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How can I predict Math.random results?

How can I predict the results from a roulette gaming website csgopolygon.com, given that it is calling Math.random and Math.floor?

Your hunch that it is, in theory, possible to predict the results of Math.random is correct. This is why, if you ever want to build a gaming/gambling application, you should make sure to use a cryptographically secure pseudo-random number generator. If they are using such, then forget about it.
If however you are correct and they are using System.time as the seed to the standard Random generator that comes with Java, there might be a way. It would involve generating millions of numbers sequences with millions of numbers in each sequence, based on seeds corresponding to (future) timestamps, then observing the actual random numbers generated by the website and trying to find the specific sequence among the millions you generated beforehand. If you have a match, you found the seed. And if you have the seed and know where in the sequence they are, you could then theoretically predict the next numbers.
Problems with this approach:
You need to know the exact algorithm they are using, so you can make sure you are using the same
It would take huge amounts of processing power to generate all the sequences
It would take huge amounts of storage to store them
It would take huge amounts of processing power to search the observed sequence among the stored sequences
You don't have the full picture. Even if you found the right seed and position in that seed's sequence, you still need to predict the next number that you will get, but as it's a multiplayer site (I assume), they might be giving that number to another player.
In other answers it is said that predicting the results of Math.random is impossible. This is incorrect. Math.random is actually very predictable, once you know the seed and the iteration (how many numbers were generated since the seed was set). I actually once built a game that generated random levels. I was messing with the seed and found that if I always set the same seed, I would always get the same levels. Which was cool because my game had infinite levels, but level 27 (for example) always looked exactly the same.
However,
They are not using Java. Check out the 'Provably Fair' link at the top. They discuss how you can verify past rolls yourself by executing PHP code.
These guys are smart. They are publishing the old seeds once they dismiss it. This allows you (using the predictable behavior of pseudo-random number generators) to re-generate all rolls and verify that they never tampered with them.
Basically, you want to find the seed that is currently in use... However, point 5 I mentioned above still holds: you don't have the full picture, so how would you predict what roll you would be getting? Apart from that, finding the seed will prove near impossible. These guys know cryptography, so you can bet they are using a secure random number generator.

You can't, and you probably shouldn't develop a gambling addiction as a 16-year-old. That said, even if you could, that site isn't using JavaScript to generate a number, but a server-side language like PHP or ASP.NET.

How to smooth/reduce/filter large amounts of sensor data?

I'm building a visualization for some industrial devices that produce large amounts of time-based data like temperatures, currents or voltages. All data is constantly written to a SQL Server database (can't control that part).
The HTML5 frontend consists of an interactive zoomable chart I made with d3.js. Data series can be added(loaded) to the chart on demand, in which case the frontend sends an ajax request, ASP.NET MVC and EF6 fetches the values from the DB and returns them as Json.
Each data element simply consists of a DateTime and a value. Please note that the values do not get written in regular intervals (like every 2 seconds or so), but in irregular intervals. This is because the device doesn't get polled regularly but sends data on specific events, like a raise/drop of a temperature by a given change of 0.1 °C, for example.
So far everything works really well and smooth, but the large amount of data becomes a problem. For example, when I want to show a line chart for a selected period of lets say 3 month, each data series already consists of appr. 500.000 values, so the Json response from the server also gets bigger and bigger and the request takes longer with growing time periods.
So I am looking for a way to reduce the amount of data without losing relevant information, such as peaks in temperature curves etc., but at the same time I want to smoothen out the noise in the signal.
Here's an example, please keep in mind that this is just a chosen period of some hours or days, usually the user would like to see data for several months or even years as well:
The green lines are temperatures, the red bars are representations of digital states (in this case a heater that makes one of the temp curves go up).
You can clearly see the noise in the signals, this is what I want to get rid of. At the same time, I want to keep characteristic features like the ones after the heater turns on and the temperature strongly rises and falls.
I already tried chopping the raw data into blocks of a given length and then aggregating the data in them, so that I have a min, max and average for that interval. This works, but by doing so I the characteristic features of the curve get lost and everything gets kind of flattened or averaged. Here's a picture of the same period as above zoomed out a bit, so that the aggregating kicks in:
The average of the upper series is shown as the green line, the extent (min/max) of each chop is represented by the green area around the average line.
Is there some kind of fancy algorithm that I can use to filter/smoothen/reduce my data right when it comes out of the DB and before it gets send to the frontend? What are the buzzwords here that I need to dig after? Any specific libraries, frameworks or techniques are highly appreciated, as well as general comments on this topic. I'm interested primarily in server-side solutions, but please feel free to mention client-side Javascript solutions as well as they might surely be of interest for other people facing the same problem.

