docs: improve ZK intro

content/tutorials/build-a-zk-game/10.index.md

@@ -41,13 +41,12 @@ One way to accomplish this is by using ZK proofs.
 
 If you are new to ZK proofs, here is a very brief summary what you need to know:
 
-- ZK stands for Zero Knowledge.
-- ZK allows you to prove some information is correct without revealing all of the supporting evidence.
-(On the other side, ZK allows you to verify some information is correct without knowing the underlying data.)
+- ZK is an abbreviation for Zero Knowledge.
+- ZK allows you to prove some computation is correct, without needing to reveal all of the input data.
 - There are two steps to using ZK: 1) creating proofs, and 2) verifying those proofs.
-- When creating proofs, there are private inputs (e.g. the supporting evidence) and public outputs (e.g. the provable information).
-- There is no way to decode the private inputs from the proof or public outputs.
 - A proof and its public outputs can be verified onchain using a verifier contract.
+- An important property of ZK is that verifying the proofs is very cheap.
+  If you use a ZK proof for a large computation, the blockchain only needs to do a very small verification. This is very helpful for saving costs.
 
 ## How it will work