Each sheet has its own 🖨 Print sheet button — opens an isolated print window for that page only. No mixing.
Within each round, students freely swap cards — this is the trading mechanic. Between rounds, the teacher collects ALL Round 1 cards and replaces with Round 2 cards. The two sets have different point values and are not interchangeable.
"Every decision in this game depends on what everyone else decides. That's not just a game mechanic — it's how real economies work."
Welcome to Discover Economics — a programme by the Royal Economic Society that brings economics to students of all ages, wherever you are from, whatever school you go to.
A fast, physical card game. Each student gets one card. Find opponents. Reveal simultaneously. Score points. Win.
Gold · Silver · Bitcoin is a classroom card game for up to 100 players. Each student holds one card — Gold, Silver, or Bitcoin. They walk around the room, find opponents, and duel by revealing their cards at the same time. In Round 2 the point values change, and students can swap cards with each other before each duel.
One of three asset cards. Each has a different point value depending on which asset it faces. The card tells you everything you need to know.
One of three asset cards. Point values are printed on the card. Same win cycle applies in both rounds — only the numbers change in Round 2.
One of three asset cards. Can be traded in Round 2 — but you don't have to. Keeping your card is always a valid choice.
There is a rule printed on every card that tells you which asset beats which. Read your card — it has everything you need to play.
| Card type | Qty for 100 students | When used |
|---|---|---|
| 🥇 Gold, 🥈 Silver, ₿ Bitcoin — Round 1 | ~34 / ~33 / ~33 | Round 1 only |
| 🥇 Gold, 🥈 Silver, ₿ Bitcoin — Round 2 | ~34 / ~33 / ~33 | Round 2 only |
| 📋 Rules Card — Round 1 | ~18 cards | Reference during Round 1 |
| 📋 Rules Card — Round 2 | ~18 cards | Reference during Round 2 |
Print 4 sheets of each asset card type (9 per A4) and 2 sheets of each rules card type. Total: ~216 asset cards + 36 rules cards.
Round 1 and Round 2 use different distributions — for mathematical reasons, not arbitrary ones.
In Round 1 all wins are worth 2 points. The Nash Equilibrium for equal payoffs is exactly ⅓ each. Starting the room at that distribution means no asset has a structural advantage, and final scores cluster together — which is the direct, felt demonstration of equilibrium.
With asymmetric payoffs the equilibrium shifts to Gold ~17% · Silver ~37% · Bitcoin ~46%. Seeding at that distribution creates immediate, realistic trading pressure from the first duel rather than waiting for imbalance to develop. Students experience the market in motion from the start.
Divide the class size N by 3. The remainder (0, 1, or 2) is distributed as follows:
| N mod 3 | Gold | Silver | Bitcoin |
|---|---|---|---|
| 0 (e.g. 30) | N ÷ 3 | N ÷ 3 | N ÷ 3 |
| 1 (e.g. 40) | N ÷ 3 | N ÷ 3 | N ÷ 3 + 1 |
| 2 (e.g. 32) | N ÷ 3 | N ÷ 3 + 1 | N ÷ 3 + 1 |
The spare card(s) go to Bitcoin first, then Silver — never Gold — because Bitcoin dominates in Round 2 anyway, and this creates better opening trading tension.
Compute Gold and Silver by rounding to the nearest whole number. Bitcoin always gets the remainder — this guarantees the total is exactly N with no leftover cards.
| Asset | Formula |
|---|---|
| Gold | round(N ÷ 6) |
| Silver | round(N × 3 ÷ 8) |
| Bitcoin | N − Gold − Silver |
Bitcoin is calculated last as the remainder so rounding errors never accumulate. The result stays within 1–2 cards of the true NE proportions for any class size.
