Dark Orbit - finally a "real world" application for math

Burrito said:
"""The basic idea is to use different multiplier levels when a gate is almost completed to perform a "precision landing" with the last few parts you get from a multiplier.......Unfortunately, this does not work if we start as soon as 6 parts are missing. This will only increase the cost. But if we start as soon as only 3 parts are missing, we need on average 5-6 turns less than when using only level 2 multipliers."""

I knew about "precision landing" but I never knew the breakdown for which one is best to go for at the end...your data suggests the X3 for final hit is best....very interesting.

EDIT : It is sooo sweet to hit that X6 to finish the gate though .

 

When I performed a monte carlo simulation (1 billion spins, assuming only 3 parts away from gate built) on the "precision landing" technique, the cost of building a gate with multiplier on x3 is greater than using multiplier on x2. Checking the program, I still don't see any apparent errors. Intuition tells me that your values are correct, but could you check them again?

Great work, by the way. Thank you for spending the time to type everything up.

 

I did lots of plausibility checks especially on this result, so all I can say is that I did all I could to make sure the results are accurate. Except for comparing them to a different implementation of the same problem.
So it would be really nice if we could get the same results.

Does your program yield the same mean values I got in post #5 for a whole gate?
Which programming language did you use?

Edit: just a few ideas...
First of all, you say you ran your simulations with a gate that only has three parts missing. But how many parts in total does your gate have? While the benefit is nearly constant in the range of 45 to 128 parts, it is indeed zero if the gate only has three parts in total.
Also with a reasonable total number of parts the gate consists of, you cant expect to get the same results I did starting with only three parts left. Because when starting with an initially empty gate, there is a chance that the state "only three parts left" is skipped because I got 2 parts from multipliers when there were four parts left. So the benefit you see should even be higher.
Then since you start with an almost completed gate, your simulation will be very prone to errors caused by the initial state you give. Make sure every variable gets a reasonable initial value EVERY time the gate is completed.

Next Edit: you went back to using x2 multipliers after getting a single part, right?

 

A question: Which spin amount should I use? 1, 5, 10, or 100? Which one would make the most effective use of the x2 multiplier?

 

The only way to make sure you use every multiplier instantly on level 2 is with single spins.

 

Ok. Thanks.

 

Wow such math ... o_o

Nice and i think you're working so hard for this :/

 

Great Job. What I would like to ask though, how do you calculate the variance since every single spin is a dependent event based off like three other variables.

 

I am not sure if I got your question. Would you like to elaborate which variance you are referring to?

So far, the result of a single spin was assumed to be an independent random event with a probability of 13% for a gate part. There is no evidence in the data I collected that this assumption is not valid.
In your opinion, what are the variables the outcome of a spin depends on?

 

Well, the probability of obtaining a new part is reduced every time you receive a new one. It would actually be relatively simple to calculate the expected number of spins to build a gate if it weren't for the multiplier system. Getting multiple parts screws everything up, because then you can "skip" certain states such as 46/111 to 48/111. I'm still a bit baffled on how you managed to calculate expected amount of energy required factoring that in.

 

Now I see. You are right, this would be rather difficult with an analytical approach.
That is why used a small program that emulates the galaxy gate generator. Building a few million gates within this program, it is possible to derive the average number of turns needed to complete a gate in the actual generator. This kind of numerical approach is termed Monte Carlo simulation (the name implies that random numbers play a key role here)

 

2. What is a good configuration
2.1 Introduction

First of all: there is no such thing as THE BEST configuration. It all depends on how you use it. There may be some configurations that perform bad in my analysis but are quite useful if you know how to use them.
The focus of this analysis is a 1on1 situation. Variables like when an insta shield is used or if someone tries to hit and run can and should not be included in this simple analysis. These things usually referred to as "skill" are left to the players.

So what are the assumptions?
Both players are UFE and have everything at hand to max out damage, shield and hitpoints. The only exception from this is the additional booster from the Kappa gate which is not included throughout the analysis.
It is further assumed that a configuration either has the maximum amount of shields in the ship or no shields at all in the ship. Everything in between will be left to the PvP experts, they sure know better how to use a configuration with 5 shields and 10 Speedgens in the ship.
Both opponents use UCB-100 and RSB-75 with no delay all the time. It sure makes sense to use SAB instead of UCB 100 if you deal much more damage than the opponent, but again this is more related to skill than to the configuration alone.

