User blog:BunsenH/The Statistics of an Ethereal

Or: "I've tried like dozens of times to get a Ghazt. Is the game broken?"
People often ask how many tries it will take to breed one of the hard-to-get monsters, such as the Ethereals. It's impossible to say, not even approximately. You might get one on your first try, if you're lucky, or it may take hundreds of times if you're not. Even if you haven't got one after trying again and again, it doesn't mean that the game is broken. The math is a bit complicated to dig into, but the main idea isn't too hard.

Just for the sake of argument, suppose the game decides if you're successful by rolling a pair of virtual dice — standard six-sided dice, no cheating. If you get 12, &#8239;, you get the monster you want; otherwise you fail. (The game's real decision process is nothing like that, but dice are a randomizing system that people tend to be familiar with.)  How many times do you have to roll a pair of dice before you get 12? Again, it's impossible to say.

By statistics, the chance of getting 12 when you roll dice is 1 in 36. But that doesn't mean that if you roll dice 36 times, you'll get 12 exactly once. It means that if you roll dice many times — hundreds of times — 12 will probably come up about 1&frasl;36 of the time. The more times you roll the dice, the closer the fraction will probably get to 1&frasl;36. But for any one try, the chance is exactly the same. You're exactly as likely to get 12 on a roll right after a previous "success" as on a roll after a long string of "failures". (See here for an example of two successes in a row.)  The "Law of Averages" is a myth. There's nothing that magically makes the fraction of successful rolls balance out at some point.

In various places on the MSM wiki, people write that the chance of breeding an Ethereal is about 1% on each try. (The source of that value seems to have been lost.  Only the game's programmers know for sure what that chance is.  To get the value by experiment would take thousands of tries, with records carefully kept of the results.)  That doesn't mean that you would have to try exactly 100 times before you'll get an Ethereal, but it does mean that you will probably have to try many times. Of course, you might get lucky and get one quickly.

If you're interested in the mathematics of the probabilities, there's a nice explanation here.

As the math works out, if the chance of breeding an Ethereal really is 1% per try, after 70 tries, your chance of breeding at least one is 50%. Of course, that means that the chance of your not getting one is also 50%. After another 70 tries, the odds of not getting any have dropped by half, to 25% — that is, a 75% chance of having got at least one. After each additional 70 tries, the chances of not having got any Ethereals have gone down by half again. It's not a sudden jump, of course; it's a curve that slowly moves with each roll, touching those "milestones" at roll numbers 70, 140, 210, and so on.

There are only two things that we know for sure affect the chances of success (because the game has told us that they do). The first is the Wishing Torches; the second is some "Daily Deals" that temporarily improved the chances. Only the game's programmers know how much effect the Torches have. There has been a lot of guessing about what else might make a difference. The Ghazt's description, that it "only manifests itself when conditions are absolutely perfect", inspires guesswork and superstition about what constitutes "absolutely perfect conditions". People have suggested that the chances of breeding an Ethereal monster are better if you try around midnight, that the chances are better if your monsters are high-level (or both the same level), and so on. Since the odds of successfully breeding an Ethereal are poor even under the best circumstances (such as all ten Wishing Torches lit), measuring the real effects of these things would take a lot of effort and has never been done. The sheer randomness of the breeding process can make an irrelevant factor seem to be important. If you have finally got an Ethereal monster after many tries, you might assume that something you did differently must have made a difference. But unless you test that assumption, and can show that that factor really does matter, it's just a shot in the dark.

Your best move is to keep trying. Good luck!