The Probability of Getting Your Dream Weapon
*Disclaimer: This is an estimation based off of a worst possible (but reasonable) situation that I could think of. This is meant to be fun and informative, so please keep it that way. Probability has never been my strongest subject so I had to brush up some before I did this, and I had to make several assumptions in order to complete the problem. I will include an explanation of my numbers and a list of my assumptions. If anyone knows a specific roll mechanic in more detail, or sees an error in my logic/math, then please note it and I will adjust the probability if needed. This number ended up being so incredibly small, that I myself even have a hard time believing it, but I have yet to find an error that makes it a reasonably larger chance (even eliminating some of the variables leaves it in the millions and hundreds of millions).
Have you ever sat down as said, “this is the weapon I want, this is the mastery I want, this is the nano I want, these are the bonuses I want?” Well I hate to break it to you, but you will probably never get it.
The probability for your dream weapon (worst case) may be in the area of:
1 out of 1.45billion
Making you 8 times more likely to win the lottery, and 13 times more likely to get crushed to death by a vending machine (lol - you know who you are! O.O), than you are to get your dream weapon.
Here’s what I did:
(3/50)(1/94)(1/25)(1/20)(1/7)(1/12)(1/11)(1/2) = 1/1447600000 = 6.9^-10 or ~ = 1 out of 1.45billion
Numbers explained (all of these have notes about them in the “Here’s what I Assumed” section):
(3/50) = the chance of getting an orange out of a T4 lockbox
(1/94) = chance of getting a specific type of weapon (example: Thunder)
(1/25) = chance of getting a specific mastery (example: crit % while crouched)
(1/20) = chance of getting a specific synergy (example: Rolling Thunder)
(1/7) = chance of getting an extra bonus (T0) (example: .85 reload)
(1/12) = chance of getting the T1 bonus/nano (example: -.10 recoil) (12 = 7 bonuses + 5 nanos)
(1/11) = chance of getting the T2 bonus/nano (example: radiation) (11 = 6 bonuses + 5 nanos)
(1/2) = chance of getting the T3 bonus (example: 1.10 rate)
Here’s what I Assumed:
- I remember hearing somewhere that nano interferes with bonuses, but since I don’t know exactly how… Does it roll nano OR bonus, or does it roll them all as one set of outcomes? Does each bonus have a chance to be a nano? Do only one of the nanos effect the bonuses or is it both of them? Or… is it something else entirely?
For this reason I had to “wing” the bonus/nano rolls, so I just pooled nanos with the T1 and T2 rolls to get an idea. However, I think that each bonus roll may have a chance to be a nano or a bonus – until you have 2, or the rolls are complete. If this is true then the equation would look more like,
[(3/50)(1/94)(1/25)(1/20)[P(T0)P(T1|T0)P(T2|T0andT1)P(T3|T0andT1andT2)]]
If that is the case then the worst possible selection would be = 1/1470 (or (1/7)(1/7)(1/6)(1/5)) and the chance of getting that combination of Bonuses and Nanos = 1/11, making the probability,
[(3/50)(1/94)(1/25)(1/20)(1/11)(1/1470)] = 1/12666500000 = 7.89^-11 or ~ 1 in 12.6 billion.
(^^Hey, at least it’s less likely than the probability of winning the lotto then getting crushed to death by a vending machine! :-P)
If it’s something else entirely, then I don’t know that yet :-P.
-I used 6% (or 3/50) for the chance of getting an orange out of a T4 lockbox - from previous data collected and posted by other people.
-I counted 25 masteries that might make sense on an AR/LMG/SMG from the guide – I do not know if more or less masteries are available to the LMG/SMG/AR type, so this was just a guess.
-I don’t know if “no synergy” is an option for an orange, so I did not include it.
-I know that you can get an LMG/SMG/AR with no extra bonus, but I don’t know if that is due to getting a nano instead. For this reason I did not include “no extra” in the possibilities – since I tied nanos directly to T1 and T2.
-Since the ideal weapon would be orange, I pooled the charge blade with the other weapons. I do not know how the charge blade is rolled, and it may not be this way. I pooled it with the other weapons because it can impact you getting your dream weapon. I have a feeling (like the notes for the new T4 boxes) that the charge blade is rolled for on only one of the rolls; it also may not be weighted equally with the other weapons. Currently I have given it a 1% chance (once the orange roll is won) by assuming that the orange roll you win is also the roll capable of yielding a charge blade.
-I do not know if any of this has weighting that would change the chances.
My Thoughts on this and Suggestion:
Now, I may have made some “flimsy” assumptions (especially since I’m pretty sure the nanos are different than what I did), I may have even made a mistake or two, and this is intended to be a worst case scenario; but with all of that in mind, I still think this system is just a little bit too improbable (lol) - because no matter how I cut it, a player’s chances work out to be really really REALLY small.
I would like to suggest adding an option in the salvage matrix that allows players to strip a bonus, synergy, or mastery from a weapon and add it to another (of the same) weapon.
