Summary: Fermi Poker is an estimation game that combines the betting mechanics of poker with making estimates about questions like "How many dentists work in the US?"
Tags: small to large, experiment, repeatable
Note: Fermi Poker works with as few as three players (or even two), and scales to dozens or even hundreds in a tournament format. If possible, seat no more than six players per table, preferably at round tables, with enough space between them that everyone can write down their guess secretly.
Purpose: Rationality training with a bit of socializing. The game involves Fermi estimation, calibration, Bayesian updating, world-modeling, and perspective taking. You also get to know the other players better and find out how they think about all kinds of topics.
Materials:
Each player needs an equal stack of chips and writing supplies. A standard 500-chip poker set (around $60) usually covers up to 20 players. For writing down guesses, pen and paper work great, as do mini-whiteboards with dry-erase markers. You’ll also want the one-page rule sheet to hand out, ideally one per table.
You also need enough questions, each with two hints and an answer.
The easiest, least effort way to get those is fermi.org/play. One person per table opens the site on their phone, and everyone reads that. If a question repeats or someone at the table has seen it before, just skip to the next question. (You're on the honour system!) This is ideal if the organizer also wants to play.
If you prefer physical cards, you can download a 63-question set here. Print the question, hint and answer cards on 160 gsm paper or thicker so nothing shows through, then cut them out. You can also put the cards into envelopes for a more premium feel.[1] As the organizer, you can also write your own questions, for example about your university, city or country.
You can also let players write questions, either at home before the meetup or in a 20-minute question-writing session at the start. Players sit out any question they wrote.
(If you or your players think you've come up with good questions and want to share them with others, send the questions, hints, and answers to contact@fermi.org!)
You’ll need a clock if you want to raise the ante[2] on a fixed schedule (a phone timer works fine). An example schedule is shown later in the description. Alternatively, raise the ante whenever it looks like the game will run too long.
Announcement Text:
We're planning to host a Fermi Poker tournament. The game is like poker, but instead of random playing cards, you get to answer Fermi estimation questions like “How many smartphones were sold worldwide last year?” You secretly write down a range, bet on it, get two hints, bet again, and the narrowest range that contains the answer wins, unless someone bluffs everyone else out first. No poker experience or math background needed; we’ll explain everything at the start. Chips have no cash value, and there is no gambling involved - just skill and wits!
Description:
1. Form groups and hand out supplies
Form groups with around four to six players, each at their own table. Each table should have at least one copy of the rules handout, one stack of question, hint and answer cards (or a phone with fermi.org/play loaded), and enough chips for each player. (Poker chip sets come with different values. A good default is to give each player chips worth 1,000, with the ante starting at 25.)
More about poker chip sets without printed values
If your chips only have colors and no printed values, assign the values yourself. Most 500-chip sets come as 150 / 150 / 100 / 50 / 50 chips per color, which can give up to 20 players a stack worth 1,000 each if done correctly.
Make the two colors with 150 chips worth 25 and 50, and the color with 100 chips worth 100. Each player gets 6 × 25, 7 × 50 and 5 × 100, which is 18 chips worth 1,000.
The leftover chips stay with the organizer for making change. The two colors with 50 chips become 500s and 1,000s. Later in the game, players can trade stacks of small chips for these, which poker players call “coloring up.” Otherwise, in a bigger tournament, the chip leader at the final table could end up with a pile of 200 or more small chips.
2. Once people are settled, explain the rules (about 5 minutes; you can read this aloud!)
Fermi Poker is like poker, but instead of being dealt random cards, you make estimates about Fermi questions, like "How many new smartphones were sold worldwide last year?"
After a question like this is revealed, everyone secretly writes down a range they believe contains the correct answer. Since you probably don't know the answer, you can break the question down the way Enrico Fermi would. So, about 8 billion people live on Earth. If everyone bought a new smartphone every four years, that would be about 2 billion phones sold per year. But small children and very old people often don't have one, so we have to subtract them. Maybe those are 2 billion people, and then another billion might not be able to afford a smartphone. That leaves us with about 5 billion people, which would mean that roughly 1.25 billion phones are sold per year. So your estimate might be "1 billion to 1.5 billion". Once betting starts, you can't change your range.
