You can try. You might just end up winning more on Bookie A though. It’s a catch 22 as well. The higher odds you bet on Bookie A, the more chance you’ll have of losing, but firstly you’ll also be losing more money on the dutch, and if you do happen to win it on Bookie A, suddenly you’ve now got a heap of money in Bookie A (which depending on your bank roll may or may not be a major issue).
By all means give it a crack, but you can’t definitely lose.