Best and final offer thoughts

Long time lurker first time poster!

My partner and I went to view a house on Saturday that ticks all our boxes and we loved so we put in an offer later that afternoon - house has been on the market for a week, asking 230k and we decided to offer 242k, based on the fact that it's exactly what we've been looking for.

We are in a string position - no chain and we've a 40% deposit so have some money to play with regarding size of loan should it end up being downvalued from our offer.

This morning the estate agents have got back to me to say whilst they know we've offered over asking, the vendors have decided to go to best and final offer by 12pm this wednesday.

This feels grabby to me but obviously ive no idea what other offers are, only that several have been made.

We are of the opinion that we dont want to go any higher and will take a chance on ours being highest and accepted; if it's not then we are pragmatic about other housing will come along.

Just wondering what other's thoughts are on this?