Psychometric function target - what y value on a psychometric function will a staircase hit

psychometric function target

downRule = 3 # How many correct answers in a row do you need to drop down a level?
upRule = 1 # How many incorrect answers in a row do you need to step up a level?
stepSizeDown = .25 # If the current staircase value is 1, how much do you subtract to get to the next level down?
stepSizeUp = 1 / (1 - stepSizeDown) - 1 # This assumes that staircase values are fixed

ratio = stepSizeUp / (stepSizeDown + stepSizeUp)

exponent = downRule / upRule
inverseExponent = 1 / exponent # because we're solving in reverse

# the percent correct target
ratio ^ inverseExponent