I have a minor point: Should the match probability be calculated after subtracting N-back from the trial count? That way the actual match probability is reflected in the trials where a match is possible?

For example, in a dual 4-back session with 24 trials and a match rate of 0.25 means that there are 6 possible audio and position matches each. But there are no possible matches on the first 4 “trials”, so technically there are 20 trials where a match is possible. The actual probability of matches is then 6 / 20 which is 0.3. It’s not a big deal for lower n-back, but perhaps it changes the game as one progresses towards 8-back or even higher.

For 8 back with 28 trials, if you specify a match probability of 0.25, 28 * 0.25 = 7. That means 7 out of the 20 trials have possible matches. So the real match rate is over 1 / 3, not 1 / 4, which does change the game a bit. The only way right now to get as close as possible to the actual specified match probability is to do more trials.

If it’s too much to change the back end, maybe you could allow the match probability to be between 0 and 1 so users can set as an easy fix? Another one is to just allow the user to set the actual number of matches, in addition to the match probability.