Speaking of betting, there are four betting rounds: one after everyone has written down their guess, one after the first hint, one after the second hint, and one after the answer is revealed.
Betting works like in poker and moves clockwise around the table. When it’s your turn, you can bet as many chips as you want, which the others then have to match to stay in. Matching a bet is known as calling. If someone is very confident, they can raise, which means putting in an even larger bet than yours. Or they can fold, meaning they give up on this question. That’s best if they’re completely unsure, or think the other players have better estimates.
If nobody has bet before you in a betting round, you can also just pass the action to the next player; that’s called checking. If everyone checks, the betting round ends without any bets. Otherwise, it ends once everyone has either matched the highest bet or folded.
So, what about the hints we mentioned earlier? A hint could be, for example, the number of new smartphones sold in Africa last year. You can’t change your range, but the hint can help you decide how much to bet, or whether to fold if it suggests you’re way off.
At the showdown, which comes after the last betting round, everyone remaining reveals their range, and the narrowest range that contains the answer wins the pot. Say two players remain, one with a range of "1 billion to 2 billion" and you with "1 billion to 1.5 billion". If both ranges contain the answer, you win, because yours is 500 million narrower.[3] If nobody's range contains the answer, the range whose midpoint is closest wins. And if everyone else folds before the showdown, you win without having to show your range at all, so a terrible guess can still win if you bluff well enough.
A few more things: before each question is revealed, everyone has to pay the ante, a small mandatory bet. It goes up over time, so you can't wait forever for a question you're sure about. For the first question, the youngest player at each table acts first during the betting rounds. For the next question, the player on their left acts first, and so on. And please don't use calculators or the internet. Any questions? If not, we can play a quick practice round!
Note: The description above leaves out a few rules concerning minimum bet size, all-in mechanics, side pots, and ties. They’re all on the rule sheet, or you can see them here:
Ranges include both endpoints. Any clear and unambiguous notation works: be it 3,000,000, 3M, 3 million or 3 × 10⁶.
The minimum bet size is the current ante, and a (re-)raise must be at least as big as the last bet or raise in that betting round.
You can go all-in by betting all your chips at any time, even if what you have left is less than the highest bet. You can only win as much from each player as you put in yourself. Extra bets go into a side pot that only the players who paid into it can win. If you can’t pay the ante, you’re automatically all-in.
When everyone, or all but one, is all-in, no more betting is possible. Read the remaining hints and the answer, then go straight to the showdown.
If two ranges are equally narrow and both contain the correct answer, split the pot.
3. Play (about 1–3 hours)
Start with a practice round that doesn’t count. Then hand the chips back and start for real.
A player with no chips left is out, but can stay seated for a while and keep guessing for fun, just without betting. If you have several tables, merge them as players drop out, until one final table remains.[4] Players who are out can also play casual games together or just socialize.
If you want to use a fixed ante schedule, here’s a good default for players starting with chips worth 1,000:
25: first 20 minutes
50: 20-40 minutes
75: 40-60 minutes
100: 60-80 minutes
150: 80-100 minutes
200: 100-120 minutes
300: 120+ minutes
The game ends when one player has all the chips. If your meetup has a fixed end time, you can instead stop on time, and whoever has the most chips wins.
Variations:
60-second clock
Once half the players have written down their guesses, the rest have 60 seconds. Use a phone timer or a one-minute sand timer. A time limit like this is less awkward than having to constantly urge a player who keeps everyone else waiting. Alternatively, all players have 60 seconds, or another fixed time, from when the question is revealed.
Single numbers or powers of ten instead of ranges
Guess a single number instead of a range, or allow only powers of ten (101, 102, 103…)
Determine the winning range using a log scale
Judge ranges by how many times bigger the high endpoint is than the low endpoint, instead of by the difference between them. If the correct answer is 600, “500–1,000” (ratio 2) would then beat “200–600” (ratio 3). This fits order-of-magnitude thinking better, but it’s harder to calculate quickly, and for most questions it makes little difference, so we slightly prefer the standard rule.
Mirror card: copy another player’s guess without seeing it
Each player can use one Mirror card (or coin, or whatever else you use for it) per game. Instead of a range, you write down the name of another player and put your Mirror card in the middle of the table, so everyone can see you’ve used it. You now have the same guess as that player: their range is also yours, even though you don’t know what it is.
