Disclaimer: This post contains a lot of math and a few assumptions/guesses.
TL;DR: The Smeeta Kavat – probably the most played companion in Warframe – has the lovely ability mod Charm. Among other buffs this ability can provide the player with a double XP and ressource buff. Which stacks multiplicatively with market boosters and itself, if it procs again during the first buff. Theoretically this buff can stack up to 6 times, resulting in 64x the normal XP and ressources. And according to my math this has most likely happened several times already. Allthough probably unnoticed.
Setup & Basics
For the sextuple buff to occur, the player has to have Charm on max rank as well as Tek Enhance equipped on their Smeeta Kavat. That way the XP-buffs lasts for 156sec. That way if an XP-buff procs at t0, a second one could proc at t27, a third at t54, … a sixth at t145 leaving a 11sec window with the sextuple buff.
Note that while there are usually six different buffs that might occur, one of them can be eliminated from the pool of possibilities. The instant reload buff can't proc if the player has no primary or secondary weapon equipped (and no Arch-gun segment in their gear wheel). This makes the sextuple XP-buff a lot more likely, however most players will have one of those with them most of the time making it less relevant for the point of this post.
Probability of a sextuple XP-buff
Let the math begin! The chance to get any of the six possible buffs with Charm is 28%. This chance is rolled every 27sec. 28% equals a 1:3.57 chance. Wanting a specific one of those buffs (in our case the XP buff) has a 16.67% or 1:6 chance. These probabilities have to multiplied, resulting in a 1:21.42 chance to receive the XP buff. To get the likelyhood of getting the XP-buff back-to-back we have to multiply our chance with itself. Since we want six back-to-back XP-buffs we have to to this six times. 1:21.426=1:96,818,714.99 so roughly 1 in 100 million. This chance is rolled every 27sec as long as you have a max rank Charm and Tek Enhance equipped and are in a mission.
As mentioned earlier you can reduce the amount of possbile buffs to five. Doing the same math as above but with the five different buffs the chance of a single XP-buff is 1:17.86 and for six back-to-back buffs 1:32,424,391.75, so almost three times as likely. But still unlikely. I won't use this number for further calculations, this is just a little info for the melee-only players among you.
Average playtime per sextuple XP-buff
Based on the math we just did, we can estimate how often the sixtuple buff will occur on average. With the emphasis on average, meaning that it's not even guaranteed that there has ever been a single sixtuple buff in Warframe. But let's take a look at some more math.
Since the 1:96,818,714.99 chance is rolled every 27sec, we can just multiply these two factors to get our average playtime. 96,818,714.99x27sec=2,614,105,304sec. Deviding this by 3,600 to change it from sec to hours we get an average playtime of 726,140.3624h (or roughly 30 days of raw palytime) per sextumple XP-buff.
Over 700,000 hours of in-mission playtime with a Smeeta Kavat seems like a lot. However Warframe has a lot of ative players. Let's take a quick look at my personal stats: On steam i have exactly 3,000h of playtime. However of those I have only spent around 1,400 in a mission. I have used my Smeeta for around 38% of my playtime, so that's 532h. You would need around 1,400 players who have played with the Smeeta for as long as I have to reach the 726,140h per sextuple XP-buff. Now according to this forums survey the Smeeta Kavat was the most used companion a few months ago, so there're probably more then enough other players with a high percentage of playtime with the Smeeta Kavat. Also, Warframe is pretty consistantly in the top 20 and sometimes even in the Steam charts with 35,000+ players at any time. Since we don't have any official usage stats on companions it's very hard to tell exactly how much the Smeeta is used. Especially now that we also have the Panzer Vulpaphyla that is also very popular the Smeeta has a serious competitor. But taking a look at the linked forums post more then a third of the players had the most playtime with their Smeeta previously to the introduction of Deimos.
Tek Enhance was only introduced 2018, before that it was impossible to get a sextuple XP-buff. That nullifies any playtime before that. Also not everyone playing with the Smeeta playes with both Charm and Tek Enhance – allthough they should.
All the numbers under "The estimations" are very vague and I don't even want to take any more specific guesses on how much playtime the community actually has with the Smeeta Kavat. Any number would be just that: a guess.
Since not all playtime is in one go, but with many breaks through mission ends, some streaks might have been disrupted. Also by ending not within the 27s cicle a few seconds of total playtime are lost per mission for our purpose.
On the other hand it's hard to say how average I am as a player. I know some players with twice my playtime, but among all the players on Steam there are also plenty newer players, some of whom might not even own a Smeeta Kavat.
Speaking of Steam: Not all players are playing via Steam, so the number of total players is higher then what the the platform's stats tell us. Not only can you play Warframe by just downloading the client directly from the homepage, you can also play it via the Epic Games launcher and obviously also on Xbox, PlayStation and the Switch. Which I btw forgot until just now.
It's hard to tell any specific guess of how many sextuple XP-buffswe as a community have had so far. But taking the precise math from the beginning as well as all the estimations into account I'd say it's fair to assume that at some point some player has won the Warframe lottery. But because our interface is telling us barely anything about the current buffs we have, they probably didn't even notice …
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