Mei Guan Xi（没关系）

My friend got his bike stolen on Friday night. Already on his 3rd bike, this one had a lifespan of only 5 months. Not uncommon though because according to this report (in chinese) 95% of shanghainese bikers have had at least 1 bike stolen, 50% 3 bikes, 34% 4 bikes! Plus, there are over 470 million bikes in China, so that’s a lot of stolen bikes. So it’s not exactly uncommon….

But incredibly enough, as he was walking around the next day pondering whether he wanted to plunk down the dough for yet ANOTHER bike, he saw someone riding around on his LAST stolen bike! The girl probably was not the thief, but likely purchased it knowing that it was stolen - so all it took was a threat to call the police for the girl to give up the bike.

So it got me thinking, what are the chances of this really happening? It’s it like winning the superlotto or like the local pick 3?

To take a stab at figuring this out, I first had to figure out the bike recovery rate in Shanghai. Unfortunately, I couldn’t find any official reports, but I did find that it’s 2% in New York City. Given how this article (in chinese) mentions that people don’t seem to get their bikes back, coupled with the sheer volume of bikes and adding a grain of corruption, I think even 1 in 500 is optimistic. But let’s go with that.

Now that we have some idea about the likelihood of him getting his bike back, what are the chances that he gets it EXACTLY 5 months after he lost his bike? I assumed that getting your bike back is a power law distribution. It intuitively make sense to me, meaning that if you’re going to get your bike back, you’d likely get it sooner than later. So using the zipf power law distribution, the chances of getting his bike back before day 150 (5 months) is about 99.33333% (1-1/150).

But what’s remarkable is that he got it back on day 150 and not day 151 or any day after. So to figure that out, you take (P(get bike back within 151 days) - P(get bike back within 150 days) which is 0.993377 - 0.993333 = 0.0000442. This just means that there is a 0.00442% chance that he gets it back exactly on day 150.

So now that we have both probabilities we can just multiply them together to see what the chances were for him to get his bike back AND exactly on day 150. This turns out to be (1/500)*(0.0000442)= .0000000882 which is about 1 in 10 million. Plus, I am ignoring that he got his bike stolen on day 149…but seeing as how common it is for a shiny bike…I’ll ignore it. haha

Clearly, it’s a rough estimate, but clearly it’s not exactly winning the powerball (1 in 146 million) but sure beats your state Pick 4 (1 in 10,000). Unfortunately for my friend, his prize wasn’t commensurate with the odds. doh!

上个周末我的朋友的自行车又被盗了，这次不多于五个月就没了。 我搜了一下，看起来这个问题是蛮普及的，据报道，95%上海市民至少1辆以上被偷过。50%三辆以上，34%四辆以上！ 在中国有4.7亿辆，多少赃车呀？

可是最巧的是，第二天他在犹豫是否要买新一辆车时在路上发现了一个女孩子骑着他上一辆被盗的自行车！把她揽下来之后，说了要报110，她就把车还给我朋友了。

那么我突然想起，怎么那么巧？这个巧合的概率实际上有多小？

我也不太清楚但是有一点好奇怎么去估？首先，可以看看找回来的概率。我在网上搜不到，但是参考了纽约城市的概率在2%左右(英文)。但是在上海，车量多了纽约的好几倍，而且加上了跟黑市场勾结的问题，我估计不会超过五百分之一吧。

但是这只说明找回来的概率，没考虑到恰恰在五个月之后找回来的概率。我猜测这个可以用幂律分布来模拟因为对我来说如果你能找回来，肯定越早越有可能。 因此，用了zipf幂律分布，正在第150天之内（5个月）找到的概率为99.33333% （1-1/150）

可是这个只是150以内，如果正要第150天，那就要用（P（151天以内找到）- P（150天以内找到）等于0.993377-0.99333=0.0000442。 于是，正好在第150天找到的概率为0.00442%。

最后我们可以把找回来的概率乘第150天的概率就等于(1/500)*(0.0000442)= .0000000882; 差不多千万分之一。 这个还没考虑到他的自行车在第149天被偷！

总之这个概率算不上什么双色球，不过总是比天天彩选4巧的很！最遗憾的是他所得到的奖跟概率不是相称的。