I discovered e by accident

I'm a linguist with almost no math learnin'. So imagine my surprise two weeks ago when I discovered e (the transcendental number that =~2.718) during the course of playing around with probability! I also learned some very useful things about probability that I didn't know.

It all started when I was thinking about a video game I'm playing, FFXII. In this game, when you kill a monster it has a certain chance to drop an item. If you want the item, you run around the area looking for these monsters and killing them until one of them drops the item you want. One of the most elementary questions to ask, then, is how many monsters you have to kill before you get the item. As a non-math person, I thought I had learned the answer to this question in third grade. I was extremely wrong, and I think (hope, for the sake of my self-esteem) that other non-math people are surprised by the answer to this too. If you have more math than me, you might enjoy my naivety :)

Anyway, the monster I was dealing with had a 10% chance of dropping the item I wanted, a 1 in 10 chance. So I asked myself, if the chance is 1 in 10 and you kill 10 monsters, what is the chance you'll get the item? When I was a kid I would have said 100%. . . 10% probability added ten times makes it a sure thing that if you kill 10 monsters, at least one will drop the item. But by now, I knew that successive probabilities are multiplied, not added, and that even if you kill 10 monsters there is still a chance that none will drop the item. I guess at that point I would have said the chance would be even, a 50-50 chance. The reason I chose 50% is because I thought the probability for a 1-in-n event happening in n repetitions had to be somehow special. As it turns out, I was both wrong and right.

To compute the probability of getting a 10% drop chance item after killing 10 monsters, you actually compute the chance you WON'T get the item in 10 kills, and then subtract that from 100% to get the chance you WILL get it. Since each monster has a 0.9 chance of not dropping the item, the chance of NOT getting the item after 10 kills is 0.9 times itself ten times, or 0.9^10. This comes out to about 0.3487, which means the chance of GETTING the item is 1- that number, which is about 0.6513, or a 65% chance. This really surprised me! I was sure that if an outcome happens 1 in 10 times, and you repeat the event 10 times, you would be more likely to get the outcome than just 65%.

I wanted to generalize, so I imagined killing 100 monsters, each with a 1 in 100 drop probability. I did the math, and the chance of getting the drop turned out to be 63%. Was the chance decreasing with lower odds? I calculated the drop chance with 100,000 kills of a 1 in 100,000 drop chance monster, and the result was a 63% chance. So no, the chance wasn't decreasing with lower odds, it was actually approaching a limit. It turned out that killing n monster, each with a drop chance of 1/n, the probability of getting the item would always be about 63%. This seemed like such useful information that I couldn't believe I didn't hear about it in school or anywhere else. I called my brother, who is an engineer at Boeing, and asked if he had ever heard of this strange number. After thinking a bit, he asked me again about the chance of NOT getting a 1/n drop chance item in n kills. I told him it was about 0.3679. Aha, he said, that number is simply 1/e! He was surprised that I had discovered the transcendental number e by dicking around with video games.

But all of that didn't answer my original question, which was, how many monsters do you have to kill to get the item you want? I now realized I had to express the question in terms of probability, so I rephrased it: If a monster has a 1 in 10 chance of dropping an item, how many monsters do you have to kill to PROBABLY get the item, i.e. have greater than a 50% chance of getting it? The answer, it turns out, is 7 monsters.

you know I was thinking that this was going to be a story about some older guy who stumbled on a rave for the first time and had some delicious little crumpet give him a hit tongue to tongue.

But this works too.

[Professor Chaos]

When I'm bored I masturbate.

[Choobus]

If you have a 25% chance of getting caught masturbating, how many fists of fury will you enjoy while your wife pops out to the shops before the humiliation ensues?

[Professor Chaos]

Choobus wrote

If you have a 25% chance of getting caught masturbating, how many fists of fury will you enjoy while your wife pops out to the shops before the humiliation ensues?

Hmmm...In all likelihood, only once, as I often enjoy a good nap and/or smoke after wanking. Two other activites that my wife frowns upon.

[inkadu]

Professor Chaos wrote

When I'm bored I masturbate.

:lol::lol::lol:

[Philboid Studge]

My prom date discovered roofies 'by accident'

[Smellyoldgit]

Professor Chaos wrote

I often enjoy a good nap and/or smoke after wanking. Two other activites that my wife frowns upon.

I assume this to be a confession that the tobacco habit has not yet been beaten?

[Kate]

[Professor Chaos]

Smellyoldgit wrote

I assume this to be a confession that the tobacco habit has not yet been beaten?

:whistle:

[GodlessHeathen]

Gathercole wrote

I'm a linguist with almost no math learnin'.

Are you a cunning linguist?

I can't TELL you how thrilled I am that I beat everybody else to that!

[anthonyjfuchs]

Professor Chaos wrote

When I'm bored I masturbate.

I eat fast food.

That's not how drop probabilities in on line games work at all.

If there's a 1 in 100 chance for an item to drop, the actual probability of it dropping are directly related to how much of an annoying asshat you are.

For example, if you're a casual player that thinks 'raid' is what you spray on bugs, you can kill a Kajillion Hojillion monsters and never see that item. It's the AH for you, noob!

On the other end of the spectrum, if your guild was speed raiding Rag before fire pots became too expensive to buy, and you go on thottbot and post comments like "LOL STFU NOOB! You can get the hand of rag in only 8 weeks if you get off the carebear server and start playing!!" Then every monster you kill will have the item drop... at least according to your thottbot comments, anyway.

anthonyjfuchs wrote

I eat fast food.

You guys masturbeat? That's some fuched-up PC craziness.

[calpurnpiso]

Hmmm..when I'm bored I call an LCT and Pray to the Lord and Saviour Penis-Christ..or Holy Mother Cave....:lol: