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Author Topic: Why does luck in Dominion feel streaky?  (Read 9943 times)

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jaybeez

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Why does luck in Dominion feel streaky?
« on: June 30, 2015, 07:26:35 pm »
+4

I just had a very demoralizing day of Dominion, including having shuffle luck that ranged from below average to comically horrible in about three-quarters of the games I played.  It's frustrating.  And just a few days ago, I beat Marin three times in a row, in large part due to luck (because really, how else would I have pulled that off?  I'm not that good).

And I was just thinking, luck (both good and bad) in Dominion always feels to me like it comes in bunches, and that I have good days and bad days.  After the first 2-3 games I play in a session, if I keep playing it always seems like the luck, good or bad, generally continues for the remainder of the day, only changing the next day, or maybe after I take an extended break.

I know enough about statistics to know that there's no possible way this could actually be true.  But a lot of people I've chatted with while playing say that it seems the same way to them too, that their perception is always that luck seems to come in streaks, and does not seem to follow what you'd expect to be a normal distribution pattern.

Do you feel the same way?  And, why is this true?  What is it about our perception that tricks us into thinking that there's discernible patterns to shuffle luck?
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AdamH

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Re: Why does luck in Dominion feel streaky?
« Reply #1 on: June 30, 2015, 07:32:31 pm »
+11

I know enough about statistics to know that there's no possible way this could actually be true.

What I know about statistics suggests that this kind of stuff happens more often than we think it "should." So speaking from a statistical point of view I don't think you have a mark against this.

their perception is always that luck seems to come in streaks

What is it about our perception that tricks us into thinking that there's discernible patterns to shuffle luck?

Well part of this is probably confirmation bias, but there's something to be said for the idea that when I'm in a good mood I play better, and winning puts me in a good mood. Same thing with bad moods and losing. This may be true for other people too.

Something that helps me (maybe it won't work for you) is to remember that losses are the best way to get better at the game in the long term. If you are dedicated and willing to challenge your own beliefs and think critically, you will benefit more from a bad day than a good day. The downside is that you have less bad days :P
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Re: Why does luck in Dominion feel streaky?
« Reply #2 on: June 30, 2015, 07:35:26 pm »
+6

Well, you make your own shuffle luck so obviously on a bad day you're worse at it than you would on a good day.
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Re: Why does luck in Dominion feel streaky?
« Reply #3 on: June 30, 2015, 11:39:28 pm »
+3

I totally agree with what Adam said.

There is certainly something to be said for playing better when you are clear headed and playing cleanly, and playing badly when you are frustrated, but I would guess that this is mostly influenced by false expectations of what random looks like, and confirmation bias.

This is a pretty good article about randomness.  It is quite long, but there is some good stuff at the beginning if you want something shorter.
What does true randomness look like?

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Re: Why does luck in Dominion feel streaky?
« Reply #4 on: July 01, 2015, 05:47:01 am »
0

The same thing happens in Hearthstone, for what it's worth.  And I agree with Adam, it's definitely correlated with mood.  A few consecutive losses and you get super-frustrated and start to `tilt' towards playing badly.

I think this is why I do better with brand new decks.  I'm not expecting to do well with a new deck-type that I'm just learning, so I don't get frustrated at the odd loss, so I play better.
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Re: Why does luck in Dominion feel streaky?
« Reply #5 on: July 01, 2015, 12:43:06 pm »
+2

That's a good point about the psychological feedback loop.  But I dunno, I guess what I was trying to say is more that, irrespective of how I'm playing, games where I have good shuffle luck and games where I have bad shuffle luck feel like they come in clusters.  I understand that that actually will happen sometimes, in fact it's inevitable.  But it's also inevitable that I'll get games with good shuffle luck interspersed with games with bad shuffle luck, it's just that it never feels like that's what's happening.

