Eauix

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18th Dec 2016

20th Dec 2016

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gaussian 20000years impossible game waiting timekiller sparkmaze randomizer long gaussagain

Comments

polobob 20th Dec 2016

If something has a 1 in x chance of happening, if you do it x times, you have a 63% chance of hitting it at least once. So after 18,595 years, at 60 fps, you would have a 63% chance of hitting it at least once.
TheNik 20th Dec 2016

Anyway, every spark has about a chance of 0.0000000000002273737 % to reach the end. The framerate of 60 fps and the fact that one spark is generated every 8 frames means we have 60/8 = 7.5 sparks per second. So if we know that, on average, one out of every 2^42 sparks hit the light, we just have to divide this number by 7.5 to get the number of seconds that pass, on average, until the spark hits the light. This works out to 18-thousand-whatever years.
TheNik 20th Dec 2016

For the actual math you requested... The spark has 1/2 chance to travel left. If we assume it did travel left, it has 1/2 chance to travel left even more. By now, it has only (1/2)^2 = 1/4 chance to be where it is. Three times is (1/2)^3. And so on. 42 times is (1/2)^42 ~ 2.274 * 10^-13. It does not matter if it has to go left or right, it has to take one exact predetermined path, and the probability to hit it exactly with 1/2 a chance to miss every single step is minuscle.
TheNik 20th Dec 2016

Also, I used the framerate to estimate the time required to win this game, it is needed to calculate the number of tries per second.
TheNik 20th Dec 2016

If I understood you correctly, you assume that the spark is equally likely to hit ANY of the outputs. This is NOT so. It hits them in a gaussian distribution, meaning the middle ones are the likeliest to be hit, the outer ones the least likely. This is because to hit the outermost output, the spark has to travel left EVERY time, it cannot go right even one single time. It cannot get back if it does.
SpaceRocket 20th Dec 2016

So it's impossible to calculate the exact probability.
SpaceRocket 20th Dec 2016

Due to pseudorandomness, the probability for a win will be somewhat off, because the random number generator isn't 100% random.
WhiteStork 20th Dec 2016

it is also the same as binary number consisting of 42 ones. (or howmuch ever there are steps i lost count)
WhiteStork 20th Dec 2016

isnt it 1 in 2^42? 1s step is 1/2 if its true 2nd is also 1/2 together 1/2 * 1/2 = 1/4 and so on. length of the side is irrelevant to probability here.
muzau 20th Dec 2016

1 in 82,944. if anyone can prove those odds wrong with actual math I encourage you to do so

The Powder Toy

waiting game by Eauix

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