Moons – The Theory of Space Oddity 6969km

Introduction

As everyone probably knows, a moon is created in battle. It is either a consolation prize for a player—a sort of impulse to better understand the fleet save mechanics—or, as is much more common, the result of a well-planned and calculated action: moonmaking.

The most important parameters of a moon are its diameter and the probability of its formation. The temperature parameter has no practical application in the game.

1. The diameter and chance of a moon appearing are related to the amount of debris created as a result of the battle. For a moon to form, a minimum of 100,000 units of debris is required, while values above 2,000,000 do not affect the moon's parameters.
2. A larger moon diameter means it is harder to destroy using a Death Star. Typically, players aim to maximize this parameter.
3. The probability of a moon forming consists of the base debris chance p_z (ranging from 1% to 20%), the effect of lunar quantum gravity p_q (which increases the chance by +0% to +3% depending on the phase of Earth's moon, where a new moon = +0%), and bonus days p_b (which increase the base chance by +5% or +10% on special occasions like OGame's birthday, or by +20% during a moon event).

Theory

Probability of Creation

The percentage from battle p₀ is the unrounded base probability of moon formation from debris z, given by the formula:

p₀ = min(z/100000, 20)/100

The probability of a moon forming p depends on the rounded debris percentage p_z = ⌊100·p₀⌋/100, the effect of lunar phases p_q ∈ {0%, 1%, 2%, 3%}, bonus days p_b ∈ {0%, 5%, 10%, 20%}, and additional probability from the Kaelesh Supra-Refractor building P_F12K.

p = p_z + p_q + p_b + 0.005·P_F12K

Diameter

The moon's diameter is related to the battle percentage p₀ ≥ 1% and a random number X ∈ {0, 1, 2,…, 10} with a uniform probability distribution, given by the formula:

d = ⌊(1000·sqrt(10+X+300·p₀)) (1+0.005·P_F12K)⌋

Conclusions: For the same amount of debris z, 11 different moon diameters can be obtained, each equally probable. Assuming no Supra-Refractor (P_F12K = 0), these diameters typically range from 3605 km to 8944 km, differing by 1 km. By adjusting the debris amount, any diameter within this range can be obtained, such as 6969 km, provided the fleet composition and debris on the universe allow it. With the Supra-Refractor bonus included, the maximum diameter reaches 9400 km.

Lunar Quantum Gravity

If you want to make smallest moons when chance is 1%-during the full moon time, you have 4% chance of success. But is better to wait for event max 40% or special date with max 30% chance. Why to do that? Small moons are easy to destroy and good to hunt the "blind wolves". Anyway during full moon only meanly 25 tries are needed, when new moon it is 100. Have Max Moon Chances Increased?

Hidden Trophy

To test the presented theory firsthand, one may attempt to unlock the hidden trophy – "Space Oddity". The task involves obtaining a moon with an exact diameter of 6969 km.

History

A brief history of my discovery… I would like to begin by stating that, initially, I wasn’t particularly interested in achievements. I think the concept is great, but the execution leaves much to be desired. Earning the proverbial "platinum" should be feasible, but as things stand, it is currently out of reach for anyone. I felt the developers went overboard, finding yet another way to push microtransactions, which, ironically, don’t even improve your account but rather provide the illusion of satisfaction for having "wisely" invested billions of resources in five-star achievements.

Only the limited-time seasonal skins and tasks—those that can realistically be completed to a perfect score—encouraged me to return to the game. Credit to the developers for that. And then there are these hidden achievements, rewarding the most non-intuitive yet creative approaches to gameplay. For years, I have been hunting for hidden game mechanics, statistical facts, and ways to mathematically describe and optimize them… The moon concept seemed promising, but I abandoned it after reading a guide that explicitly stated that moon diameters are discrete and could be listed in a small 20x11 table: https://owiki.de/index.php/Mond.

Now, back to the seasonal universe. My bad moon luck continued, with over 20 failed attempts, and the accumulated losses resulted in fleet wreckage dropping to 19% instead of 20%. As a result, an unusual moon diameter appeared—one that wasn’t in the table! But how was that possible? This marks the beginning of the short history of this moon—an attempt to identify and remove an anomaly from the theory. To keep things brief, since the rest of the dots connect themselves, let’s just say that a special formation of 3131 kamikaze espionage probes perished, and with a 12% probability, a moon was created… with a very special diameter—exactly the one I was hoping for. Unlocking the trophy in the OGame category was indeed an exceptional experience, something OGame hadn’t given me in a long time, and for that, I have to thank the discoverers of the other hidden trophies.

Calculations for the Achievement

Summary

What else can be said? Happy hunting this and other missing hidden trophies! And orginal post in Polish: https://forum.pl.ogame.gamefor…?postID=147563#post147563