I think confirmation bias might be a reasonable explanation for that.  But I guess then my follow-up question is, why does my confirmation bias make me notice the clustered luck, and not the more evenly dispersed luck?  Why am I (why are we?) predisposed to noticing one and not the other?
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Re: Why does luck in Dominion feel streaky?
« Reply #6 on: July 01, 2015, 12:48:44 pm »
+3

Presumably because it doesn't induce a particularly strong emotion.  If you win a bit, lose a bit, you're not feeling anything about that. 
But if you win a lot or lose a lot, you feel either pretty happy or pretty sad/angry.  And we tend to remember things that induced such emotions more easily than things that didn't trigger an emotional response.
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AdamH

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Re: Why does luck in Dominion feel streaky?
« Reply #7 on: July 01, 2015, 12:58:15 pm »
0

But I guess then my follow-up question is, why does my confirmation bias make me notice the clustered luck, and not the more evenly dispersed luck?  Why am I (why are we?) predisposed to noticing one and not the other?

You have exited the area where I have any idea what I'm talking about. Good luck finding your answer :P I'll be interested in seeing it though.

irrespective of how I'm playing, games where I have good shuffle luck and games where I have bad shuffle luck feel like they come in clusters.

*Covers ears with hands* YMYOSL I CAN'T HEAR YOU LALALALALLALA YMYOSL YMYOSL LALALALLALALALALAAAAAAA!!!!!!!


EDIT:

What does true randomness look like?

This article is quite good, BTW. The coin-flip example is exactly what I had in mind when I made my first post in this thread (only it was with zeroes and ones and it was in a cryptography class, but it's the same thing).
« Last Edit: July 01, 2015, 01:00:57 pm by AdamH »
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DG

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Re: Why does luck in Dominion feel streaky?
« Reply #8 on: July 01, 2015, 01:05:37 pm »
+6

A quick google found me this explanation (from a problem gambling site, surprisingly enough).

Quote
People will often judge the coin-tossing sequence of H, H, H, H, H, H as being less random than H, T, H, H, T, H, even though the probability of obtaining each of these given sequences is identical: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.015625. Note that this is the probability of getting a specific sequence compared to the probability of getting a second specific sequence. Kahneman and Tversky (1982) call this tendency the representativeness heuristic. People who make this error are often computing the probability of getting 6 consecutive heads compared to every other possible sequence. Most random sequences of heads and tails do not have an easily recognizable pattern. This tends to reinforce the belief that a sequence of all heads is less likely. However, any one specific arbitrary combination of heads and tails has exactly the same chance of occurring as any other specific combination. Another factor that contributes to this error is that there is only one possible way of getting 6 heads and only one possible way of getting 6 tails, while there are a total of 64 possible ways of tossing six coins, 20 of which produce exactly 50% heads (e.g., H, T, T, T, H, H or H, T, H, H, T, T). This gives the illusion that combinations that “look random,” are more likely, but in fact each one of those specific combinations (e.g., H, T, T, T, H, H) has the same chance of occurring as H, H, H, H, H, H.

Another reason for errors in our understanding of randomness may be confusion between the way the word random is used in everyday speech and the way it is used in statistics and mathematics. According to the Merriam-Webster Online Dictionary, the most common meaning of the adjective random is “lacking a definite plan, purpose, or pattern.”  It also lists “haphazard” as a synonym (www.m-w.com). Judging solely by its appearance, a sequence of 6 heads in a row might appear to have a pattern. Probability theory, however, is concerned with how the events in a sequence are produced, not in how they appear after the fact.

A third reason is the tendency of the human brain toward “selective reporting”—the habit of seizing on certain events as significant, while ignoring the other neighbouring events that would give the chosen events context and help to evaluate how likely or unlikely the perceived pattern really is. Big or salient events will be recalled better. We recall plane crashes because they are highly publicized. Uneventful flights are ignored. Because of the occasional well-publicized plane crash many people are afraid to fly, even though plane crashes are much rarer than car crashes. Kahneman and Tversky (1982) call this tendency the availability heuristic.

