Under the Slope

1A price that is a formula#

On an ordinary exchange, a price is whatever the last buyer and seller agreed on. On a launchpad there is nobody on the other side. You trade with a contract, and the contract quotes its price from a formula. The formula has exactly one input: how many tokens it has already sold.

Every buy takes tokens out of the contract and leaves ETH in it, so the next token costs a little more. Every sell does the reverse. Plot price against tokens sold and you get the curve this page is named after.

Figure 1. The curve. The dot is where the launch is right now. Pick buy or sell, choose a size, and press the button. The shaded strip is the ETH that changes hands: the area under the curve between where you start and where you stop.

Watch the shaded strip as you change the size. It is not a rectangle. Your first token is bought at the price where the dot started, your last at the price where it stops, and you pay for every token in between. Everything else on this page grows from that one idea: a trade does not happen at a price, it happens along a stretch of the curve.

Selling walks you back down the same stretch. If nobody else traded in between, selling everything you just bought returns exactly the ETH you put in1. Once other people trade, that stops being true, which is where it gets interesting.

2Early, late and slippage#

The curve gets steeper as it goes, so the same ETH buys plenty of tokens near the start and far fewer near the end. Below, the curve is cut into ten equal slices of 80 million tokens. Each bar is what it costs to buy that slice whole.

Figure 2. The cost of each slice. Drag the marker to choose when you buy; the bracket on the axis shows how many tokens your budget gets from there.

This is the whole appeal of buying early, and it is worth being clear-eyed about. Early tokens look valuable only because later buyers pay more for theirs. If the later buyers never arrive, the early tokens are worth what the curve will pay to take them back, and nothing more2.

Price impact

Inside a single trade the same thing happens on a small scale. The price you see before you buy is the : the height of the curve at the dot. A bigger order walks further up, so your average price is worse than spot, and the price you leave behind is worse still. That move is your .

Figure 3. A zoomed piece of the curve around one order. Three horizontal lines: the spot price you saw, the average you paid, and the price after you. Drag the teal dot to grow the order along the curve.

Slippage tolerance

Between the moment you press buy and the moment your transaction runs, other trades can land in front of yours. Each one nudges the dot up, so you get fewer tokens than you were quoted. A is the worst shortfall you will accept: “fill me only if I get at least 97% of the quote.” If the shortfall is bigger, the transaction is rejected and you keep your ETH.

Figure 4. One , up to three transactions. Set how much someone buys just before you and how much shortfall you will tolerate, then send the block.

When a loose tolerance lets you fill, the buyer in front can sell straight after you and keep the difference. That move has a name: a . It only works because your tolerance promised you would accept a bad fill. Wide tolerances are sometimes needed in fast markets, but each extra point is an invitation. Keep them as tight as the trade allows.

Two buyers, one block

Even with no one trying to squeeze you, order matters. Two people who press buy at the same moment pay different prices, because one of them lands first and moves the curve for the other. On many rollups the simply takes transactions in the order they arrive.

Figure 5. You and a rival each spend the same ETH in the same block. Arrival times jitter randomly; a head start tilts the odds. Race once, then run twenty blocks.

3Graduation#

A curve like this cannot run forever: it keeps getting steeper and only holds part of the supply. So launchpads give it a finish line. In our model, once 800 million of the billion tokens are sold, the curve closes. That is .

At that moment the contract takes all the ETH it collected and the 200 million tokens it held back, and puts both into an ordinary trading . From then on people trade against the pool instead of the formula. In this model the are locked away, so nobody can pull the liquidity back out3.

Figure 6. A simulated launch, trade by trade. Press play or drag the trade slider. Panel 1 is the curve filling, panel 2 what the curve contract and the pool hold, and the bottom chart the price across the whole run.

Three things to notice. The price barely jumps at graduation, because the pool is seeded at almost the price the curve ended on4. After graduation, sells no longer slide anyone back down a fixed curve; they simply trade against the pool. And there is no finish line any more. Graduation is a change of machinery, not a prize.

Same order, different machine

How much a trade moves the price depends on how much ETH sits behind it. The curve's price leans partly on , pretend ETH that sets the starting price; the pool has only real ETH. Compare the same order on both.

Figure 7. Price change from one buy and one sell of the same size, on the curve at a point you choose and in the pool right after graduation.

4Taxes and splits#

Many launches charge a small fee on every trade, usually called a . A 2% tax means 2% of every buy and every sell is skimmed off. Where the skimmed ETH goes is a design choice. Here it is split three ways: to holders as a reward, to the creator, and to a that removes tokens from circulation5.

Figure 8. One simulated day of trading. Drag the handles on the bar to change the split, set the tax, then play the day. The stack shows where the fees went; tick marks on the axis are individual trades.

Fees are a real cost to whoever trades. A round trip at 2% each way costs about 4% before the price has moved at all. That is fine if you plan to hold and expensive if you plan to flip.