When you reveal at the showdown, the player you named must show their range too, even if they folded. It’s the only time a player who folded has to show their guess.
Mirrors can chain: if Alice names Bob and Bob names Carol, Alice and Bob both get Carol’s range.
If a chain loops back on itself, for example when Alice names Bob and Bob names Alice, every guess in the loop is invalid. Invalid guesses lose to any valid range at the showdown, but can still win if everyone else folds. If only invalid guesses are left, they split the pot.
While a Mirror card is on the table, nobody may erase their guess before the question is over, even after folding, because anyone could turn out to be the player who was named.
Vary the topic of questions
You can make the questions be about a particular field, like literature, charity, or astronomy. You can also aim for easier or harder questions depending on your audience, though judging difficulty can be tricky!
Blinds instead of antes
Instead of everyone paying an ante, only two players pay forced bets before each question: the two seated to the right of whoever acts first for that question. One pays a small blind (half the minimum bet), the other a big blind (the minimum bet), and everyone else must at least match the big blind to stay in. Players who haven’t paid anything can fold questions they don’t like for free.
Notes:
The betting typically confuses non-poker players more than the estimating. If you can, seat one person who knows poker at each table.
You may want to open the evening with a short introduction to Enrico Fermi and his famous question about how many piano tuners work in Chicago, or the time he estimated the yield of the first atomic bomb test by dropping scraps of paper.
Chips should have no cash value. A small prize can add some excitement, though. But don’t fund it through entry fees, since that starts to look like gambling. Instead you might want to ask a local business to provide a gift card or some of its products for the prize pool.
If you're excited about Fermi Poker, or want to receive support in running a tournament, please reach out at https://fermi.org/host/ or get in touch at contact@fermi.org.
The cards are 9.44 × 6.39 cm (3.72 × 2.52 inches), so they fit standard 4 × 2.75-inch mini envelopes (like these) or European C7 envelopes. Put each question’s cards into their own envelope, in order, so the question comes out first, then hint 1, hint 2 and finally the answer.
This format is called a freezeout, and it’s what we recommend, because rebalancing tables as players drop out keeps the game running smoothly. The alternative is a shootout: each table plays on its own until only one or two players are left, who then move on to a final table (or to semifinals first). Its big advantage is that players who are out can stay at their table and keep guessing along until it finishes. In a freezeout, they can do the same for a while, but eventually have to make room when tables are merged.
Summary: Fermi Poker is an estimation game that combines the betting mechanics of poker with making estimates about questions like "How many dentists work in the US?"
Tags: small to large, experiment, repeatable
Purpose: Rationality training with a bit of socializing. The game involves Fermi estimation, calibration, Bayesian updating, world-modeling, and perspective taking. You also get to know the other players better and find out how they think about all kinds of topics.
Materials:
Each player needs an equal stack of chips and writing supplies. A standard 500-chip poker set (around $60) usually covers up to 20 players. For writing down guesses, pen and paper work great, as do mini-whiteboards with dry-erase markers. You’ll also want the one-page rule sheet to hand out, ideally one per table.
You also need enough questions, each with two hints and an answer.
(If you or your players think you've come up with good questions and want to share them with others, send the questions, hints, and answers to contact@fermi.org!)
You’ll need a clock if you want to raise the ante[2] on a fixed schedule (a phone timer works fine). An example schedule is shown later in the description. Alternatively, raise the ante whenever it looks like the game will run too long.
Announcement Text:
Description:
1. Form groups and hand out supplies
Form groups with around four to six players, each at their own table. Each table should have at least one copy of the rules handout, one stack of question, hint and answer cards (or a phone with fermi.org/play loaded), and enough chips for each player. (Poker chip sets come with different values. A good default is to give each player chips worth 1,000, with the ante starting at 25.)
More about poker chip sets without printed values
If your chips only have colors and no printed values, assign the values yourself. Most 500-chip sets come as 150 / 150 / 100 / 50 / 50 chips per color, which can give up to 20 players a stack worth 1,000 each if done correctly.
