How to guess country populations in fewer tries using game theory and geography knowledge.
The fastest way to find an unknown number in a range is to cut the range in half with each guess. Computer scientists call this binary search, and it is provably optimal when all you get back is "higher" or "lower." In Popdle, that is exactly the feedback you receive.
Country populations span a huge range — from around 10,000 (Vatican City, Nauru, Tuvalu) up to roughly 1.4 billion (India, China). But you do not need to search that entire space blindly. Before you type a single digit you already know something about the country, and that prior knowledge lets you start with a much narrower range.
As soon as you see the country name, place it in a rough size bucket. Think about its continent, its physical area, and whether you associate it with a large or small population. You do not need to be precise yet — just pick a plausible range.
Take the middle of your range. For Colombia you might guess 55 million. If the answer is "lower," your new range is 30–55 million. If "higher," it is 55–80 million. Either way you have eliminated roughly half the possibilities.
Repeat the process. If Popdle said "lower" after 55 million, guess about 42 million next. After two rounds of halving, your range is typically narrow enough that you are already within 25% (orange zone) or 10% (yellow zone).
Once you are in the yellow or green zone, small adjustments are all you need. At this stage, think about whether you are slightly above or below and adjust by a few million (or a few hundred thousand for smaller nations).
In information theory, each yes/no answer gives you exactly one bit of information. The more bits you collect, the faster you zero in on the answer. A guess of "1 million" against a country that obviously has 200 million people wastes your guess — you already knew the answer was higher, so you gain zero useful information.
The ideal guess is one where you consider both outcomes equally likely. If you genuinely think a country has between 20 and 60 million people, guessing 40 million is better than guessing 25 million, because 40 million splits your uncertainty evenly. This is the principle of maximum entropy reduction — each guess should eliminate as much uncertainty as possible.
Memorizing a handful of anchor populations gives you starting points for comparison. Here are some useful benchmarks organized by region:
| Region | Country | Population (approx.) |
|---|---|---|
| Asia | India | 1,430 million |
| Asia | China | 1,410 million |
| Asia | Indonesia | 275 million |
| Asia | Japan | 124 million |
| Asia | Philippines | 115 million |
| Americas | United States | 335 million |
| Americas | Brazil | 215 million |
| Americas | Mexico | 130 million |
| Americas | Colombia | 52 million |
| Americas | Argentina | 46 million |
| Europe | Germany | 84 million |
| Europe | France | 68 million |
| Europe | United Kingdom | 67 million |
| Europe | Italy | 59 million |
| Europe | Spain | 48 million |
| Africa | Nigeria | 220 million |
| Africa | Ethiopia | 125 million |
| Africa | Egypt | 105 million |
| Africa | DR Congo | 100 million |
| Africa | South Africa | 60 million |
| Oceania | Australia | 26 million |
| Oceania | New Zealand | 5 million |
New players often guess 1 million or 2 million as a safe starting point. But most countries have populations well above 10 million, so this guess wastes a turn telling you something you could have figured out from context. Start higher unless you are confident the country is very small.
The win condition is within 5%, which means the absolute size of your acceptable error scales with the country. For a country of 100 million, you need to be within 5 million. For a country of 1 million, you need to be within 50,000. This means small countries require more precise guessing in absolute terms, even though the percentage target is the same.
If your guess is in the red zone ("Very Far," more than 25% off), you need a big adjustment — not a small one. A common trap is guessing 50 million, getting "Very Far / higher," and then guessing 55 million. That five-million jump is only a 10% change, which is unlikely to get you out of the red. You should be doubling or halving, not nudging.
Suppose you know the population lies somewhere between L (low) and H (high). A perfect binary search narrows this to a range of (H−L)/2n after n guesses. You win when that remaining range is smaller than 10% of the true population (5% above and 5% below).
For a country with a population of P, you need (H−L)/2n ≤ 0.10 × P. Rearranging: n ≥ log2((H−L) / (0.10 × P)). If your initial range is 200 million wide and the true population is 80 million, you need at least log2(200/8) ≈ 4.6 guesses — so five guesses with good binary search should do it, leaving one guess as a safety margin.
The takeaway: the tighter your initial range estimate, the fewer guesses you need. This is why geographic knowledge is so powerful — it shrinks your starting range before you even begin.
After finishing the daily Popdle puzzle, use practice mode to drill countries you find difficult. Over time you will build a mental map of population sizes across the world. Many players find that after a few weeks of daily play, they can guess most countries in two or three tries.
Popdle uses live data from the World Bank and Wikidata, so you are always working with current figures — a good way to stay up to date on how the world is changing.