DEX Resources — AMM Formulas, Pre-Trade Checks, Signature Guide

Formula reference

Constant product AMM

invariant:     x × y = k
spot price:    price of A in B = y / x
output for Δx: Δy = y − k / (x + Δx)
average price: Δx / Δy
price impact:  (average price − spot price) / spot price

Where x and y are the pool's reserves of the two tokens.

Worked example

Pool: 1,000 ETH and 2,000,000 USDC, so k = 2,000,000,000 and spot = 2,000 USDC/ETH.

Buy with (USDC)	ETH out	Average price	Price impact
1,000	0.4998	2,001.0	0.05%
10,000	4.9751	2,010.0	0.50%
100,000	47.619	2,100.0	5.0%
1,000,000	333.33	3,000.0	50%

Zero-fee pool, for checkable arithmetic. A real pool adds a swap fee (commonly ~0.30%) taken from the input.

The property to remember: execution impact is dx / y — your spend divided by the pool's quote reserve. It is linear in trade size, so what matters is your size relative to the pool. The pool's own spot price moves quadratically, (1 + dx/y)^2 - 1, and the tokens you forgo versus spot grow faster than linearly.

Total cost of a swap

total = swap fee + price impact + gas

Small trade, deep pool → gas dominates. Large trade, thin pool → impact dominates.

Pre-trade checklist

Trading from a wallet sized to this trade, not my main holdings
Reached the site by typing the domain, not via a link or ad
Token selected by contract address, not by name
Address obtained from a project-controlled source; chain confirmed
Source code verified on an explorer
No asymmetric or owner-mutable sell fee
Pool reserves checked; price impact acceptable at my size
Slippage tolerance at the smallest value that reliably executes
Holding native asset for gas
Exit path considered — same pool, same curve
Every signature read before confirming

Signature reference

Prompt	What it does	Gas	Risk
Connect	Shares address, allows prompts	None	Low — grants no spending power
Message	Proves address ownership	None	Low, but read it
Approve	Standing permission to move a token	Yes	High — persists until revoked
Permit	Same authority, via signature	None	High — easy to sign without reading
Transaction	Executes a specific action now	Yes	Bounded to that action

A gasless signature is not a harmless signature.

Order type decision

Situation	Choice
Small trade, deep pool, want it done	Market swap
Price-sensitive, not time-sensitive	Limit order (signed intent)
Size large relative to pool	TWAP, or reduce size
Thin pool, any size	Limit order, or reconsider
Need a guaranteed fill at a price	Not available on an AMM — use an order book

Risk-to-check mapping

Risk	Check
Impersonator token	Contract address from a project-controlled source
Honeypot	Verified source; no asymmetric or mutable sell fee
Malicious approval	Read every prompt; prefer finite; use a small wallet
Thin pool	Pool reserves and displayed price impact
Cloned interface	Type the domain yourself
MEV / sandwich	Minimal slippage tolerance; split size; private relay
Rug pull	Liquidity lock verified on-chain; holder concentration

Incident response

Order matters — secure funds before investigating.

Move funds from a clean device to a wallet whose seed never touched the suspect machine
Revoke approvals on the affected wallet
Assume the seed is burned if it may have been exposed; generate a new wallet
Secure surrounding accounts — email first, then exchange
Capture evidence — URLs as text, addresses, transaction hashes
Report to the impersonated party, the hosting platform, and your jurisdiction's authority
Ignore recovery offers — anyone approaching you afterwards is running a second fraud

The two habits that do the most

Trade from a wallet holding only what you are trading. Bounds every mistake.
Verify identifiers, not labels. Contract addresses over token names; typed domains over links.

Neither requires correctly judging whether something is malicious — which is exactly the judgement attackers work to defeat.

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