Fill Level Volume Estimation Game

About Fill Level

Fill Level shows you a single glass with some blue liquid in it and asks one question: how full is it, by volume? You answer with a slider from 0 to 100 percent and lock in your guess. The first rounds use a plain straight-sided glass, where the height of the liquid and the amount of liquid are the same thing, so a glass filled to the 40 percent mark is simply 40 percent full.

Then the shapes start to change. A funnel-shaped glass is narrow at the bottom and wide at the top, so the lower half of it holds far less than the upper half. A vase swells in the middle, and a bowl is wide and shallow. In these glasses the liquid line can sit at the halfway height while the glass is only a quarter or three quarters full. The game is built around that gap between what you see (height) and what you are asked about (volume).

How to play

1. Look at the glass. The outline is the full glass and the blue area is the liquid. Ignore the number on the slider until you have a first impression.
2. Ask yourself how much of the whole glass the liquid fills, not how high it reaches. If the glass gets wider toward the top, remember that the top slice holds more than the bottom slice.
3. Drag the slider, or use the minus and plus buttons to nudge your guess one percent at a time. Holding a nudge button scrolls faster.
4. Press Lock in before the timer runs out. The true value appears as a green marker on the slider and the game shows your score for the round.

Look at the glass and drag the slider to the percentage of its volume that is filled. Careful: wide tops hold more than they look.

How scoring works

Your score is based on the absolute error in percentage points. At the easiest setting a miss of 38 points gives a score of zero, and every point of error costs roughly 2.6 score points, so a guess that is 5 points off earns about 87. At the hardest setting the zero point shrinks to 22 points, so the same 5-point miss earns about 77 and only a guess within about 1 or 2 points reaches the 90s.

The timer starts at 16 seconds and drops to 11 seconds at the highest difficulty. If it runs out, whatever is currently on the slider is submitted, but a late answer counts for half. Difficulty also changes the glass: levels 1 to 3 use only straight glasses, levels 4 and 5 add the funnel, and from level 6 upward you can meet funnels, vases, bowls and straight glasses in any order.

What it trains

This game trains volume estimation and, more specifically, the habit of not trusting a single cue. Height is the cue the eye grabs first, but volume depends on the whole cross-section at every height. Learning to mentally slice a container into layers and weigh each layer by its width is a transferable skill.

It shows up when you pour from a carafe into a wine glass, judge how much paint is left in a tapered can, decide whether the last of the soup will fit in a bowl, or estimate how much fuel a tank on the ground still holds. Bartenders, cooks and anyone who eyeballs a pour do a quick version of this calculation without noticing.

Tips for a higher score

• Split the glass into a lower half and an upper half by height, then decide how much of the total each half holds. In the funnel here the top half holds roughly three quarters of the volume.
• Look at the width of the glass at the liquid line. A wide surface means the liquid has been getting wider all the way up, so the fill percentage is lower than the height suggests.
• For the vase, remember that the belly in the middle holds the most. A liquid line just below the belly is still a smaller share than it looks.
• On straight glasses, use landmarks: quarter, half and three quarters are easy to judge, and you only need to refine from the nearest landmark.
• Do not spend the whole timer. A first impression refined once usually beats a long deliberation, and a late answer is cut in half.

The idea behind it

People are good at judging height and width separately but notoriously bad at combining them into a volume. Jean Piaget's classic conservation experiments with children pouring liquid between a tall thin glass and a short wide one showed that even the idea of constant volume takes years to develop, and adults still show traces of the same bias when a tall narrow glass looks like it holds more than a short wide one.

Perception researchers have also found that people underestimate the capacity of wide containers and overestimate tall ones. Studies of drinking behavior have repeated this: people tend to pour more into short, wide glasses than into tall, slim ones while believing they poured the same amount. The error you correct for in this game is the same one that shapes real pours.

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