Quick-lookup table — how many of each card to print per round.
| Students (N) | Round 1 — Equal thirds | Round 2 — Nash Equilibrium seed | ||||
|---|---|---|---|---|---|---|
| 🥇 Gold | 🥈 Silver | ₿ Bitcoin | 🥇 Gold | 🥈 Silver | ₿ Bitcoin | |
| 15 | 5 | 5 | 5 | 2 | 6 | 7 |
| 20 | 6 | 7 | 7 | 3 | 8 | 9 |
| 24 | 8 | 8 | 8 | 4 | 9 | 11 |
| 25 | 8 | 8 | 9 | 4 | 9 | 12 |
| 30 | 10 | 10 | 10 | 5 | 11 | 14 |
| 35 | 11 | 12 | 12 | 6 | 13 | 16 |
| 40 | 13 | 13 | 14 | 7 | 15 | 18 |
| 45 | 15 | 15 | 15 | 8 | 17 | 20 |
| 50 | 16 | 17 | 17 | 8 | 19 | 23 |
| 60 | 20 | 20 | 20 | 10 | 22 | 28 |
| 75 | 25 | 25 | 25 | 12 | 28 | 35 |
| 100 | 33 | 33 | 34 | 17 | 38 | 45 |
Print 2–3 extra cards of each type per round. Cards get lost, torn, or pocketed during trading. Spare cards also let you correct the distribution mid-session if a card goes missing and one asset becomes noticeably scarce.
Understanding which cards can be swapped, and when, is essential to running the game correctly.
Round 1 cards and Round 2 cards have different point values printed on them. They are two separate sets. You cannot mix them. The teacher manages the transition between rounds by collecting all Round 1 cards and replacing the full deck with Round 2 cards.
The whole point of Round 2 is that the same game with different rewards produces different behaviour. If students held Round 1 cards (showing 8 pts per win) while others held Round 2 cards (showing 3 or 5 pts), they'd be playing a different game — and the lesson about incentives shaping behaviour would be lost.
Both students must agree. No one can be forced to trade. Refusing a trade is a valid strategic choice.
You swap your card for their card. You cannot hold two cards at once, and you cannot trade without getting something back.
During the trading window, do not show your card. Negotiation is verbal only. You may say what you hold — truthfully or not.
You may lie about what you're holding during negotiations. This is intentional — it mirrors real markets where information is incomplete and not always trustworthy.
Round 1 is pure strategy. Cards are fixed. Students can only choose who to challenge — not what to hold. The trading mechanic is exclusively a Round 2 feature.
When the teacher signals trading is over, everyone keeps whatever card they currently hold. Find an opponent and reveal simultaneously.
No trading. No negotiation. Just you, your card, and your read on the room.
Hand each student one Round 1 card — roughly equal thirds of Gold, Silver, and Bitcoin. Students should not compare cards yet. Distribute a Round 1 Rules card to each group for reference.
Cards are fixed throughout Round 1. Students keep their assigned card. Strategy means choosing who to challenge, not what to hold.
No. If someone challenges you, you play. You can choose who you approach — but you cannot turn down a challenge. Sitting out scores zero. Inaction is still a choice, and it has a cost.
Let students play freely for 5–8 minutes, circulating the room. Encourage them to play different opponents each time.
Cyclic — like Rock–Paper–Scissors.
| Outcome | Points |
|---|---|
| Win | +8 points |
| Lose | 0 points |
| Draw (same asset) | +1 point each |
Same game. Different rewards. Now you can trade. Everything changes.
Collect all Round 1 cards. Hand out one Round 2 card to each student — again roughly equal thirds. Do not allow students to carry Round 1 cards into Round 2. Distribute the Round 2 Rules cards.
| Win with… | Points |
|---|---|
| 🥇 Gold beats Silver | +3 pts |
| 🥈 Silver beats Bitcoin | +8 pts |
| ₿ Bitcoin beats Gold | +5 pts |
| Any draw (same asset) | +1 each |
Bitcoin vs Bitcoin = +1 point each. Not 5. The draw rule applies to all assets equally. Write this on the board.