"Is there some kind of fancy algorithm that I can use to filter/smoothen/reduce my data right when it comes out of the DB and before it gets send to the frontend? What are the buzzwords here that I need to dig after?"
I've asked a friend at the University where I work and she says Fourier Transforms can probably be used... but that looks like Dutch to me :)
Edit: looking at it a bit more myself, and because your data is time sampled, I'm guessing you'll be interested in Discrete Time Fourier Transforms
Further searching around this topic led me here - and that, to my (admittedly unexpert) eyes, looks like something that's useful...
Further Edit:
So, that link makes me think that you should be able to remove (for example) every second sample on the server-side: then on the client-side, you can use the interpolation technique described in that link (using the inverse fourier transform) to effectively "restore" the missing points on the client-side: you've transferred half of the points and yet the resulting graph will be exactly the same because on the client you've interpolated the missing samples.... or is that way off base? :)

Is it possible to sum a huge amount of numbers in parallel using the GPU in a browser?

Suppose I have the task of summing 1048576 numbers. Suppose I can also ignore the time involved sending those numbers to the GPU (they don't need to - they can be derived from a simple mathematical formula). Is it possible to sum all those numbers in parallel there?
My attempt: I was going to go with an usual parallel reduction, making the texture 1/4 of its size on each pass, so I'd need log(N) passes. The problem I am having is that a texture holds Vec4<byte> values. I am interested in float values! There is an extension to write Vec4<float> values, but it doesn't allow reading them back, and they are still Vec4s!
Does anyone have a solution for that problem? Considering the tricky nature of WebGL, a minimal code demo would be very helpful.

You may use Web Worker for doing your calculation in another thread in parallel.
Please see this for more details:
https://developer.mozilla.org/en-US/docs/Web/Guide/Performance/Using_web_workers

Are you looking at using WebGL because you need a mobile solution ? There are many limitations in having compute with WebGL. Have you looked at WebCL instead.
If you still want to pursue WebGL, you can take a look at encoding threads like below:
How do I convert a vec4 rgba value to a float?

What are the best practices for making online high score lists in JavaScript based games? [closed]

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[I know there have been similar questions about preventing cheating on high score lists, but no answer didn't really help me for JavaScript based games, so please try to think about my question, before telling me about similar posts. I ask about best practices because the JavaScript is always visible for the user and therefore it is not possible to prevent cheating completly, I just want to make it harder.]
I'm developing a JavaScript based game that works in the browser. I want to make a high score list that contains the user name and the score of all users. To achieve that the browser sends the username and the score to my server (via AJAX).
Submitting fake scores to this list would be fairly easy: One could take a look at the AJAX requests and then make an own AJAX request with a faked score. Using something like a token that has to be send with the other data is pointless, as it will be easy to discover.
My only approach, that would prevent cheating, would be to send a description of every user action to the server and calculate the score there. But this is not really practicable as it would be too much for the server.
I accepted an answer, but in case anyone has other ideas about how to make cheating harder, please create another answer!

I like to play cheat the cheater - something like using a token to authenticate the score that changes every time the update is called... but I accept the cheat score that gets posted using a duplicate token. Then I display that cheat score to only the cheater, so it appears that it worked, but now the cheater is seeing his results in a sandbox.

You pretty much answered your own question. If you want to really make it harder for users to cheat, send game log to the server, where you'll calculate the score.
You don't have to send all the events, just ones that affect result score.
There are some techniques, though, that may help you:
include signature in your request. Something like MD5(secret_key + params). Although, "secret key" will have to be in JS source, it will effectively protect you from simple request interception (see Tamper Data and Charles)
if it's a multiplayer game, accept scores calculated by clients and compare them. Cheaters will be pretty visible (assuming that the majority of users are honest).
you can set a score cap, an "unreachable" result. Everyone who posts score higher than this is a cheater. For example, speed typing game: no one can type correct text at 1500 chars/minute, even 700 is pretty damn hard (though achievable).

