Acredito haver várias possibilidades, minhas sugestões são:
How much did you pay for these shoes?
- Try to guess!
- I'll "chutar alto [take a rough guess]" - $500.00
- No, it was cheaper than that!
- How much did he pay?
- $500.00, at a guess.
"What's the time?" "It's about 5 o'clock, at a guess (= without knowing exactly)."
We can't be certain but I'll take a rough guess [ vou chutar alto]and say the £1200 a night.