That is for you to figure out. Read your card, look at who wins around you, and decide. The scoring table above tells you everything you need — the rest is your call.
Before each duel, a 45-second trading window opens. Students may swap cards with anyone willing.
Voluntary — both must agree
One-for-one — swap your card for theirs
Hidden — no showing cards, verbal only
Bluffing allowed — you may lie
Trades: refusable. Duels: not. Once trading closes and you face an opponent, the reveal happens. No one can turn down a duel.
If everyone holds Bitcoin and no one will trade, introduce: "No player may hold Bitcoin for more than 3 consecutive duels." Frame it as a regulatory intervention — itself a real-world lesson.
One box per duel. Fill in your points as you go. Total at the end.
Run the game first. Reveal the economics after. This page is for your eyes only before play begins.
Hand out cards. Explain only the rules printed on the cards. Do not discuss strategy, optimal choices, or what beats what beyond what is already printed. Let students discover.
Distribute Round 1 cards — equal thirds. 5–8 minutes of free duelling. Collect top scores. Brief debrief using the experiential questions on page 5.
Collect all Round 1 cards first. Distribute Round 2 cards. Announce the new point values. Open 45-second trading windows before each duel. Run 4–5 windows. Keep energy high.
Now reveal the economics. Use the questions and explanations on this page. This is where the concepts land — after students have felt them.
In Round 2, students will chase Bitcoin (5 pts). This is understandable — it looks best. Do not correct them. Let the room discover what actually happens.
As Bitcoin becomes common, Silver holders will quietly accumulate points. Don't point this out during play. Save it for the debrief — it lands much harder when students work it out themselves.
A handful of students may hold Gold throughout. If Silver becomes common (as it should at equilibrium), Gold earns 3 pts per duel — the highest reward. These students are doing second-order reasoning without knowing it.
"Everyone is going Bitcoin!" — true, false, or a deliberate bluff. Notice who says it and whether it changes behaviour. This is pure market dynamics.
If everyone holds Bitcoin and refuses to trade, invoke: "No player may hold Bitcoin for more than 3 consecutive duels." Frame it as a regulatory intervention — itself a lesson worth noting.
Trading: yes. Refusing a trade is a valid strategic choice — that is what voluntary exchange means.
Duels: no. Once trading closes and you face an opponent, the reveal happens. You cannot opt out.
If a student refuses to play, they score zero for that round. Frame it as their decision: "Sitting out is a choice — but it has a cost." That is itself an economics lesson: inaction is still a decision, and markets do not wait for you.
Ask each question after both rounds. Let students answer first, then read the explanation aloud.
Debrief: The payoffs changed — and payoffs are incentives. When you reward something differently, people do it differently. This is the foundation of how economists think about policy, taxes, and market design.
Debrief: Bitcoin earns 5 pts against Gold — but Silver beats Bitcoin every time for 2 pts. As more people chased Bitcoin, Silver became the rational counter. Bitcoin is high risk, high reward: it only works if you are not facing Silver.
Debrief: Silver earns 2 pts against the most popular card (Bitcoin). In a Bitcoin-heavy room, Silver is the rational choice — not glamorous, but consistent. In real markets, this is called a contrarian strategy: not chasing what everyone else wants.
Debrief: Gold earns 3 pts against Silver — the highest win reward — but Bitcoin (held by ~46% of players) beats Gold for 5 pts. The risk of losing to Bitcoin outweighs the reward of beating Silver. Rational players avoid Gold when Bitcoin is common.
In Round 2, there is a mathematically stable mix: Gold ~17% · Silver ~37% · Bitcoin ~46%.
At this distribution, no player can improve their average score by switching assets — because the room is already balanced against every strategy. This is a Nash Equilibrium: the point where individual decisions, taken independently, produce a stable collective outcome.
Ask: did your class drift toward these proportions during Round 2? Usually yes — without being told.
Debrief: Information was hidden and unverifiable. This is called information asymmetry — when one side of a transaction knows more than the other. It is how real financial markets, job markets, and negotiations work.