A closely related tendency is for people to underestimate the likelihood of repeated numbers, sequences, or rare events occurring by pure chance. The basic problem is that we do not take into account the number of opportunities for something to occur, so we are often surprised when random chance produces coincidences. As an example, in a class of 35 students, we assume that the chance of 2 people sharing a birthday is very small, say 1 in 365, or maybe 35 in 365 (Arnold, 1978). The actual probability that at least two people will share the same birthday is close to 100% because there are actually (35 x 34) / 2 = 595 possible combinations of people in the class. Because the possible combinations of people (595) exceed the number of days in the year (365), the chance that at least 1 pair of people will share a birthday is surprisingly high.

Our minds are predisposed to find patterns, not to discount them. It is argued that we have evolved the ability to detect patterns because to do so was often essential for survival. For example, if a person was walking in the jungle and saw a pattern of light and dark stripes in the shadows, it would be prudent to assume that the pattern was a tiger and act accordingly. The consequences of incorrectly assuming that the pattern is not a tiger far outweigh those of incorrectly assuming that it is. But when applied to random events, this survival “skill” leads to errors.
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Re: Why does luck in Dominion feel streaky?
« Reply #9 on: July 01, 2015, 01:21:51 pm »
+1

While I agree with the whole "when you play better, you're in a better mood; and when you're in a better mood, you play better" thing, this doesn't explain why I feel that 90% of the games in which both my opening buys missed my first shuffle occur either back-to-back or very close to each other.  Luck does come and go in streaks on Goko, and I would love to be convinced otherwise (preferably with actual empirical evidence).
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Haddock

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Re: Why does luck in Dominion feel streaky?
« Reply #10 on: July 01, 2015, 01:28:06 pm »
+2

While I agree with the whole "when you play better, you're in a better mood; and when you're in a better mood, you play better" thing, this doesn't explain why I feel that 90% of the games in which both my opening buys missed my first shuffle occur either back-to-back or very close to each other.  Luck does come and go in streaks on Goko, and I would love to be convinced otherwise (preferably with actual empirical evidence).
There are two different factors at play here.
1) You feel better, you play better.
2) Humans are very bad at recognising true randomness.

If you are setting aside 1) for now, the answer to your story is 2).  True randomness can be expected to produce clustering as you describe - and you remember the times when it happens because it feels weird.  That makes you think it is happening more often than it is.  Moreover, statistics say that such clustering should happen pretty often - much more often than our (misguided) intuition would have us believe.  The combination of confirmation bias and incorrect expectation leads people to think that things aren't random when they are.
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M Town Wins-Losses (6-2, 75%): 71, 72, 76, 81, 83, 87 - 79, 82.  M Scum Wins-Losses (2-1, 67%): 80, 101 - 70.
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AdamH

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Re: Why does luck in Dominion feel streaky?
« Reply #11 on: July 01, 2015, 01:32:08 pm »
+1

While I agree with the whole "when you play better, you're in a better mood; and when you're in a better mood, you play better" thing, this doesn't explain why I feel that 90% of the games in which both my opening buys missed my first shuffle occur either back-to-back or very close to each other.  Luck does come and go in streaks on Goko, and I would love to be convinced otherwise (preferably with actual empirical evidence).

So I think you should think about this differently: the statistics-based arguments here are suggesting that your bolded statement isn't actually true, but you think it is for various reasons. I'd suggest that your statement is the one that needs to be backed up; that you can't shift the burden of proof here.

Think about what you're saying. You're not just saying that the RNG that Goko uses isn't uniform-random (or whatever fair thing is used, sorry if I said the wrong thing) but rather you're suggesting that you get unlucky outcomes more often in streaks than lucky outcomes. First you have to define what lucky and unlucky outcomes are at every single point in the game where RNG becomes a factor -- compute the odds of each of these things (the fact that these are almost never equally likely makes your calculations extremely difficult), then determine if those odds are being represented in a large sample size of games...

Wow, that last sentence is actually extremely complicated, you have to find some heuristic to determine what your "streaks" are and how these outcomes fit into them. You also need to verify that you're not misplaying (which is pretty much impossible to actually do).

