Why Being Twice as Big and Half as Small Score the Same

In Plain Game, guessing 200 for a target of 100 earns exactly as many points as guessing 50. That surprises people who expect a miss of 100 to be worse than a miss of 50. The reason is simple: for positive numbers, the game compares your answer with the target as a ratio, not as a difference.

This guide shows what that means in practice, how many points typical misses are worth and how to choose a number when you are unsure. The exact rules are on the scoring page; here the focus is on using them.

The formula in one line

For a positive target and a positive answer, the base score is round(100 × exp(−2 × abs(ln(answer / target)))). You never need to calculate it during a flight. What matters is the shape: the score depends on how many times too high or too low you are, and it falls smoothly as that factor grows.

An answer within a factor of 1.01 of the target also earns a Bullseye and 25 bonus points, which is why a near-perfect guess can be worth 125 rather than 100.

What common misses are worth

Here are base points for a positive target, before any Bullseye bonus or golden-round doubling:

Two things stand out. First, a 10% error costs only 17 points, so there is little reason to freeze over the last digit. Second, once you are off by a factor of five, almost everything is gone. The biggest gains come from getting the order of magnitude right, not from polishing a number that is already close.

Why high and low guesses are treated alike

Imagine a question about the height of a building. If you guess 200 metres for a 100-metre building, you were twice too tall. If you guess 50 metres, you were twice too short. In everyday terms these are mistakes of the same size: each misjudges the scale by a factor of two. A subtraction-based score would punish the high guess twice as hard, which would push players to guess low to be safe. Ratio scoring removes that incentive.

It also means a tiny target and a huge target are treated fairly. Missing a 40-year-old date by two years is nothing like missing a distance of thirty thousand kilometres by two kilometres, and a ratio compares each against its own scale.

How to choose a number when you are unsure

When you cannot narrow the answer down, treat your uncertainty as a range and pick the middle in ratio terms, not in simple terms. If you think the answer is somewhere between 100 and 10,000, the ratio-midpoint is 1,000, not 5,050. From 1,000 you are at most ten times off in either direction. From 5,050 you could be 50 times too high.

A practical routine:

1. Decide the unit and a rough low and high bound, ignoring precision.
2. Multiply the bounds and take the square root. That is the number that is equally far from both ends, measured in factors.
3. Nudge towards any clue you have, such as a comparison with something you know.

You do not need a calculator. Rounding to one significant figure and thinking "is this nearer ten times or a hundred times?" is enough for most questions. The companion guide on getting better at estimation covers reference points and splitting a problem into parts.

A zero answer and other edge cases

A zero answer to a positive target earns no accuracy points, because no ratio can be formed. If a question asks for a count or an amount, answer with at least a small positive number rather than 0. Calendar years are scored differently, by the number of years away, so the ratio idea does not apply there; the next guide covers estimating years.

Reading the reveal

After each answer, the reveal shows how far off you were, including notes such as "11× the target" when a miss is large. Use it as feedback on scale: did you misjudge the unit, the order of magnitude or only the final digits? Keeping a note of which of those three errors you make most often is the quickest way to improve over a week of daily flights.

You can read more about the labels, the golden round and altitude in the FAQ and in the scoring examples. Then open Plain Game and try a practice flight with the ratio idea in mind.