Trivial musings on probability

[Mr Wyrd]

So, it's easy to intuitively think that if you take 2 attempts at a thing, then you are twice as likely to succeed than if you take only one attempt.
But this is typically not true. if the event is a raffle, say, with a fixed number of tickets, then that is a case where it is true.

But if you are playing RS and doing Big Game Hunter in pursuit of a Dragon Mattock drop, then it is not.
It is in fact the inverse of the odds of not getting it both times, i.e. 1- (100/101)².

It's also easy to think that if you face a 1 in 101 chance, then after 101 attempts, you must be bound to have it by then.
In fact the odds are around .63. If there is a 1 in n chance and you give it n attempts, then the odds stabilize as n gets larger
with a limit of 1 - (1/e) [where e is the irrational constant know an Euler's number] and this is about .63.

So having done more than 101 attempts at Big Game Hunter I was not too surprised to still not have got that Mattock.

In fact, I got to the point of wondering how long a streak of _not_ getting a Mattock would it take, before such
a streak was more unlikely than the 1/101 chance of getting it that you have on each and everu one of those attempts.

The answer to that, it turns out is 464.

So given that my own Mattock free streak has just hit 465, I thought I would mark the occasion with this little rant.
And ask a long overdue sanity check. Could I be missing something?

I remember that Jagex made a chance to the way Boss Pet drops work, and that if you have made 1000 Boss kils and not got the
1/1000 Pet drop, then they would increase the odds to 2/1000, and increase to 3/1000 if you still didn't have it after 2000 kills.

Having to do 1 millions kills to actually be sure that your unlucky streak does eventually end may seem like small comfort
to the Boss Pet hunters, but for the Dragon Mattock, I'd welcome it about now.

Anyway, thanks for the read, if you got this far. I'm off to check the price of the Dragom Mattock on the GE.
I've probably earned enough in normal drops to afford one, and by Murphy's law, buying one would probably
mean I'd get the drop on my next go.

[Cally Raven]

I was very lucky with both my mattock drops had them in 6 tetracompasses, but yet I've done many many more and no key for Tony's mattock, will prob never get one lol. I wish you luck in finding a dragon mattock before you buy one. And thank you for your musings.

[Gridenough]

I got a mattock drop just a couple thousand shy of 120 in the skill. I sold it. The 2nd best mattock is fine. You can't augment it, but it uncovers materials well. The one purchase that I made -- well-made-- for the skill was the grace of the elves. I wish I had bought it earlier. Not only did it save running to the deposit carts so often, but the frequent prizes do add up in value pretty well. I did also, at some point after about 110 start buying energy to make more porters, as I had run out of the ones stolen from elves by then, but the cost of those energies was more than made up for by selling the proceeds from the compass caches. More to your point, I, too, have found that probability has little bearing on luck, unless you are counting cards at blackjack. Even then, sometimes knowing the odds doesn't insure that the other guy will not get that card that the odds are 100 to one against. I loved probability section the best of all my advanced math classes, except maybe matrices. Math was my addiction in my teens and twenties. I remember once when my father was totally disgusted with me when he discovered I was doing geometric proofs in the backseat during a trip to Yellowstone. I did not figure out how to trisect an angle. I did do the hike to see the colored rocks by the geysers.