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{table from wiki

Quality        Common        Uncommon    Rare
Intact (default)    76% (25.33%)    22% (11%)    2%
Exceptional    70% (23.33%)    26% (13%)    4%
Flawless        60% (20%)    34% (17%)    6%
Radiant        50% (16.67%)    40% (20%)    10%
}

(tangent) chance of 1 rare with 4 players

4 intact        7.76%
3 intact 1 rad    15.29%
2/2        22.21%
3/1        28.56%
4 rad        34.39%

chance of multiple targeted rares with 4 rad

0         0.9^4 = 65.61%
1 or more        1 - (0.9^4) = 34.39%  
2 or more        (1 - 0.9^4)(1 - 0.9^3) = 9.31969%
3 or more        (1 - 0.9^4)(1 - 0.9^3)(1-0.9^2) = 1.7707411%
4        (1 - 0.9^4)(1 - 0.9^3)(1-0.9^2)(1 - 0.9^1) = 0.17707411%

chance of finding exact quantity of targeted rares with 4 rad

0        65.61%
1        34.39 - 9.31969 = 25.07031% 
2        9.31969 - 1.7707411 = 7.5489489%
3        1.7707411 - 0.17707411 = 1.59366699%
4        0.17707411%

avg quantity of targeted rares found with 4 runs 3junk/1rad

1(25.07031) + 2(7.5489489) + 3(1.59366699) + 4(0.17707411) = 

45.65750521% => 0.4565750521 rares on average

avg quantity of rares in a single 4rad run = 0.3439

0.4565750521 / 0.3439 = 1.327639

--

CONCLUSION

running 4 runs of 3 junk relics and 1 radiant relic is 32.7639% more resource efficient, but ~75% less time efficient than running a single 4 radiant relic game. however, the extra time spent is only more rewarding to multiple copies of the targeted rare; marginal benefit will be gained only in multiple copies of the targeted rare.

pros:
+32.76% more resource-efficient
+more than 32.76% more profitable disregarding time
+ducat profit from scrap commons/uncommons
+better suited to newer players looking to sell cheap rares on market

cons:
-takes 4x+ longer
-chance of getting at least 1 of the targeted rare is the same
-have to communicate with team to decide who uses radiant relic when

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