I won't say i know how much is the right amout but if it were me i would work out my avaerage weeks worth of bets and say have 4 times that amount spread through out my selected bookies and betting accounts and then have the rest of the bank in a real bank on short term deposits.

Depending if you are wanting to keep profits from the taxman i am not sure how this will effect that, but the added interest will help build the bank in the future.