Not How Many
Choosing takes time, and the price is not set by how many options you have. It is set by how surprised you are by the one that came. This page will show you eight options twice and make one of those two blocks a full bit cheaper without removing anything.
Yesterday this lab measured your hand as a channel with a bit rate. Fitts, 1954, and the finding that the distance to a target is free. Today is the same shape of law pointing the other way, and it was written eight years earlier in the same units.
The version of Hick's law that gets quoted in design books is the weak one: reaction time grows with the logarithm of the number of choices, used ever since as an argument for shorter menus. That is not what Ray Hyman showed in 1953. Hyman held the number of alternatives fixed and changed only how often each one came up, and reaction time tracked the entropy anyway.
The number of options is not in that formula. It is in the popular version only because equally likely options are the one special case where H happens to equal log2(N). Move the probabilities and the two come apart, and that gap is the experiment you are about to run on yourself.
Five blocks. Four are the classic ladder: 1, 2, 4 and 8 equally likely boxes, so H = 0, 1, 2, 3 bits. A box lights, you press its key, that is the entire task.
The fifth block has eight boxes, the same eight keys as the 8-block, and you will not be told anything else about it. One box will come up half the time, one a quarter of the time, and the remaining six once in twenty four. Eight options carrying 2.15 bits instead of 3.
So the headline is three measured averages and nothing fitted. If the price is set by the number of options, the skewed block costs exactly what the 8-block costs, because both have eight. If Hyman was right, it lands next to the four-option block. Those two predictions are not close, and your hands pick between them.
The obvious way to build this is to make you tap whichever box lit up. That is a Fitts task wearing a Hick costume: more options means smaller boxes further apart, movement time climbs for reasons that have nothing to do with choosing, and the slope comes out inflated by an amount nobody can separate afterwards.
So the response set here is fixed. Eight boxes, always all eight on screen, always the same size in the same places. What changes between blocks is how many of them can light, never where they are. On a keyboard your fingers rest on the keys and there is no travel at all. On a touchscreen there is a little, so the page measures it and prints the slope with it and without it.
- Lag lands in the intercept. A reaction time here is an absolute latency and every bit of your machine is inside it: display pipeline, key scan, USB polling, the event loop. This page has no idea how much, and does not need to. That lag is the same constant on every trial in every block, and a constant added to every point on a line moves the intercept and cannot touch the slope.
- The headline is a difference. Two block means subtracted from each other, so the constant cancels there outright rather than folding into a parameter.
- Bits have no units. The x axis is entropy, so it is the same axis on a 240 Hz gaming monitor and on a phone.
- What can reach it: jitter, not lag. Variable frame delivery adds noise to every trial and widens every interval, so frame gaps are measured live and printed. And a browser that coarsens its clock against fingerprinting quantises every number here, which is detected from your own data and refused.
- ⌨️ Rest four fingers on A S D F and four on J K L ; and leave them there. Touch works too: the boxes are tappable.
- ⚡ Answer as fast as you can without making mistakes. Both halves are measured.
- 🔴 A wrong key gets a red flash. That is the only feedback on this page, and it is there to keep the mapping honest, not to teach you anything.
- 🧊 Sixteen practice trials first, thrown away. Then five blocks in a shuffled order.
- ⏱️ About four and a half minutes. Nothing is recorded, nothing leaves the page. Escape aborts.