# Warframe: Radshare Math

This is a short appendix to my Radshare and Intshare explainer, providing the details behind the calculations. We’ll first look at how a few example probabilities are calculated, then give the whole set of relevant probabilities in a few tables. If you’re already comfortable with the math involved, skip on down to “The Results.”

## The Basic Calculation

Each Void Relic has a total of 6 possible items it can drop: 3 common, 2 uncommon, and 1 rare. When refined to Radiant, a relic has a 10% chance of dropping its rare item, a 40% chance of dropping any uncommon item (thus a 20% chance of dropping a specific uncommon item), and a 50% chance of dropping any common item (or a 16.67% chance for a specific common item). For example, a Radiant Lith H3 has:

- A 16.67% chance of dropping an Astilla Prime Receiver (Common)
- A 16.67% chance of dropping a Nezha Prime Systems Blueprint (Common)
- A 16.67% chance of dropping a Paris Prime String (Common)
- A 20% chance of dropping a Forma Blueprint (Uncommon)
- A 20% chance of dropping a Titania Prime Blueprint (Uncommon)
- A 10% chance of dropping a Harrow Prime Systems Blueprint (Rare)

The idea behind radshares (and intshares, etc.) is that if everyone in a group is running, say, a Radiant Lith H3, there is a good chance that at least one of the four will drop the rare, or the specific uncommon that you’re looking for. Since everyone who contributes a relic to a mission gets to pick whichever prize they want, the only way for us *not* to get the rare (if we want it) is for all four players to fail to roll the rare. Each player individually has a 90% chance of *not* rolling the rare, so the probability that all four players will fail to get the rare is

`0.9 × 0.9 × 0.9 × 0.9 ≈ 0.656 = 65.6%`

So about 2/3 of the time, even with a 4-player radshare, we’re only going to see common and uncommon relic drops in our end-of-mission loot.

The chance that at least one player rolls the rare is therefore

`1 - (0.9 × 0.9 × 0.9 × 0.9) ≈ 0.344 = 34.4%`

This means that around 1/3 of the time, we’ll have the option of selecting the rare from our end-of-mission loot.

## Why 34% and Not 40%?

A potential point of confusion is that even though each relic has a 10% chance of containing the rare in this scenario, the overall chance of finding the rare is not 4 × 10% = 40%, but a lower number. This is because the players’ chances of rolling a rare are independent, and a successful roll by one player can coincide with a successful roll by another.

To make this more intuitive, we can think of flipping two coins, which we’ll call A and B. Each coin may have a 50% chance of landing heads-up, but that doesn’t mean we’ll see heads every time we flip the two coins together. Instead, there will be some times when both coins turn up heads and some times when both turn up tails.

Heads on Coin A (50%) | Tails on Coin A (50%) | |

Heads on Coin B (50%) | H, H (25%) | T, H (25%) |

Tails on Coin B (50%) | H, T (25%) | T, T (25%) |

Likewise, if we were doing a radshare with just two players (A and B), we would have:

A Rolls Rare (10%) | A Doesn’t Roll Rare (90%) | |

B Rolls Rare (10%) | Rare Shows Up Twice (1%) | Rare Shows Up Once (9%) |

B Doesn’t Roll Rare (90%) | Rare Shows Up Once (9%) | No Rares (81%) |

In that simple example, the probability of being able to pick the rare at the end of the mission is 19%, not 20%. Running two copies of the same relic in the same mission increases, but doesn’t quite double, the chance of getting the rare—just as flipping two coins at once increases, but doesn’t double, the chance that we’ll see a heads-up coin.

## The Results

With all that in mind, here are the chances, rounded to the nearest percent, of getting a specific common, uncommon, or rare for radshares and intshares of different party sizes. I realize that single-player runs aren’t “shares” per se, but I’ve included those values for reference.

*Radshares*

Rare | A Specific Uncommon | A Specific Common | Only Commons | |

1P | 10% | 20% | 17% | 50% |

2P | 19% | 36% | 31% | 25% |

3P | 27% | 49% | 42% | 13% |

4P | 34% | 59% | 52% | 6% |

Notice that the odds of getting a specific common are actually lower than those for getting a specific common. Thus a party radsharing Lith H3 is actually less likely to see a Paris Prime String than they are a Forma Blueprint. Note too that with a 4-player radshare, you’re extremely likely (94%) to see at least one uncommon or rare.

*Intshares*

Rare | A Specific Uncommon | A Specific Common | Only Commons | |

1P | 2% | 11% | 25% | 76% |

2P | 4% | 21% | 44% | 58% |

3P | 6% | 30% | 58% | 44% |

4P | 8% | 37% | 69% | 33% |

In words: intshares offer very poor odds of getting a rare, but a 4-player intshare has a nice probability of bringing you a specific common drop.