My point is, I don't think you just get to say that and have that fly, it's more intellectually honest to start from the (IMO, more reasonable) assumption that the game isn't out to get you some of the time and your BFF the rest of the time and then explain why you feel that way. There have been lots of good reasons for that presented here.

I also think that dwelling on this kind of thing doesn't really make me a better Dominion player, so I find it unlikely that it would work for someone else. But then again, I'm not you so I really couldn't say. :)
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Re: Why does luck in Dominion feel streaky?
« Reply #12 on: July 01, 2015, 01:38:30 pm »
0

A quick google found me this explanation (from a problem gambling site, surprisingly enough).

Quote
People will often judge the coin-tossing sequence of H, H, H, H, H, H as being less random than H, T, H, H, T, H, even though the probability of obtaining each of these given sequences is identical: 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.015625. Note that this is the probability of getting a specific sequence compared to the probability of getting a second specific sequence. Kahneman and Tversky (1982) call this tendency the representativeness heuristic. People who make this error are often computing the probability of getting 6 consecutive heads compared to every other possible sequence. Most random sequences of heads and tails do not have an easily recognizable pattern. This tends to reinforce the belief that a sequence of all heads is less likely. However, any one specific arbitrary combination of heads and tails has exactly the same chance of occurring as any other specific combination. Another factor that contributes to this error is that there is only one possible way of getting 6 heads and only one possible way of getting 6 tails, while there are a total of 64 possible ways of tossing six coins, 20 of which produce exactly 50% heads (e.g., H, T, T, T, H, H or H, T, H, H, T, T). This gives the illusion that combinations that “look random,” are more likely, but in fact each one of those specific combinations (e.g., H, T, T, T, H, H) has the same chance of occurring as H, H, H, H, H, H.

If I'm interpreting this correctly, this is basically claiming that even though

HHHHHHHH HHHHHHHH HHHHHHHH HHHHHHHH

is equally probabilistic as

TTHTTHHT HTHTHHTT THTHHTTH THTHTHTH

we humans for whatever reason feel the latter is more random.  But this is not what jaybeez (and myself) is observing on Goko.  We feel that luck comes and goes in streaks, i.e. we observe a lot of this:

HHHHTHHH HHHHHHHH TTTTTHTT HHHHHHHH HHHHHHHH HHHTHHHH TTTTTTTT TTTHTTTT TTTTHHTT TTTTTTTT TTTTTTTT HHHHTHHH

and not an equal proportion of this:

HTHHTHTH HTHHTHTH THTHTHTH TTHHTHTH THTHTHTH THTHTHTH THHTHTHT HTHTHTHT HTHTHTHT HTHTHTHT THHTHTHT THTHTHTH

where an H is a game win and T is a game loss.  If you assume that wins and losses are based largely upon luck (which might be hearsay to some of you, but lets just assume for simplicity), then the above observation would certainly indicate luck is streaky.
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Mic Qsenoch

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Re: Why does luck in Dominion feel streaky?
« Reply #13 on: July 01, 2015, 01:56:48 pm »
+4

we humans for whatever reason feel the latter is more random.  But this is not what jaybeez (and myself) is observing on Goko.  We feel that luck comes and goes in streaks, i.e. we observe a lot of this:

HHHHTHHH HHHHHHHH TTTTTHTT HHHHHHHH HHHHHHHH HHHTHHHH TTTTTTTT TTTHTTTT TTTTHHTT TTTTTTTT TTTTTTTT HHHHTHHH

and not an equal proportion of this:

HTHHTHTH HTHHTHTH THTHTHTH TTHHTHTH THTHTHTH THTHTHTH THHTHTHT HTHTHTHT HTHTHTHT HTHTHTHT THHTHTHT THTHTHTH

where an H is a game win and T is a game loss.  If you assume that wins and losses are based largely upon luck (which might be hearsay to some of you, but lets just assume for simplicity), then the above observation would certainly indicate luck is streaky.

