# How can I design a staircase function that converges on a given hit-rate?

I'm in the process of creating a simple contrast staircase function where subjects are initially presented with high-contrast Gabor patches and are subsequently queried as to their orientation in a forced-choice task.

I only understand staircase functions superficially, which is to say that I conceive them as follows:

1. present a stimulus
2. query some feature of the stimulus
3. If correct, reduce the intensity of the stimulus by n, else increase its intensity by m where m < n.

Intuitively, it seems like this should converge on a hit-rate of .5, but I know for a fact that a staircase can be designed to converge on an arbitrary hit-rate. How would I modify my simplistic algorithm to converge on, say, .8 ?

Thank you!

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If n != m then it will not home in on the 50 % threshold. In these simple N-up/N-down staircases, you can modify either the stepsize (as you proposed) or the number of successes/failures to act as a criterion for upgrade/downgrade.