What does randomness look like? • Hacker News Board

Re: What does randomness look like?

#51

Post by sskates » Sat, Dec 22, 2012, 3:37 AM UTC

baddox wrote: post #44

thurn wrote: post #14

Earlier quoted context omitted.

This is actually an important lesson for game designers. Real randomness is very frustrating for players! Games should be designed to not be random. For example, there's an expansion to The Settlers of Catan that lets you use cards instead of dice to ensure a nice smooth distribution of resources... I think it's a lot more fun!

I was under the impression that a uniform distribution is still considered random, but that there are simply many other random distributions. If you have a flat 1/10 chance of receiving a certain item, then sure, you might do the task 30 times without getting it. But if it were programmed such that you will always receive the item at some point within the first 10 completions of the task (i.e. 10% of players receive…

The distinction is between independent identically distributed random variables, where it's possible to not get the item after 1/p tries, and what you described, which the events are not identically distributed. In the case you describe, the probability you'll get an item when you have a second completion is 1/9, not 1/10.

This is the distinction that the original article highlighted and gives rise to the Poisson distribution, which can have unintuitive results because it is not a uniform distribution. You are describing a uniform distribution. (A Poisson distribution characterizes the number of hits you would expect after running some number of iid random events.)

Re: What does randomness look like?

#52

Post by Steko » Sat, Dec 22, 2012, 3:45 AM UTC

Zenst wrote: post #29

True randomness is a system that say generates a 10 digit number and 11111111 has the same odd's as appearing as the other permutations. But then thats not strictly true as we all know any system that monitors the outcome (a good example will be fruit machines) to make sure there is a even distribution of all permutation will in essence remove that level of definition we like to think as truely random. With that it g…

"hard to truely say what is random or what is a as yet unknown pattern."

No, it's just saying that it's much easier to get pseudorandomness out of a computer than true randomness.

"This is why many have taken the approach of not having a single source of random numbers but use many and average out from there. There again is that random as the chances with such an approach of getting a high or low value would be biased out."

Technically speaking you wouldn't average you'd add them together and take the decimal portion (modulo 1). That can negate bias as long as one of the sources is good even if you don't know which one.

Of course you can remove bias from a single source by Von Neumann's method although this might be computationally harder than the above:

http://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_b...

Re: What does randomness look like?

#53

Post by michaelochurch » Sat, Dec 22, 2012, 3:53 AM UTC

chimeracoder wrote: post #45

michaelochurch wrote: post #36

Earlier quoted context omitted.

Real randomness is very frustrating for players! Games should be designed to not be random. This reminds me of Magic: the Gathering and the misery of mana screw. I disagree with the uniform "should be", because there are so many different design objectives. Slot machines aren't "good games" by Euro standards, but people spend a lot of money on them. (One can argue about whether that's enjoyment or addiction. I'll ski…

> This reminds me of Magic: the Gathering and the misery of mana screw. Incidentally, apparently people complain about the online versions of the game providing a land distribution that's "too even". Also, while mana screw sucks, between the fact that you can decide whether or not to begin with a certain opening hand and the fact that you can design your deck around such circumstances (mana fixing, proper distributio…

Incidentally, apparently people complain about the online versions of the game providing a land distribution that's "too even".

Online bridge has a similar problem. Four riffle shuffles (which does not fully randomize hands) is typical in bridge games, and this means that long suits (and, thus, better hands) are more common. Early online bridge games randomized hands fully and therefore delivered crappier (flatter) hands than people were typically used to.

between the fact that you can decide whether or not to begin with a certain opening hand and the fact that you can design your deck around such circumstances (mana fixing, proper distribution of card costs), it's far more fun than the alternative.

When I played (mid-90s) a lot of those options didn't exist. There weren't mulligans unless you had no land. With one, you had to play it. Also, a lot of the newer mana sources didn't exist. If you drew only 2 lands in your first 10 cards, you were screwed, but you couldn't develop an interesting deck with more than 22 land.

Re: What does randomness look like?

#54

Post by huggah » Sat, Dec 22, 2012, 4:10 AM UTC

baddox wrote: post #48

henrikschroder wrote: post #23

Earlier quoted context omitted.

Oh yes. Our intuition is that random is fair and uniform, but it's absolutely not. I was bit by another random quirk in World of Warcraft. There was a long-running achievement called "What a Strange Long Journey it has Been", which took at least a year in real-time to complete, and you had to actively play during each of the ten or so in-game festivals and holidays, and do some quests and tasks during each. If you mi…

> Oh yes. Our intuition is that random is fair and uniform, but it's absolutely not. But a uniform distribution is random, isn't it? This sort of phrasing is rampant in this thread, and I'm confused by it. How can a uniform distribution be considered non-random, or "less" random than another distribution?

