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While trying to get 3 stars on the more complex levels (the ones with a lot of destructible entities) I noticed that even after playing the same level over 50 times, doing always the same thing, I've never seen the same final result. Something always goes differently.

Does the same input always result in the same output, or is there a random factor in there?

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How can you be sure the input you're giving is 100% identical? –  user9983 Dec 29 '11 at 16:34
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@Origami: I can't be sure, if I could be I wouldn't have needed to ask here would I =) In any case what makes me suspect that there may be a random factor involved is that the input resolution can't be so high –  Andreas Bonini Dec 29 '11 at 16:37
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Perfect input can be given via emulation of a phone, special programs or, simply, the desktop version of the game with the mouse, as agent86 has done. –  Ben Brocka Dec 29 '11 at 17:47
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Guys, this whole discussion is nonsensical. In IT a program is deterministic if every time you run it, without changing the operating system settings, it always gives the same result. So if the program calls rand() it's not deterministic even if the number is not really random; there is no need to go so deep with the meaning of the word. We'll soon end up in a discussion about the existence of free will if we continue to try to go up the chain –  Andreas Bonini Dec 30 '11 at 3:35
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@AndreasBonini but...you asked the question –  Ben Brocka Dec 30 '11 at 15:30

4 Answers 4

up vote 307 down vote accepted

The algorithm is deterministic, but it's arguable that the overall result of launching a bird is effectively non-deterministic because it relies on (extraordinarily sensitive) user input.

To test the algorithm and the effect user input has on it, I used the following procedure:

  • Load the Google Chrome version of Angry Birds
  • Load level 1-1
  • Pull the mouse back to a specific X-Y coordinate. (This was past the point of "full draw" for the bird.)
  • Release the bird, and wait for the game to reach a steady state.

To measure my X-Y coordinate, I opened a background Chrome window, and navigated it to this page. I aligned the two windows so that I could see the X and Y positions of the mouse while still able to cause something to happen when I released the bird. I aligned my mouse cursor with the lower left hand corner of the box around these two numbers, and then released. I noted the position of my mouse cursor then (as the display only updates when the mouse is not released and the cursor is over that window) and then noted the resulting score in Angry Birds. If you're having issues with exact mouse positioning, you might try an accessibility option offered by your OS, for instance, Mouse Keys on Windows.

I got the same score, so long as my cursor was in the exact same spot as it was on previous iterations.

Prior to coming up with an enhanced test rig that allowed me to measure my cursor's position to the pixel, I ran this experiment about 10 times, using a reference point in the background image of the game. I got scores by firing the first bird that varied between 8,000 and 11,000 points. Using the enhanced testing strategy, if I was off by a single pixel, I could expect score differences of anywhere between 150 and 500 points.

I will note that the cursor was beyond the edge of the game area, outside the browser window, far beyond the maximum distance the bird can be drawn back, and I still noticed differences when moving my cursor even a single pixel.

Further, I took screencaps for an extreme case where my cursor was on a different monitor than the game window, and ran several iterations where I kept my cursor in the same location, or moved it slightly. By my calculations (based on measuring distance from screencaps) the game was able to create a different result (score 32960 vs 31520) based on a one pixel difference in height (544 vs 545 pixels) over a distance of approximately 1,284 pixels of width. This works out to be an angular difference of 0.03 degrees.

I'd say that for any practical purposes, you can expect to employ the same general strategy on the same level repeatedly and expect wildly varying results. The level of sensitivity in the controls is so extreme that there's no practical way to get it to do the same thing twice. This is exacerbated by the fact that if you're playing on a touchscreen, it would be extraordinarily difficult to reproduce the same movements down to the individual pixel.