Now tick the box for . A creator who trades with themselves pays the full tax, gets back only their own slice, and loses money doing it. They do it anyway, because a busy volume chart is the cheapest advertising there is.

5What you pair against#

So far every price has been in ETH. But a curve can be priced in any token: ETH, a stablecoin, or a . The is what you pay with, what the curve holds, and what the graduation target is counted in.

The token's price on the curve does not care what the pair is worth in dollars. Your dollar result does. It is the token's move times the pair's move.

Figure 9. Ninety simulated days with the same token moves, measured against two different pairs. Switch the pair and drag the day marker. The ETH and stock-token prices are invented and start at $3,000 and $180.

A stock-paired launch is not safer by default; it just carries a different second risk. ETH tends to swing harder day to day. A share has its own news, its own trading hours and, for a token that tracks one, the extra question of how closely and reliably it tracks6. Whichever you choose, you are holding two bets at once.

6Spot the trap#

Everything so far is mechanics. This chapter is about people. The same curve that makes a fair launch easy also makes a few tricks easy, and they leave fingerprints: who holds the supply, where those wallets got their ETH, and who is trading with whom. The worst of them end in a .

Figure 10. Four made-up launches. The top bar shows holders, biggest first; the tape below shows a day of trades. Tap holders or trades to inspect wallets, reveal who funded them, then tick the signs you see and check your read.

. If the top few wallets hold most of the supply, they can sell into you whenever they like.
Shared funding. Ten holders funded from one wallet minutes before launch are one holder.
The creator selling. Watch the creator's wallet. A launch-minute buy followed by large sells is the oldest exit there is.
Circular volume. Matching sizes, seconds apart, opposite directions: a performance, not demand.

7Ten figures, one quiz#

No multiple choice. Each question is a small figure, and you answer by moving it. Starting positions change every attempt, so no peeking at a friend's screen. Finish all ten and you can draw yourself a certificate.

=The short version#

Six things worth carrying to any real launchpad. Each links back to the figure that shows it.

The price is a formula. It depends only on how many tokens are sold. Before buying, find out where the curve starts and where it ends. Figure 1
You pay along the curve, not at the quote. Look at the price impact of your size, not only the spot price. Figure 3
Tolerance is a promise. Keep slippage as tight as the trade allows; a loose one invites a sandwich. Figure 4
Graduation changes the machine. It is not a prize. Check whether the pool shares are locked or burned. Figure 6
Taxes come out of traders. A round trip at 2% each way costs about 4%, and volume can be faked. Figure 8
Read the wallets before the chart. Concentration, shared funders, creator sells and circular volume. Figure 10

If you try a real launch, try it on a testnet first, with nothing you would mind losing.

§The model, honestly#

All figures share one small model, written for teaching. It was shaped with the testnet launchpads of the Robinhood Chain ecosystem in mind, yet it is not the contract of any real launchpad, and real ones differ in every detail below.

Supply: 1,000,000,000 tokens. 800M are sold through the curve, 200M are held back for the pool.
Curve: Constant product with virtual reserves: (1.5 + E) × (1,060M − S) = 1.5 × 1,060M, where E is real ETH paid in and S is tokens sold. Spot price is the ETH side over the token side, (1.5 + E) / (1,060M − S), which starts at 1.42 gwei and ends at 23.5 gwei.
Graduation: When S reaches 800M (about 4.62 ETH raised) the curve closes, and its ETH and the 200M tokens seed an x · y = k pool that opens at 23.1 gwei. Pool shares are treated as locked.
Fees: Zero in chapters 1 to 3. In chapter 4 and the last quiz question, a flat tax on every trade, split as you choose. Gas is ignored everywhere.
Order: Transactions in a block run in the order shown. In the race, arrival time is uniform random jitter of 60 to 210 ms per buyer, minus your head start.
Trades: Random sizes from a log-normal spread, from fixed seeds so runs are repeatable. Each simulated launch draws its own appetite for buying, which is why some stall.
Pairs: ETH and stock-token dollar prices are random walks with invented starting values and volatilities.

The page fetches nothing and sends nothing. It is a fan-made explainer, not affiliated with any launchpad, and nothing here is advice to buy, sell or launch anything. If you try a real launch, try it on a testnet first.

Glossary

Notes

Ignoring fees and gas. The curve is path-independent: the ETH it holds depends only on how many tokens are out, not on how they got there. ↩
Before graduation, “what the curve will pay” for all tokens out is exactly the area under the curve back down to zero, and it is shared by everyone holding. Whoever sells first gets the best of it; the last sellers get far less. ↩
Not every launchpad locks or burns the pool shares, and some route part of the raise elsewhere. This is one of the first things worth checking on a real one. ↩
The model's parameters were picked so the pool opens about 2% below the curve's last price. Real designs tune this differently. ↩
“Burn” here means the fee buys tokens and destroys them. It is modelled simply as a share of the ETH collected. ↩
A token that tracks a share is only as good as whatever backs it and keeps it in line. That is a separate subject from bonding curves, and worth reading about on its own. ↩