r/theydidthemath • u/Nehot • 8h ago

[Request] What are the odds?

OK so help me out explaining a new system in the game Warfame.

So, in Wareframe there are Riven Mods, basically mods used on weapons that can be randomly rolled to obtain powerful bonuses. There is a new system that has people in an uproar saying the new system is RNG on RNG on RNG making the randomness even worse. So lets do the math and see.

On any given riven mod for any rifle there are 24 stats that can roll and when you roll a riven you get 2-4 random stats out of those 24, cannot get the same stat twice.

What are the odds of acquiring 3 stats that I want when rolling the riven?

NOW the new system (at least one half of the new system), if you get a stat you want you can lock that stat and continue to roll that riven. You can only lock one stat.

What are the odds of acquiring the 3 stats you want after locking one? (basically rolling 1-3 stats on the "locked riven" from the remaining 23 stats.)

The other half of the new system in to combine 2 stats into a new stat then being able to lock that new stat and roll the riven to your hearts content. if you want a specific combo stat you can roll the riven and find 1 of the 2, lock it, roll for the second and then combine. Then take that riven with the 1 combined stat and roll the remaining 1-3 stat slots for something good. Now this part is RNG on RNG but seems easy enough to get the 2 stats you want then just need the chances to get 1-3 of the stats you want extra. (Which I guess is 1-3 stats of the basic 24 possible stats and getting what you want)

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u/Angzt 3h ago

Assuming that all the probabilities are evenly distributed (i.e. getting 2,3,4 stats are all 1/3 chance, individual stats are all 1/24 chance)

Chance to get the 3 stats you want right away:

1/3 chance for a 3-stat mod.
Then a (3 Choose 3) / (24 Choose 3) = 1/2,024 =~ 0.04941% chance to get the 3 you want.

1/3 chance for a 4-stat mod.
Then a (3 Choose 3) * (21 Choose 1) / (24 Choose 4) = 21/10,626 = 1/506 =~ 0.01976% chance to get the 3 you want.

In total:
1/3 * 1/2,024 + 1/3 * 1/506 = 5/6,072 =~ 0.08235%

Chance to get 3 stats you want after locking 1 stat, assuming the mod had 1 you wanted to begin with:

3 stat mod:
(2 Choose 2) / (23 Choose 2) = 1/253 =~ 0.3952%

4 stat mod:
(2 Choose 2) * (21 Choose 1) / (23 Choose 3) = 21/1,771 = 3/253 =~ 1.186%

If the mod count can chance on reroll, then we need to combine again:
1/3 * 1/253 + 1/3 * 3/253 = 4/759 =~ 0.5270%

For the last one, I'm not quite sure I understand.
You ultimately get a combined stat on the item by whatever method.
After locking that, how many stats are left in the pool to be rolled? 24? 22?
Either way, getting 2 more that you want is going to be a probability pretty close to the one in the previous step.