The argument is that you don't actually observe the streaks more, you just notice them more.
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AdamH

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Re: Why does luck in Dominion feel streaky?
« Reply #14 on: July 01, 2015, 02:13:41 pm »
0

I think you may be operating under the assumption that the game result is determined more by luck than anything else. Ignoring the fact that what you're saying isn't really backed up by any sort of actual "evidence" (I know you made up those sequences for the sake of argument but one of the things that's being said is that this is what you remember and if you looked at all of your games you might not see data that backs up what you're saying you see); this last post assumes that the game outcome only depends on luck.

There are many different ways that luck can enter into a game of Dominion. While some of them can be game-decisive at times, it's silly to think that luck is the only thing that decides a game of Dominion. The tippy-top of the list of these factors includes:

Your skill
your opponent's skill
how good are you at this type of kingdom?
how good is your opponent at this type of kingdom?
How much can luck really impact the outcome of the game? (Is it an Embassy+BM mirror or are you playing a high-skill engine with strong trashing?)
How good are you at capitalizing off of good draws? Recovering from bad draws?
How good is your opponent at that stuff?
Are you really playing all that well? Are you distracted? Feeling outside pressure? What about your opponent?
Have you misplayed at any point? Why? How bad was it? Did you even see it?
Who is playing the best strategy?

It seems to me that attributing one's swings and streaks in game results to luck above all else gets less reasonable when you realize that all of these other things have an impact on the game (and that you can do something about quite a few of them!). Dare I say ymyosl? I mean, this is exactly the attitude that ymyosl means, and I keep on saying it because I've stuck with it and consistently gotten better at the game for three years now.

If you believe you played all of these games optimally and all of this stuff was taken into account and you can look at all of your games and still see those kind of streaks and that those kind of streaks are more than what you'd expect to see from a true random distribution (taking into account your iso rating and the ratings of your oppoenents, I guess?) then maybe we'd look at Goko's RNG?
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Deadlock39

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Re: Why does luck in Dominion feel streaky?
« Reply #15 on: July 01, 2015, 02:28:01 pm »
0

Quote
...

A third reason is the tendency of the human brain toward “selective reporting”—the habit of seizing on certain events as significant, while ignoring the other neighbouring events that would give the chosen events context and help to evaluate how likely or unlikely the perceived pattern really is. Big or salient events will be recalled better. We recall plane crashes because they are highly publicized. Uneventful flights are ignored. Because of the occasional well-publicized plane crash many people are afraid to fly, even though plane crashes are much rarer than car crashes. Kahneman and Tversky (1982) call this tendency the availability heuristic.

This is veering off topic, but this part of the quote DG posted reminded me of an interesting podcast I listened to about the "Psychology of Risk". I recommend listening to it if you find that quote interesting.
David Ropeik: Airplane Disasters and the Psychology of Risk

pubby

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Re: Why does luck in Dominion feel streaky?
« Reply #16 on: July 01, 2015, 03:04:59 pm »
0

You're not just saying that the RNG that Goko uses isn't uniform-random
That reminds me of a stupid, strange, and probably incorrect hunch I have. My theory is that Goko picks the starting player based on some arbitrary timing issue rather than true RNG. Believing this comforts me when having to restart league matches fifty-thousand times.
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Re: Why does luck in Dominion feel streaky?
« Reply #17 on: July 01, 2015, 03:21:34 pm »
+2

You're not just saying that the RNG that Goko uses isn't uniform-random
That reminds me of a stupid, strange, and probably incorrect hunch I have. My theory is that Goko picks the starting player based on some arbitrary timing issue rather than true RNG. Believing this comforts me when having to restart league matches fifty-thousand times.

You could well be correct.
Both goko and MF failed at shuffling:
http://forum.makingfun.com/showthread.php?7064-Shuffle-Bug
So I would not be surprised if they can't flip a coin.
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Mic Qsenoch

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Re: Why does luck in Dominion feel streaky?
« Reply #18 on: July 01, 2015, 03:37:23 pm »
+2

You're not just saying that the RNG that Goko uses isn't uniform-random
That reminds me of a stupid, strange, and probably incorrect hunch I have. My theory is that Goko picks the starting player based on some arbitrary timing issue rather than true RNG. Believing this comforts me when having to restart league matches fifty-thousand times.