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One pixel can easily mean a large difference in score. That is not an answer to whether it is deterministic or not; you have to be certain that your input is identical. –  Myrddin Emrys Dec 29 '11 at 16:48
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Even in deterministic scenarios, a miniscule difference in starting state can result in a massive difference in end state. It's called chaos theory. –  StrixVaria Dec 29 '11 at 16:58
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@MyrddinEmrys, as I mentioned I was planning to do, I re-ran the experiment with down to the pixel accuracy. I found that the damage done was the same, if I was that precise. I'd say for any practical purposes of playing the game, the controls are so exact that you can expect the final behavior of the system to be effectively non-deterministic for any "normal" human input usage scenario. The game itself is deterministic though. –  agent86 Dec 29 '11 at 17:04
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+1 for using science! –  jadarnel27 Dec 29 '11 at 19:19
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Angry Birds: a millimeter game on a centimeter device. Maddening. –  splattered bits Dec 29 '11 at 20:31

Some levels are subject to random explosions shortly after the level starts, and some bricks can fall on their own before you've ever thrown a bird. These events occur rarely but by the time you've three-starred every level in every game you'll probably have seen it a few times, as I have.

I would expect that this occurs because of timing issues, possibly related to threading. I'm quite sure that if you did a test where you loaded every level a dozen times and waited thirty seconds you'd end up with a non-zero score at least once. In light of Pubby's answer I can only assume that the Angry Birds app does not always provide the same input to the Box2D functions at the start of a level.

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Angry Birds uses Box2D library for physics.

Is Box2D deterministic? For the same input, and same binary, Box2D will reproduce any simulation. Box2D does not use any random numbers nor base any computation on random events (such as timers, etc).

However, people often want more stringent determinism. People often want to know if Box2D can produce identical results on different binaries and on different platforms. The answer is no. The reason for this answer has to do with how floating point math is implemented in many compilers and processors. I recommend reading this article if you are curious: http://www.yosefk.com/blog/consistency-how-to-defeat-the-purpose-of-ieee-floating-point.html

http://code.google.com/p/box2d/wiki/FAQ#Determinism

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This is great (thanks for actually checking with the source); for the sake of completeness, do you have a reference that Angry Birds uses Box2D? And where did you pull this quote from? –  user3389 Dec 29 '11 at 20:56
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@MarkTrapp geek.com/articles/mobile/… and en.wikipedia.org/wiki/Box2D –  Royal Flush Dec 29 '11 at 21:06
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And I bet physics FPS varies as well, due to numerous factors (not enough CPU, overheating, page faults, etc), thus affecting the 'accuracy' of the simulation. :) –  muntoo Dec 30 '11 at 1:35
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@agent86 I would change your wording to "[...]but per-platform and per-Box2D release each simulation will run the same way each time." (that "same binary" part in the first paragraph seems to indicate that). –  João Portela Dec 30 '11 at 18:38
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@Jake Yes, it is deterministic but with the limitations mentioned in the second paragraph. –  Pubby May 13 '12 at 5:25

I did 10 tests, pulling to the same point every time (also Chrome Angry Birds, level 1, as in agent86's tests).

Red Crosshair of test spot

I never received the same score twice, despite being careful to pull to the exact same spot, and doing it about as soon after start of level. I believe Angry Birds is very much not deterministic.

This is rather easy to explain: it was designed to work on small touch screens. If it was deterministic, users could easily repeat moves due to the limited precision of the input device. This could be bad, in that their device could literally not have the precision necessary to aim at the exact angle and power they want. By having it slightly jiggle the results, and owing to the input of a 'finger', users would not notice the lack of precision, and they would also not be frustrated by never being able to make a desired shot.

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agent86's additional test indicates I could well be wrong. I will re-test when I get home, because I was quite certain that I had been placing my cursor with precision. –  Myrddin Emrys Dec 29 '11 at 17:12
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I think you're wrong. The touch screen actually makes it extremely hard to get the same input each time. For example, the iphone has 614400 pixels. Each of those would produce a differing output. –  Daenyth Dec 29 '11 at 18:16
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@Daenyth not necessarily each of them. Once you're beyond the maximum distance, there may be a set of pixels at the same angle from the center that could reasonably be assumed to cause identical –  Random832 Dec 29 '11 at 22:02
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@AndreasBonini, Further testing seems to indicate that it's so precise that a single pixel can cause differences in the results, even over crazy distances - see the latest edits to my answer. –  agent86 Dec 31 '11 at 1:29
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This is an example of chaos (tiny changes in input leading to huge changed in outcome) rather than non determinism –  Richard Tingle Jan 27 at 13:38

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