Odds of missing a save with advantage when making multiple saves

[jk7275]

When you make a save with advantage and have to make multiple saves what are the odds of missing at least one

[Expected]

In order to calculate that we'd need modifiers or assume values for said modifiers and work off of those. If I can ask, how are you getting advantage on saving throws?

[NNescio]

When you make a save with advantage and have to make multiple saves what are the odds of missing at least one

P(¬X ≥ 1) = 1 - (1 - (1 - p)^2)^n
= 1 - (2p - p^2)^n

Where P(¬X ≥ 1) is the probability of missing at least one save, n the number of consecutive saves required, and p the probability of making a single save without advantage/disadvantage. This is, of course, assuming that each save has the same DC and tests the same attribute.

Edit: And to be pedantic, the "odds" is given by the ratio P(¬X ≥ 1)/ P(¬X = 0) = 1/(2p - p^2)^n - 1. Though I think you intended to say "probability" or "chance(s)".

[Contrast]

In order to calculate that we'd need modifiers or assume values for said modifiers and work off of those. If I can ask, how are you getting advantage on saving throws?

Gnomes and yuan-ti leap to mind. Barbarians also get adv to Dex saves.