{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