101–110 of 123 posts
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I can give you one simple argument. Ten items shuffled have 10! entropy, while ten independent rolls have 10^10 entropy. How is that not far less random?
Because amount of entropy has nothing to do with "amount of randomness."
You can try it out yourself in your browser. This scriptlet generates random and non-random dot distributions side by side (refreshing regenerates, at least in Firefox 17): javascript:" foo foo var canvas = document.getElementById('tutorial');var ctx = canvas.getContext('2d');ctx.fillStyle = \"rgb(000,0,0)\";for (var i=0;i var canvas = document.getElementById('tutorial2');var ctx = canvas.getContext('2d');ctx.fillSty…
Here’s a web page displaying those dot distributions plus a more readable version of that code: http://bl.ocks.org/4358325 .
Were the bombs actually mostly random?
No, they were aimed but it was a matter of trial and error. To get the data about where they'd landed, some had radio transmitters. They sent a message back to armourers in France (I assume some were deliberately non-explosive). Meanwhile German agents in England were also observing the success or failure of the V2s, and in particular where they'd landed. However, in an effort to deceive the Germans, the British star…
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!
Wesnoth is a good example of a game which is frustrating for many people. I think the reason is that it has random outcomes of decisions. Suppose you order a unit to attack another one. There's a base 0.6 chance to hit. The unit has 3 attacks each dealing 12 damage. What is the expected damage output ?
- 0 damage: ~ 6%
- 12 damage: ~ 28%
- 24 damage: ~ 43%
- 36 damage: ~ 21%
Counterexamples: Neuroshima Hex (board game), Seasons (board game), Mission in Space: Lost Colony (flash game). In all of these games randomness is used to improve variety. In MIS there's actually little randomness and it feels more like a puzzle. The most visible effect of randomness in the game is randomly chosen alien spawned. All 3 aliens have the same HP and movement speed, so it's not a big deal. Seasons is a card and dice game, but an unusual one. Each side of dice gives some options to choose and there are no good or bad sides, there only good or bad sides at this very moment. The cards you start with are not really random either, because the game uses draft mechanic: you take one card from your hand and pass your hand to your neighbor on the left. Neuroshima Hex is essentially a game with hexagonal cards. Randomness only determines what cards you draw, and once you do you place the hex-cards on the board. Once the battle resolves, it's deterministic.
The bottom line: I noticed that I much more enjoy games where randomness is used not to determine success/failure, but instead options available. That is, as long as the options are balanced relative to each other. Heroes of Might and Magic 3 has randomly selected spells and skills at levelup, but they range from awesome to pathetic. The result is frustration.
All of the games I mentioned (Except Heroes 3) are free. You can actually play both board games online, too.
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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…
Have you actually tried the alternatives ? There's a trivial variant of M:tG where you can play any card face down to act as a land.
You have a point, though - constructing a deck in M:tG is far more fun than playing one.
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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…
So, I did a quick bit of math. You can pull one piece every hour for two weeks, but sleeping, not playing, missing days etc, meant that I effectively pulled ~100 pieces. The chance of missing a certain piece is 7/8, so missing a certain piece 100 times in a row is (7/8)^100, which is roughly a little bit more than one in a million. The chance of failure would be 8 times that much because there are 8 pieces you could…
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!
This is a gross oversimplification. Randomness in games is like a knife. It can be used to make nice things, or to hurt. Wesnoth is a good example of a game which is frustrating for many people. I think the reason is that it has random outcomes of decisions. Suppose you order a unit to attack another one. There's a base 0.6 chance to hit. The unit has 3 attacks each dealing 12 damage. What is the expected damage outp…
Another classic example of this randomness-pain is earlier versions of the Civ series, where you could lose tanks against pikemen or other ancient unit types. Not likely, but it hurt when it happened.
So for all you entrepreneurs, if you fail, don't fall into a depression. Sure you worked just as hard as everyone else, maybe even harder. And yeah it's annoying to see others surpass you even though you've got everything they do. But that's life, you just got a bad batch of rolls.
Here's a weird thing about randomness that has always bothered me: In quantum mechanics, if you measure two incompatible observables (like position and momentum) of a system, and then repeat that experiment many times, you will get two lists of real numbers. QM says you can predict the distribution of these numbers, but you cannot predict the individual numbers themselves. The popular way of thinking nowadays is that…
how do you expect to implement the "as-yet-undiscovered pseudorandom number generator" without any state ("hidden variables")?
However, it is well known that any QM system can be simulated using a classical computer, with the penalty of exponential slowdown. Let's say that I have a hypothetical, ultra-powerful classical computer and I want to simulate a gigantic system of particles including aggregates of particles (e.g. people) performing measurements of other particles. When it comes time to determine the particular values for these measurements, I must generate a random number from a Gaussian distribution. So I use something like the Mersenne Twister. From the perspective of the simulated people, their observations would entirely match our own observations in studying a quantum system.
tl,dr: state isn't necessarily a one particle concept or a local concept. Individual particles have their own properties (spin, charge, etc.) and then maybe a collection of a million particles also has unique properties.
But my proposal is basically superdeterminism, which -- while being a loophole that has yet to be ruled out -- is unpopular. Since I'm not sure why, I guess I would need to get a degree in theoretical physics to find out.
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> 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…
I think you're committing a Texas Sharpshooter Fallacy. Yes, people are designing their decks around mana screw. In other words - they discard all those decks ideas that suffer more from randomness. Also remember mana screw works both ways. Later in the game getting a streak of lands when you no longer need them can be disastrous. Your opponent can draw juicy cards instead. Have you actually tried the alternatives ?…
That's not really eliminating randomness, since you're just evaluating (at runtime) whether or not a given card is more valuable as a mana source or at face value. There's still some randomness in determining how high the opportunity cost of playing a land is.
A better example of nonrandomness - which I have considered playing with my friends - is enforcing an even mana draw by increasing access to mana each turn in a manner proportional to the number of lands in the deck. That's deterministic.
> You have a point, though - constructing a deck in M:tG is far more fun than playing one.
I've been playing Magic: The Gathering for far longer than I should admit, and I'd disagree.