How to Get Better at What's Your Guess? Estimation Strategies That Hold Up

Most runs in What's Your Guess? do not end on a question that was impossible. They end on a slip: a zero dropped, a unit misread, a figure per day treated as a figure per year. The ten-times margin is generous, and the players with long streaks are mostly the ones who stopped giving it away.

What follows is a set of habits, roughly in the order you would use them on a question. None of them needs a head for maths. They need a little patience, and the game gives you all the time you want: there is no clock on a question.

Three things on the card decide the answer's size, and all three are easy to skim past.

• The unit in the box. It tells you what you are counting. If it says "Olympic pools" or "elephants", the question is a comparison, and the answer is one quantity divided by another.
• The line under the question. Many questions carry one, fixing a year, a definition or what counts as full. It is there because the answer depends on it.
• The exact wording. "How many times as tall" and "how many more" are different questions. So are "per day" and "per year", and "laid end to end" and "stacked".

A careful read costs ten seconds. A misread costs a run.

Almost every question can be tied to a number you already carry: the world's population, the distance around the Earth, the seconds in a day, the weight of a car. Start from the nearest anchor and move outwards, rather than pulling a number out of the air.

If you find you have no anchor at all for a type of question, that is worth fixing between runs. We keep a list of numbers worth knowing for estimation, each rounded to something easy to remember.

One number you cannot know becomes three or four you nearly do. Most questions take one of two shapes.

A chain multiplies. Take an invented question: how many litres of milk does a primary school drink in a school year? Say 300 pupils, a small carton each of about 0.2 litres, and around 190 school days. 300 × 0.2 × 190 is about 11,000 litres. Each piece is a guess, but each is a guess you can make.

A comparison divides. How many cats weigh as much as a horse? A horse is roughly 500 kg and a cat roughly 4 kg, so about 125. The trick with comparisons is to put both things in the same unit before you divide, and to write the unit down beside each figure.

You can type a chain straight into the answer box, as 300 × 0.2 × 190, and the box works it out. The calculator beside it has a scratch pad for the pieces.

The scoring is generous about the first digit and strict about the number of digits. So the most useful way to hold an estimate is as a power of ten: 300 is 3 × 10², 0.2 is 2 × 10⁻¹, 190 is about 2 × 10².

Written that way, multiplying is adding exponents. 10² × 10⁻¹ × 10² is 10³, and the leading digits 3 × 2 × 2 make 12, so the answer is about 12 × 10³, or 12,000. You can do that in your head, and you can see at a glance whether the answer is in the thousands or the millions, which is the thing that matters.

Round every piece to one significant figure, or to 1, 2, 3 or 5 times a power of ten. A rounding that moves a piece by 20% is invisible next to a margin of ten times.

Two rules keep rounding honest. Round some pieces up and some down, so the errors cancel rather than pile up. And never round the same way twice on purpose to make the sum easier: four pieces each rounded up by half end up five times too big.

This is the single most useful idea in the game. A guess survives anywhere from a tenth of the answer to ten times it, so the safe window around your guess is a hundred times wide. If you can say "it is somewhere between A and B" and B is no more than 100 times A, there is a guess that cannot lose: the middle of A and B on a log scale.

That middle is not the ordinary average. Between 2,000 and 50,000, the average is 26,000, but the log-scale middle is 10,000, the square root of 2,000 × 50,000. A guess of 10,000 survives anything from 1,000 to 100,000, which covers your whole range. A guess of 26,000 would lose if the answer were the 2,000 at your lower end.

There are two quick ways to find it. Take the middle of the exponents: between 10³ and 10⁵ the middle is 10⁴. Or let the box do it, since it understands powers: type (2,000 × 50,000)^0.5 and it reads 10,000.

When your honest range is wider than a hundred times, no guess is safe. The middle is still your best bet, but it is a sign to find the piece of the problem you are least sure about and think harder about that one. Being honest about how wide your range really is turns out to be a skill of its own, and most people's ranges are too narrow; we look at that in overconfidence in estimates.

• Size grows faster than you think. A ball twice as wide holds eight times as much, and a square twice as long covers four times the area. Questions about filling or covering things punish linear thinking.
• Gaps between things. Balls poured into a container fill only about 64% of it, and a ball sitting in its own cube fills about 52%. Leave room for air.
• Per what. Check whether a rate is per second, per day or per year before you multiply, and say the units aloud as you chain them.
• Percentages have a ceiling. On a percent question an answer of 30% lets anything from 3% to 100% survive, but an answer of 2% needs a guess between 0.2% and 20%. When you are unsure how small a share is, do not guess the very bottom.
• Time hides its scale. The same stretch is a small number of years and an enormous number of seconds. Before you type, check which unit your chain ended in and convert it to the one in the box.

The reveal is a free lesson. When you were far off, open How it adds up and read the working against your own. Usually one figure did the damage: you thought of a stadium of 10,000 when the working uses 80,000, or a car of 4 tonnes when it is nearer 1.5. Note the figure that surprised you. Over a few dozen runs, those notes become a set of anchors nobody else has.

When you were close, look anyway. Sometimes you were right for the wrong reasons, and two errors that cancelled once will not cancel next time.

From the ninth question of a run, every question comes from the hardest group. This is where patience pays. Use the scratch pad. Try two different routes to the same answer, say one from population and one from a physical size, and if they disagree badly, find out why before you type. If they roughly agree, take the log-scale middle of the two.

For more practice at the method itself, with nothing at stake, work through some guesstimate questions with worked answers, then bring the habits back to a run and see how far they carry you.