This is a good way of looking at it. If you deposit e.g. $1m ETH and $1m USDT in an ETH/USDT pool and then short $1m of ETH perpetual swaps you are delta neutral, lose if the px goes up or down, and collect on pool fees and swap funding rate (assuming funding rate is positive)
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Simplest liquidity pools are constant product - the total reserves x, y of the two coins always satisfy xy=k where k is a constant. Also the price p=y/x so you have x=sqrt(kp) and y=sqrt(k/p), and total value of the pool is x+yp = 2 * sqrt(kp)
The amount of asset y is your delta, and like a short straddle your delta decreases as price increases and vice versa. So you need to rehedge delta if you want to stay flat (many don't because they want the price exposure, but staying flat makes the straddle analogy clear)
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Pools with px ranges have a formula like (x+a)(y+b)=k rather than xy=k, where you can choose a, b to set a px range. The effect is that you participate more in swap fees when px is within the range, but you get completely wiped out if px moves outside the range.
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I had a go at explaining it (with more math) here -https://twitter.com/macrocephalopod/status/1414639678947475462?s=20 …
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