On score submit:
Request some token from the server, this should be time based and only valid for about 2 seconds
Only accept submits that include a valid hash of this token, some salt and the score.
This prevents manual tampering with the request as it would timeout the score. If you want to account for high-latency give it a little more time until the timeout.
The hashing function:
Scramble the hashing function inside packed code (http://dean.edwards.name/packer/ really produces nasty to read code) if you use jQuery or some other library just drop the hashing functionality inside the library file and it gets pretty bad to find, escpecially if you use a function name like "h" :)
Handling the score-variable itself:
Well everybody with a debugging console can change the variable on runtime when doing this but if you encapsulate your whole Javascript inside a function and call it nothing is in the global namespace and it's much harder to get to the variables:
(function() {
//your js code here
})();

I have had lots of thoughts about it and, eventually, decided to only have local individual highscores, so cheating is not really beneficial for player and not harmful to others. Yet my game is just a simple minesweeper, and there were people who complained about the lack of competitive table.
Option 2, is approach taken by WebSudoku - to show your place "among the people of internet". So you will not see any other results, and people wont see your results - but you can compare yourself to crowd.
p.s: And seriously - any kid with Firebug/WebInspector can easily hack your JS game and, eventually, to be able to reach very high score.

If you are relying on the client to send the final score to the server, then there is no way (afaik) to prevent a genius from cheating. But I think you might be able to prevent stupid people (and honest people) from cheating, so that only geniuses and their friends will dominate your leaderboards.
There are two ways I can think of
1.) "security through obscurity."
Come up with an algorithm that transforms simple scores into something else (and to transform them back). Then obfuscate it. Complicate it. Write a function that multiplies it by q and divides it by ralph. Apply a bunch of functions to it, and among the 5-15 functions that do random stuff to it, include one that multiplies the number by 19 ( a prime number ). On your server, check to make sure every incoming number (or letter) is divisible by 19, and decode
You have to write a bunch of complex code that transforms simple scores into something crazy-looking. You have to write a series of functions in the least-efficient, most spaghetti-code fashion possible. Use
One thing you cold do is to have a set of disallowed values. I.e., perhaps all points awarded are even. If anyone tries to submit an odd number, they are obviously cheating (and very stupid).
2.) time
You should be able to know when the user started the game. You should have a session started and record when they requested the page. Then you should also be able to tell when they submitted their score. And you should also know what the time series is for max points. I.e. can you get 5 points per minute, 100 per minute, minute^3, etc... If user submits more points than are possible during that time, they are cheating.
You could also strike a balance between server and client processing and make the client should send progress update every x minutes by ajax. And if it fails to report, you assume it's been compromised (much like in Bond movies, when he's infiltrating the enemy's lair and he snaps some guard's neck. When the guard doesn't respond to his next 10-minutely check-in, the alarms will go off).
If you've ever played Zynga Poker, you've probably seen what happens when someone at the table has a slow internet connection.

Depending on the nature of the game, you could use other players to verify the results. In simple games this works great, on others you have to be clever and develop many aspects around this feature. E.g. sometimes is possible to replay and verify results based on logged actions. This trick works specially well for Human versus AI, as long as the model is deterministic.
Another option is redefining the score concept to be more user-centric, this is pretty easy to implement, but tends to be hard to devise, and only applies to a few categories of games.
Purely speculative approaches are also possible, it's sometimes pretty easy to know when some parameters don't fit. It would not avoid cheating, but would moderate it a lot.
The most complicated part is getting a small enough replay log, but since most data isn't random (except for player actions, which, actually aren't that random because depend on the game) it's essentially a matter of getting the design right.
Also, if gameplay is extended enough, for action games and the like you can get a lot of compression from doing some approximation, merging (e.g. motion vectors), and clipping uninteresting stuff.

Ideally you would send your entire event log to the server for checking. Perhaps you can implement a heuristic so you can easily determine if the score is within a set of bounds. For instance, if the total game time is 5 seconds you might expect a much lower score than with a much longer game time.
Alternatively, you could choose to manually check the event log for really high scores (the overall top-X, which should be fairly stable).
You will need a seeded random number generator if you're doing anything with randomness (like random events). Which might be tricky if you hadn't already thought of it.
You can find many more resources but it really just boils down to server-side checking. JavaScript is not unique in this, but likely easiest to exploit because you not only see the client-server communication but also the client-side source code!
HTML5 Multiplayer Game Security Solutions
http://lanyrd.com/2011/jsconf/sfggb/
Games like Starcraft only record the mouse clicks and key presses. The actual commands are then simulated. I expect 'Worms Armageddon' to do something similar but their random events (like the bounciness of bananas) aren't seeded properly so in the instant replay you might get a different result.
You could imagine something similar for MMORPGs. The server calculates your position based on the keypresses, the client merely tries to give a good early interpretation but you may warp around when you're lagging because the server will place you elsewhere on the map because it didn't get the keypress events timely.
If you attack something, the server will check if you're close enough and how much damage you can expect to deal with current stats and equipment.

