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IIAOPSW t1_j9irsvq wrote

Reply to comment by BunLife in 2 Teens’ Deaths Underscore Dangers of ‘Subway Surfing’ by thenewyorktimes

It makes perfect sense. Suppose each time he surfs there's a 1% chance of fucking up and dying. If he surfs every day, the probability of making it to his next birthday is (1-.01)^365 (about 2.5%). If he only surfs every other week, then his chances exponentially improve to (1-.01)^26 (about 7.7%). If he only does it once a year, as a treat, for old times sake, he his probability of making it to his next birthday is 99%.

Put another way, if you decide to only play Russian roulette every other week rather than every day, you have in fact drastically reduced the odds that you will die playing Russian roulette. From the outside you might say playing it at all is stupid, but you can't objectively reach that conclusion without knowing how much value they get out of it and how strongly they value their lives. The decision to play might be totally rational with respect to what they want and what they are willing to risk to get it, even if it seems insane to you.

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Lalalama t1_j9j2j8u wrote

Yeah but if you do it everyday you get better at it. Say you remember the dangerous points etc. if you stop, you might forget thrmc

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IIAOPSW t1_j9j4ovk wrote

Yes. I implicitly assumed events were uncorrelated to make the math simple to understand and simple to explain. Its a sketch not a photograph. What you're describing is an optimization problem wherein the chance of failure P is some function of the trials per time frame n. So if you're doing it n times per week then the probability of not dying in a given week is (1-p(n))^n . The obvious question to ask is what is p(n)? Well we know some properties it must have. It has to only be decreasing in n (it shouldn't be possible to get worse with more experience). It has to have a diminishing return and eventually stop getting smaller with n (you can't get better than 0% chance of failure). It has to be smooth (your skill doesn't change in sudden discrete jumps). The obvious candidate distribution for this is exponential decay. e^{-rn} * (p_0 - p_inf) + p_inf where p_0 is the absolute worst no-practice value p(0) and p_inf is the is the absolute best attainable value. r is just some constant that determines how quickly the practice pays off. Now based on the assumptions so far the probability of dying in a given time frame becomes (1-e^{-rn} * (p_0 - p_inf) - p_inf)^n. The last step is to just take the derivative with respect to n and set it to 0. I'm tired so exercise for the reader yada yada.

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