You could well be correct.
Both goko and MF failed at shuffling:
http://forum.makingfun.com/showthread.php?7064-Shuffle-Bug
So I would not be surprised if they can't flip a coin.

I could never actually figure out what that guy was saying, and I didn't see anything weird in the log he posted. Did I miss something?
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Re: Why does luck in Dominion feel streaky?
« Reply #19 on: July 01, 2015, 03:40:52 pm »
+7

My theory is that Goko was a social experiment supervised by a big tech company looking to cut costs and interested in exactly how shitty a service you can provide before you start losing the bulk of your userbase. It proved a monstrous success: some faithful customers even took it upon themselves to salvage the product by implementing vital functionality gaps on their own!

While the experiment was concluded well over a year ago, they kept it online as a cheap way to boost morale, for it continues to provide fuel for the biggest running gag the company has ever known. As a testament to this, they renamed the shell company babysitting the thing to "Making Fun".
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Re: Why does luck in Dominion feel streaky?
« Reply #20 on: July 01, 2015, 03:49:30 pm »
+1

Back in the early days of World of Warcraft--late 2005 when we first started actually killing things in raids--there were all sorts of theories about how you could get loot to drop "more randomly."  People suggested that the first letter of the first person to enter the raid was tied to the RNG, or that the name of the raid leader was tied to the RNG, or the date the instance was started, or any number of these things.  This was of course backed up by anecdotes ("Double Netherwind pants have always dropped from Ragnaros whenever [player X] is here, no matter how many mages we have!") and of course apocryphal stories ("In [guild X], they always start the raid on Wednesday, and use a different person to enter each time, and they've gotten full gear for everyone").

And of course everyone was superstitious about it.

This is exactly the same thing.  The human brain, for whatever reason, can understand probability well in the short term, but not in the long term.  This is why casinos and lotteries are still in business.
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DG

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Re: Why does luck in Dominion feel streaky?
« Reply #21 on: July 01, 2015, 03:55:37 pm »
+1

My theory is that Goko was a social experiment supervised by a big tech company looking to cut costs and interested in exactly how shitty a service you can provide before you start losing the bulk of your userbase.

They didn't need to create a social experiment. They could have asked a politician.
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Rabid

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Re: Why does luck in Dominion feel streaky?
« Reply #22 on: July 01, 2015, 05:11:41 pm »
+1

You're not just saying that the RNG that Goko uses isn't uniform-random
That reminds me of a stupid, strange, and probably incorrect hunch I have. My theory is that Goko picks the starting player based on some arbitrary timing issue rather than true RNG. Believing this comforts me when having to restart league matches fifty-thousand times.
You could well be correct.
Both goko and MF failed at shuffling:
http://forum.makingfun.com/showthread.php?7064-Shuffle-Bug
So I would not be surprised if they can't flip a coin.

I could never actually figure out what that guy was saying, and I didn't see anything weird in the log he posted. Did I miss something?
I assumed it was the same bug as last time, without reading properly sorry.
Hard to test this without being able to control the kingdom.
But from the testing I just did I haven't found anything wrong with the shuffler yet.
That will teach me for believing what I read on the internet !
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eHalcyon

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Re: Why does luck in Dominion feel streaky?
« Reply #23 on: July 01, 2015, 05:43:38 pm »
+3

I remember reading articles by game designers where they talk about randomness.  In particular, they gave anecdotes about implementing something random and then having players complain that the game was rigged.  The solution was to actually rig the game by forcing a more uniform distribution.
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Re: Why does luck in Dominion feel streaky?
« Reply #24 on: July 01, 2015, 05:54:51 pm »
+1

I remember reading articles by game designers where they talk about randomness.  In particular, they gave anecdotes about implementing something random and then having players complain that the game was rigged.  The solution was to actually rig the game by forcing a more uniform distribution.
Dota 2 uses psudo-random distributions to reduce the probability of good/bad luck streaks on most of its chance based abilities.
https://www.youtube.com/watch?v=yR7BcWfBCsc
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