"Economics is not just about money. It is about decisions — especially when your outcome depends on what everyone else decides. Every time you traded, predicted, bluffed, or held your nerve in this game, you were doing economics."
Plain-English definitions for every concept in this game.
| Match-up | Winner | Pts |
|---|---|---|
| Gold vs Silver | Gold | +8 |
| Silver vs Bitcoin | Silver | +8 |
| Bitcoin vs Gold | Bitcoin | +8 |
| Same asset | Draw | +1 each |
No trading in Round 1. Cards are fixed.
| Match-up | Winner | Pts |
|---|---|---|
| Gold vs Silver | Gold | +3 |
| Silver vs Bitcoin | Silver | +2 |
| Bitcoin vs Gold | Bitcoin | +5 |
| Same asset | Draw | +1 each |
Bitcoin vs Bitcoin = +1 each, not 5. Trading allowed within Round 2 only.
Enter the number of wins per asset after a round. Updates live.
You have just played two rounds of the same game with the same three assets — Gold, Silver, and Bitcoin. Same cyclic win rule. Same opponents. Yet behaviour almost certainly changed between the rounds. That shift is not a coincidence. It is the core mechanism of modern economics.
In this blog we unpack what happened in each round, why it happened, and what two powerful ideas from economics it mirrors: one ancient — the search for equilibrium — and one very modern — how taxes and currency strength reshape who wins even before the game begins.
In Round 1, every win earns 8 points regardless of which asset you hold. Gold beats Silver for 8. Silver beats Bitcoin for 8. Bitcoin beats Gold for 8. The three assets are perfectly symmetric in their payoffs.
The key question: If all wins pay equally, what is the “right” way to distribute Gold, Silver, and Bitcoin across the room?
John Forbes Nash Jr. showed in 1950 that in any finite game — any game with a limited number of players and strategies — at least one equilibrium point always exists. An equilibrium is a state where no individual player can improve their expected score by switching asset, given what everyone else is doing. Nash's proof earned him the Nobel Prize in Economics in 1994.
Imagine everyone in your class is holding a Rock, Paper, or Scissors card. If you hold Scissors and nearly everyone has Rock — you keep losing. So you switch to Paper. But once lots of people switch to Paper, Scissors become good again. The chase never ends, unless everyone lands on a mix where nobody can do better by switching. That resting point is the Nash Equilibrium.
Because Round 1 is a symmetric game — every asset earns exactly the same reward per win — the mathematics of mixed-strategy equilibria guarantees a unique stable point:
This is the only distribution where no student, knowing the composition of the room, has a reason to switch cards. If Gold falls below a third, Gold-holders win more often against the now-abundant Silver, making Gold attractive again — automatically restoring balance. Each asset self-corrects the same way.
Let p be the fraction of players holding Gold, q Silver, r Bitcoin, with p + q + r = 1. A Gold-holder beats Silver (probability q) for 8 pts, so their expected score per duel is 8q. A Silver-holder scores 8r. A Bitcoin-holder scores 8p. For no asset to offer a better expected return — the Nash indifference condition — we need:
The equal payoffs force the room to split evenly. This is the unique mixed-strategy Nash Equilibrium of the symmetric game.
In Round 2, wins become asymmetric: Gold earns 3 pts for beating Silver, Silver earns 2 pts for beating Bitcoin, Bitcoin earns 5 pts for beating Gold. The cyclic win rule is identical. But the rewards have changed dramatically — and so has the equilibrium.
The new Nash Equilibrium shifts to approximately Gold 17% · Silver 37% · Bitcoin 46%. Bitcoin now needs to be the most common card before the others become rational, because its 5-point reward makes it so attractive that only abundance makes it dangerous.
Incentives shape strategy. That is the first great lesson of economics, and your class just felt it.