I can't tell if you're trolling or not. In case you aren't, a uniform distribution isn't "uniform" in the sense of the above quotation. You're right that it's not less random, but someone looking at draws from a uniform distribution would normally describe it as "clumpy"; hence the article.

Re: What does randomness look like?

#55

Post by tome » Sat, Dec 22, 2012, 4:28 AM UTC

Strange terminology. In mathematical parlance the arrangement of the glowworms is still described as "random", but the positions of the worms simply are not independent of one another.

Re: What does randomness look like?

#56

Post by bluedanieru » Sat, Dec 22, 2012, 4:31 AM UTC

tome wrote: post #55

Strange terminology. In mathematical parlance the arrangement of the glowworms is still described as "random", but the positions of the worms simply are not independent of one another.

Can you expand on this? I'm curious. It seems to me that with the glowworms, knowing the position of one worm tells you something about the position of every other worm in the sample. If it was truly random, wouldn't it tell you nothing?

Re: What does randomness look like?

#57

Post by tome » Sat, Dec 22, 2012, 4:38 AM UTC

bluedanieru wrote: post #56

tome wrote: post #55

Strange terminology. In mathematical parlance the arrangement of the glowworms is still described as "random", but the positions of the worms simply are not independent of one another.

Can you expand on this? I'm curious. It seems to me that with the glowworms, knowing the position of one worm tells you something about the position of every other worm in the sample. If it was truly random, wouldn't it tell you nothing?

No, in mathematics the eye colour and hair colour of a randomly selected human being are considered random, even though knowing one tells you something about what the other is likely to be. Mathematically, "random" means distributed according to some definite (though perhaps unknown) distribution whereas in common parlance it means something like "not distributed according to anything definite at all" (though it's not clear that this way of defining things is even meaningful).

Re: What does randomness look like?

#58

Post by Laremere » Sat, Dec 22, 2012, 5:03 AM UTC

thurn wrote: post #14

henrikschroder wrote: post #11

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…

This is actually an important lesson for game designers. Real randomness is very frustrating for players! Games should be designed to not be random. For example, there's an expansion to The Settlers of Catan that lets you use cards instead of dice to ensure a nice smooth distribution of resources... I think it's a lot more fun!

I can think of two specific examples where breaking the rules of probability resulted in better player experience: In tf2, you randomly get weapon drops, up to a limit per week. The initial obvious solution was to randomly roll if they get a new weapon every X minutes of gameplay. This lead to players getting long unlucky streaks where they got little to no gameplay. They eventually changed it to when you get a weapon drop, it rolls to see how long you have to play until you get a new weapon. Players can be unlucky still, but it's drastically better.

The other example was in civilization they showed percentage chances of winning a battle. The problem is that when a player would have three battles with say a 50% chance of winning and lost them all, they would get very frustrated. So they changed it to be much more like the average person perceives statistics to be. This means actually weighting the percentages differently from what the player is told so that if a player has a third of a chance to win each of three battles, it's actually very likely they will win one of them.

Re: What does randomness look like?

#59

Post by aatish » Sat, Dec 22, 2012, 5:05 AM UTC

marvin wrote: post #13

Regarding the bomb plot at the very bottom. Examining the number of bombs dropped in each square and comparing it to the Poisson distribution, it appears that the distribution of the bombs is random. But looking at the plot on the map, it appears that the higher incidence of bombs is focused on a specific region. The Poisson distribution doesn't account for the fact that a lot of the squares with a high incidence of…

The responses below are correct - the analysis in the article is about a smaller region of London, that essentially falls inside the large peak in the plot. I wasn't deliberately avoiding this point, it's just that the article was getting long and I wasn't sure how much detail to keep in. I've made a correction to the post to alleviate this confusion. And thanks for pointing this out.

Re: What does randomness look like?

#60

Post by aatish » Sat, Dec 22, 2012, 5:06 AM UTC

tdyo wrote: post #10

This is exactly how they determine species distributions in ecology as well - http://en.wikipedia.org/wiki/Species_distribution Uniform dispersion would suggest some territoriality aspect of the species, and clumped dispersion would suggest a heterogeneity of resources (or any other hypothesis that could then be tested).

Nice! That's a really interesting and relevant example.