Horsechestnuts/Conkers?

Hi, I have a problem with these huge house spiders in my room, they seem to only climb up one wall, just a few minutes ago I had one run across my bed and need I mention that I screamed like a little girl, anyway, I heard that Conkers are rumoured to keep them away and i am willing to try anything to keep these beastly things from snuggling up to me in bed, what I want to know is what season do Horsechestnuts blossom and fall to the ground? Thanks =)