Record key points in game, then score is submitted with these key points. When people look high scores, they can also see overview of played game, if it looks like it is impossible to play like that without cheating, then people can report these suspicious scores to admins.

I used a system using a time based request having 3 parameters
req number, curr time, score
The req number is returned from server in the response to the update score request , each time this is a new random value.
The curr time is calculated not from computer clock but from start of game and is synced with server using an ajax request.
Update score request is sent after short intervals (around 30 sec max).
Following checks are applied on the server
Time is within 10 seconds range from the server clock.
there has been not more than 40 seconds since the req number was sent.
the score change sent after 30 seconds is possible (within 2 x humanly possible range)
Score is updated only if the above checks are passed or the user gets a disconnection message :(
This is simpler than most methods and works out to eliminate all casual hackers (well, unless they read this and want to go to the trouble of updating score quickly or making a script of their own).

If not cheating is more important than the game itself, try to construct and present your game in a way that it looks like finding the solution to a math problem. So the server will give an instance of the problem to the client (example A: a chess board about to be won in 3 moves, example B: a geometry dash randomly generated level) and the user will have to solve it and post back a solution (example A: the winning moves, example b: the exact timestamps and intensity of jumps to avoid obstacles)
With this approach, it is key that the server doesn't send the same level twice, or else the cheater can plan and "design" his solution in advance. Also, the game information must be randomly generated in the server and not sent via seed, or else the cheater can fake the seed and design his solution with time.
The given time for valid submissions must be also tracked in the server so that they will only have "playing" time and no "designing" time. If the cheater is good enough to design a solution as fast as honest players can win the game, then they are talented enough to win the game honestly and deserve their points.
Back in the server, you will need to check that the submitted solution is valid for that instance.
Of course this approach requires lots of extra work: More instances of games (ideally infinite and non repeating), server side generation, server side validation of submissions, time caps, etc.
Note: I know these approach was already suggested in multiple solutions some years ago, I wanted to add my humble contribution.

What is the space efficiency of a directed acyclic word graph (dawg)? and is there a javascript implementation?

I have a dictionary of keywords that I want to make available for autocomplete/suggestion on the client side of a web application. The ajax turnaround introduces too much latency, so it would nice to store the entire word list on the client.
The list could be hundreds of thousands of words, maybe a couple of million. I did a little bit of research, and it seams that a dawg structure would provide space and lookup efficiency, but I can't find real world numbers.
Also, feel free to suggest other possibilities for achieving the same functionality.

I have recently implemented DAWG for a wordgame playing program. It uses a dictionary consisting of 2,7 million words from Polish language. Source plain text file is about 33MB in size. The same word list represented as DAWG in binary file takes only 5MB. Actual size may vary, as it depends on implementation, so number of vertices - 154k and number of edges - 411k are more important figures.
Still, that amount of data is far too big to handle by JavaScript, as stated above. Trying to process several MB of data will hang JavaScript interpreter for a few minutes, effectively hanging whole browser.

My mind cringes at the two facts "couple of million" and "JavaScript". JS is meant to shuffle little pieces of data around, not megabytes. Just imagine how long users would have to wait for your page to load!
There must be a reason why AJAX turnaround is so slow in your case. Google serves billion of AJAX requests every day and their type ahead is snappy (just try it on www.google.com). So there must be something broken in your setup. Find it and fix it.

Your solution sounds practical, but you still might want to look at, for example, jQuery's autocomplete implementation(s) to see how they deal with latency.

A couple of million words in memory (in JavaScript in a Browser)? That sounds big regardless of what kind of structure you decide to store it in. Your might consider other kinds of optimizations instead, like loading subsets of your wordlist based on the characters typed.
For example, if the user enters "a" then you'd start retrieving all the words that start with "a". Then you could optimize your wordlist by returning more common words first, so the more likely ones will match up "instantly" while less common words may load a little slower.

from my undestanding, DAWGs are good for storing and searching for words, but not when you need to generate lists of matches. Once you located the prefix, you will have to browser thru all its children to reconstruct the words which start with this prefix.
I agree with others, you should consider server-side search.