acknowledge the possibility is there and take this more seriously. As a software engineer, in the programs I create, I can control the randomness so that the very next number thats generated is exactly what I want it to be (through something called a seed) - that makes probabilistic analysis a moot point. If I can do these things, so can Blizzard's engineers, and that's just a quick example.

Diablo + Dungeon Master = Dungeons of Castle Madness

It's 100% rigged to some degree. Example, just recently: I made a dragon warrior deck to complete a warrior card quest. First opponent? Dragon warrior, can't remember the last time I'd seen one.

engagement. Engagement is pretty much about how likely a player is to come back and play another game. These engagement goals are listed in that GDC presentation by pointing out that a designer ideal is to "put players into matches that are fun" and a business ideal is to "keep the most amount of players in our game having fun."I am not raising a stupid argument like "I played yesterday with deck A and got deck B against me, thus it is rigged".

My argument and hypothesis is the following: When something really goes overboard in the sense of game balance, before release of the patch it is quite probable that company uses any measure hidden from public to overcome that issue temporarily. For example, when a certain deck is insanely strong, would it not be rational to slightly influence the matchmaking, at least sporadically , for a short time, on certain levels, or certain cases?

Quasi-stellar radio sourceSure, it's in principle possible for them to do something like that, But:

The only way to know for sure whether something like that is going on is to collect statistics (or read the code.)

Diablo + Dungeon Master = Dungeons of Castle Madness

Diablo + Dungeon Master = Dungeons of Castle Madness