Star Force Simulations
To prepare for Star Force and decide how much I would be spending, I wrote a simulation for the system. Thought I'd share the data here.
The simulation was written on MATLAB and uses MATLAB's RNG. A new seed was obtained at each trial. The simulation would run each trial until the equipment reached the target 15 stars, constantly adding the cost for each enhancement. If the item was destroyed, it would start from 0 star but would not consider it a new trial.
The simulation also recorded the average number of times the item was destroyed; since it does not add the replacement cost of the item upon destruction, you can find the real total cost by simply adding the price of the item times the average number of destruction to the mean cumulative cost given in the charts.
Here's the data for level 150, NON-SUPERIOR equipment:
[url=http://imgur.com/4SgHpsz]Graph of the cumulative costs for 100k trials.[/url]
[url=http://imgur.com/ILK656Q]Chart with numerical data for 100k trials.[/url]
Here's the data for level 150, SUPERIOR equipment, up to 12 stars (since 13, 14, and 15 take way too long due to low success rate and high destruction chance):
[url=http://imgur.com/WTrmh09]Graph of the cumulative costs for 100k trials.[/url]
[url=http://imgur.com/iGvycGS]Chart with numerical data for 100k trials.[/url]
...forgive the typo I made on the charts where I put stage 0 instead of stage 1.
I've noticed that the standard deviation for destruction count is...pretty big, even larger than the mean. Guess that means it's fairly likely you can get by without seeing a single boom.
I've also noticed that the standard deviation for the cumulative costs is also about as big as the mean, which means there will be a huge gap between the lucky folks and unlucky folks. My only explanation for the large standard deviation is the fact that you rank down upon failure.
I'll try to run a full 1-15 star Tyrant enhancing, but the sample size will be smaller.
And since I wrote the simulation pretty hastily, take the results with a grain of salt. But looking at the first few data points, they seem reasonable.
[url=http://pastebin.com/1TuPprVm]Pastebin link with the MATLAB code.[/url]
14 Comments • Newest first
[quote=slinger99]aw so i need approx 3bil to get to 8 star =(?
couldve bought like 15%cape with that money.. already spent 2.2bil on my cape =([/quote]
No lol. You need to add in boom rate multiplied by the cost of clean capes.
You are overthinking nexon's use of RNG. If anything, the RNG is against the player for the most part. The chances of getting the highest result in anything is a needle in a haystack of a chance to get.
aw so i need approx 3bil to get to 8 star =(?
couldve bought like 15%cape with that money.. already spent 2.2bil on my cape =(
[quote=lazypando]if i am reading this correct, you have the mean cost for stage 2 as 0.0003007b which is 300.7k mesos
it costs 55.8m just to try once o.o
edit: ohh nvm, this isn't for tyrants
when you finish the one for tyrants, could you upload the code somewhere (like pastebin,etc)?
i did a few thousand runs earlier in Java so I'd like to see how they compare[/quote]
I posted the code; it may be a little messy.
@cheesemochi: I didn't have the thing output the raw data. I can modify the code to output it, but not tonight; I'm way too tired and will probably break the code if I try to modify it. But considering the huge standard deviation, I'd say the points are pretty spread-out.
LOL. I love how it goes 15 to almost 30b from 10 to 11 stars and is still rising exponentially. Imagine the estimation for 12, 13, 14, and 15 stars .-.
I think it's fair to say no booms are your friend at that point
For tyrants, how much data points are above and below the average for each star?
You got my like on your thread!
[quote=lazypando]500 is the point for 14 stars
there's one more point at the very top right corner[/quote]
Ooooh okay thanks
Dang that's a bit more expensive than I thought it would be
[quote=silverphoenix]Pretty sure I'm just reading it wrong but your graph seems to contradict the table? Cumulative cost to reach 15 stars in the table is 900 whereas on the graph it's 500?
Probably misinterpreting but oh welp
LF clarification, I can't math anymore[/quote]
I think that graph was to show how much meso to each star. Ex : 14 to 15, where ever the dot it, thats how much meso it will take.
[quote=silverphoenix]Pretty sure I'm just reading it wrong but your graph seems to contradict the table? Cumulative cost to reach 15 stars in the table is 900 whereas on the graph it's 500?
Probably misinterpreting but oh welp
LF clarification, I can't math anymore[/quote]
500 is the point for 14 stars
there's one more point at the very top right corner
Pretty sure I'm just reading it wrong but your graph seems to contradict the table? Cumulative cost to reach 15 stars in the table is 900 whereas on the graph it's 500?
Probably misinterpreting but oh welp
LF clarification, I can't math anymore
So your saying.. it takes about 900mil to get to 15stars? I don't know if i read it right.
I would like the java code too pls...
if i am reading this correct, you have the mean cost for stage 2 as 0.0003007b which is 300.7k mesos
it costs 55.8m just to try once o.o
edit: ohh nvm, this isn't for tyrants
when you finish the one for tyrants, could you upload the code somewhere (like pastebin,etc)?
i did a few thousand runs earlier in Java so I'd like to see how they compare
neat.