One scientifically valid way to interpret the move from Round 1 to Round 2 is as the introduction of asymmetric taxation on different assets. In Round 1, all wins earn 8 points — a perfectly flat system with no distortions. In Round 2:
A government that imposes a higher capital gains tax on one type of investment (say, gold bullion) than another (say, equities) does not change the underlying assets — it changes the rewards for holding them. Investors reallocate. The Nash Equilibrium moves. Exactly as your class moved.
Imagine the school canteen taxes chocolate bars more than crisps. Even if you like both equally, you buy fewer chocolate bars — not because they changed, but because the rules around them did. Taxes change choices without changing the things themselves.
A key result in public economics is that taxes drive a wedge between the private reward of an activity and its social benefit. When that wedge is the same for all activities — as in Round 1 — no distortion occurs. When the wedge is asymmetric — as in Round 2 — players move away from what they would have chosen in a neutral market. Economists call the lost value a deadweight loss.
The academic literature on asymmetric tax competition — particularly Bucovetsky (1991) and the extensive work surveyed by Wilson (1999) — shows precisely this: when markets apply differential tax rates, capital flows toward lower-taxed assets and the equilibrium allocation shifts away from the socially optimal one. Your classroom reproduced this in under ten minutes.
The names in the game are not accidental. The three assets can stand for three types of national currency competing on global markets:
Historically dominant, high prestige — Gold earns +3 pts against Silver, the highest single-match reward. But it is vulnerable to Bitcoin (the reserve currency). The pound was the world's reserve currency for over a century before the dollar displaced it after World War II.
The “safe haven” currency. Silver reliably beats Bitcoin (+2 pts every time). It does not deliver the highest returns, but it is the most consistent. In periods of global uncertainty, investors flock to the Swiss franc exactly as Silver-holders profit when everyone chases Bitcoin.
The dominant reserve currency. Bitcoin's 5-point reward mirrors the structural advantages of the dollar: seigniorage, geopolitical leverage, lower borrowing costs. Over 60% of global foreign exchange reserves are held in dollars (IMF, 2024) — mirroring Bitcoin's 46% Nash share. But it is also the most targeted card in the room.
The standard economic theory for valuing currencies is Purchasing Power Parity (PPP), which holds that, in the long run, exchange rates should adjust so that a basket of goods costs the same in every country (Cassel, 1918; Taylor & Taylor, 2004). PPP is like Round 1: a world where the rules are neutral and symmetric, and no currency should persistently outperform another.
PPP is the idea that a cup of hot chocolate should cost roughly the same “effort” wherever you buy it. If it is much cheaper in Switzerland, people would buy it there and sell it at home — until prices balanced out. That automatic balancing is purchasing power parity. The Economist tracks this every year using the Big Mac Index.
But PPP consistently fails in the short and medium run, and often in the long run too (Rogoff, 1996). Why? Because other factors create asymmetric advantages — exactly like Round 2's asymmetric payoffs:
The economic insight: Currency strength, like card strength in Round 2, is relative to the distribution of everyone else's choices. A currency can be objectively powerful and still be strategically vulnerable when too many people depend on it. China holds over $800 billion in US Treasury bonds — a position that gives it strategic influence, mirroring the Silver player who beats Bitcoin precisely because Bitcoin is so common.
Together, the two rounds recreate three ideas that span centuries of economic thought:
In a level playing field, rational agents self-sort into a stable mixed distribution. No one has to be told what to do; the incentive structure finds its own balance. Nash (1950, 1951) proved this is always true for finite games.
Changing relative rewards — even without changing the rules — shifts the equilibrium. This is the economic case for why asymmetric tax systems distort investment and allocation. Ramsey (1927), Diamond & Mirrlees (1971).
In a neutral world all assets are equal — PPP holds, all wins pay the same. In the real world, structural asymmetries create persistent deviations. Cassel (1918), Balassa (1964), Samuelson (1964), Taylor & Taylor (2004).
“The rules of the game are the rules of the economy. Change the rules and you change what rational people do — without changing the people at all.”