How does it work?
First of all, we have to know the amount of hitpoints, shield and the AVERAGE damage per second a player can make.
To determine this, we have to keep in mind the rule of thumb for bonuses in Dark Orbit: similar bonuses are added, different bonuses are multiplied. For example a single shield booster gives a 25% bonus. A pro shield booster gives another 25% bonus, and because they are similar the total bonus is 25%+25%=50%. An additional bonus of 10% from a ship design on the other hand is from a different category, so the total bonus would be 50% x 10% = 65%.
The way different bonuses interact implies that one should either choose defense OR offense. Combining Havoc drone designs with a shield design for the ship is not a good idea. So I will compare only configurations that either max out shield OR damage and refer to them as "Defense" and "Offense" respectively. The only exception from this rule is the "Heart" drone formation that should always be used at least at the beginning of a 1on1.
With the assumption of either full shields or no shields in the ship, all that is left is to find out the optimum distribution of lasers and shields in the drones. The player himself has 20 different possible distributions and so does the opponent. This leaves us with only 20x20=400 possible combinations.
What it all boils down to is calculating the amount of time it would take the enemy to shoot you down minus the time it takes you to shoot down the enemy. If this time is higher than zero, you win. If a configuration wins against most configurations the opponent can come up with, it is a good one.

To get the average amount of damage per second one has to be aware that the average damage of a LF4 laser is only 175 (200 is the maximum damage, the minimum is 150). The hit chance is assumed to be 80%. It used to be 70% when the LF4 lasers were released but since then, things have changed. If someone knows anything specific about this let me know.
Concerning the combination of UCB-100 and RSB-75 ammunition: within 3 seconds, you can use 3 times UCB-100 and once RSB-75. This results in an average damage multiplier of 6 for the damage per second.

Additional damage which is independent of the configuration comes from the normal rockets, the rocket launcher and from the lasers in the PET.
I assume PLT-2021 rockets are used with a hit chance of 80%, dealing 6881 damage per second on average. The rockets from the hellstorm launcher deal another 4240 damage per second on average.
The PET may be able to deal 20000 damage per hit with RSB-75, but lets admit it, most of the time it just soars around aimlessly and does not shoot every second, so I only add another 5000 damage per second for the PET. I only do this hoping that the bug has been fixed where a player actually dealt less damage per second with the PET. Again, if you know anything specfic about this issue please let me know.

Long introduction, I know. Time to get started.

 

How did the thread go from GG materializer to Configs??

 

If you read the first post carefully, you will notice that the thread is not dedicated to the GGG alone. I will try to cover any topic that can be tackled with a mathematical approach.

 

oh.ok!

 

El_Burro
I think when you finish with configs for pvp, maybe I can help for some math on the most efective way to kill a Referee. A noob will not make as much profit as a UFE, but a UFE with pvp configs wont even come close to the max profit with such equipment.

 

Well, need a lot of CBO for that

 

Hi El_Burro, how does one calculate how many noobish posts one gets between well thought out posts. I would note, I realise I have added to the noobish post count even when trying not to.

 

Hi El_Burro, I guess you know there is a difference between damage /sec and average damage. Having performed many controlled experiments on average laser damage over the years I can say with reasonable certainty, "the damage range is an has always been when I have checked, maximum to 75% of max". The result for 50 samples produces a reasonable result and for 100 samples are remarkable good. Try it for yourself considering any other potential influencers, like in range ships with shared bosters.

Get a fellow player to test in a corner of a map, and /or test it on npcs away from other ships that may have shared boosters.

When you plot the results against the predicted liner min to max, the achieved damage per laser shot ( with as little as 100 shots) is remarkable accurate.

 

One calculates noobish posts by counting how many well-thought-out posts there are and then counting how many noobish posts there are between each well-thought-out post!

Maybe you could come up with the chance of noobish posts occuring after every well-thought-out post and deduce a 99% confidence interval for it!!