Guide · 5 min read
Why you cannot guess the colour of a black-and-white photo
Turning an image greyscale does not hide colour, it destroys it. The arithmetic that throws the information away, and why most versions of this test are broken anyway.
A photograph of a balloon, in black and white. Was it red or blue? It feels as though the answer ought to be in there somewhere, faintly, recoverable if you look hard enough. It is not. The conversion that made the image grey did not conceal the colour — it discarded it, and the arithmetic is worth seeing because it explains exactly why.
Three numbers into one
A colour on a screen is three numbers: how much red, how much green, how much blue. Greyscale conversion collapses those three into one, by weighted average. The weights in standard use are roughly:
- Red × 0.2126
- Green × 0.7152
- Blue × 0.0722
They are not equal because human vision is not equal. Our eyes are far more sensitive to green light than to blue, so a green and a blue of the same physical intensity do not look equally bright, and a conversion using equal weights produces images that look wrong. These weights approximate perceived brightness instead.
The consequence is arithmetic, not opinion. Three numbers went in; one came out. Infinitely many colours map to the same grey — a middling red, a dark yellow, a bright blue can all resolve to precisely the same value. Once the conversion has happened, no amount of looking recovers which one it was, because the information is not attenuated. It is gone.
Why most greyscale guessing games are broken anyway
The information about which colour is destroyed. But the information about brightness survives perfectly — that is the one number that came out. And real colours, as they happen to occur in photographs, are not brightness-matched. A saturated blue is intrinsically dark: its brightest possible value, at full saturation, is a little over seven per cent of white. A saturated yellow is intrinsically bright, at over ninety per cent.
So desaturate a photograph of a red balloon and a blue balloon and the blue one comes out noticeably darker — every time, reliably, as a matter of arithmetic. A player who notices this is not using intuition. They are reading a brightness cue, and the “intuition test” has quietly become an eyesight test that a careful observer can win.
How to make the test actually fair
The fix is to remove the surviving cue as well. Before any colour is shown, each option’s lightness is adjusted until every option has the same computed brightness — using the same weights above, so the match holds under exactly the conversion that will be applied. Then the colour is removed.
The result is that every panel renders as the identical grey. Not similar: identical, to within one level out of 255, which is below the threshold at which any display or any eye could separate them. There is no cue left, and your odds are exactly one in two or one in three depending on how many options are showing.
One constraint falls out of this and is worth mentioning because it shaped the game. Matching everything to a middling grey means darkening the bright hues considerably, and a yellow dark enough to sit at mid-grey no longer reads as yellow — it reads as olive. So yellow is not used. Asking “which one is yellow?” and revealing a brown-ish swatch would feel like a cheat even though the scoring was perfectly fair, and the reveal is the one moment the test cannot afford to lose your trust.
For the same reason, options are always kept well apart on the colour wheel. Ask for red and offer pink beside it and a player who picked the pink one, told it was the wrong red, is entitled to be annoyed.
What is left to measure
Nothing, and that is the point. With the brightness cue removed, the test measures your luck and reports it honestly against what luck should produce. Over enough attempts your average will settle onto the chance line, because that is what a fair coin does. The enjoyment is not in discovering a hidden ability. It is in the moment the colour comes back.
Written for Intuition Rank. Corrections welcome at hi@parallelugc.com.