Make the two colors with 150 chips worth 25 and 50, and the color with 100 chips worth 100. Each player gets 6 × 25, 7 × 50 and 5 × 100, which is 18 chips worth 1,000.
The leftover chips stay with the organizer for making change. The two colors with 50 chips become 500s and 1,000s. Later in the game, players can trade stacks of small chips for these, which poker players call “coloring up.” Otherwise, in a bigger tournament, the chip leader at the final table could end up with a pile of 200 or more small chips.
2. Once people are settled, explain the rules (about 5 minutes; you can read this aloud!)
Note: The description above leaves out a few rules concerning minimum bet size, all-in mechanics, side pots, and ties. They’re all on the rule sheet, or you can see them here:
3. Play (about 1–3 hours)
Start with a practice round that doesn’t count. Then hand the chips back and start for real.
A player with no chips left is out, but can stay seated for a while and keep guessing for fun, just without betting. If you have several tables, merge them as players drop out, until one final table remains.[4] Players who are out can also play casual games together or just socialize.
If you want to use a fixed ante schedule, here’s a good default for players starting with chips worth 1,000:
The game ends when one player has all the chips. If your meetup has a fixed end time, you can instead stop on time, and whoever has the most chips wins.
Variations:
60-second clock
Once half the players have written down their guesses, the rest have 60 seconds. Use a phone timer or a one-minute sand timer. A time limit like this is less awkward than having to constantly urge a player who keeps everyone else waiting. Alternatively, all players have 60 seconds, or another fixed time, from when the question is revealed.
Single numbers or powers of ten instead of ranges
Guess a single number instead of a range, or allow only powers of ten (101, 102, 103…)
Determine the winning range using a log scale
Judge ranges by how many times bigger the high endpoint is than the low endpoint, instead of by the difference between them. If the correct answer is 600, “500–1,000” (ratio 2) would then beat “200–600” (ratio 3). This fits order-of-magnitude thinking better, but it’s harder to calculate quickly, and for most questions it makes little difference, so we slightly prefer the standard rule.
Mirror card: copy another player’s guess without seeing it
Each player can use one Mirror card (or coin, or whatever else you use for it) per game. Instead of a range, you write down the name of another player and put your Mirror card in the middle of the table, so everyone can see you’ve used it. You now have the same guess as that player: their range is also yours, even though you don’t know what it is.
When you reveal at the showdown, the player you named must show their range too, even if they folded. It’s the only time a player who folded has to show their guess.
Mirrors can chain: if Alice names Bob and Bob names Carol, Alice and Bob both get Carol’s range.
If a chain loops back on itself, for example when Alice names Bob and Bob names Alice, every guess in the loop is invalid. Invalid guesses lose to any valid range at the showdown, but can still win if everyone else folds. If only invalid guesses are left, they split the pot.
While a Mirror card is on the table, nobody may erase their guess before the question is over, even after folding, because anyone could turn out to be the player who was named.
Vary the topic of questions
You can make the questions be about a particular field, like literature, charity, or astronomy. You can also aim for easier or harder questions depending on your audience, though judging difficulty can be tricky!
Blinds instead of antes
Instead of everyone paying an ante, only two players pay forced bets before each question: the two seated to the right of whoever acts first for that question. One pays a small blind (half the minimum bet), the other a big blind (the minimum bet), and everyone else must at least match the big blind to stay in. Players who haven’t paid anything can fold questions they don’t like for free.
Notes:
The cards are 9.44 × 6.39 cm (3.72 × 2.52 inches), so they fit standard 4 × 2.75-inch mini envelopes (like these) or European C7 envelopes. Put each question’s cards into their own envelope, in order, so the question comes out first, then hint 1, hint 2 and finally the answer.
The ante is a small mandatory bet everyone pays before each question. It goes up over time, so nobody can just wait for a question they’re sure about.
Some groups prefer to judge ranges on a log scale; see the section on game variations for more information on that.
This format is called a freezeout, and it’s what we recommend, because rebalancing tables as players drop out keeps the game running smoothly. The alternative is a shootout: each table plays on its own until only one or two players are left, who then move on to a final table (or to semifinals first). Its big advantage is that players who are out can stay at their table and keep guessing along until it finishes. In a freezeout, they can do the same for a while, but eventually have to make room when tables are merged.