When we look at
Tactics Broker and read
Anticipation we see that Tactics Broker says it modifies the iniative check. Not the roll. So rolling or re-rolling has no affect and the final check result.
This is also addressed in the official FAQ here-
Official FAQ wrote:
Q: How does Tactics Broker interact with Recon or Anticipation?
A: Multiple rolls and rerolls still result in the selected final roll being considered a 1. Only in the case of a tie (that is, the player with Tactics Broker also rolling a 1) would the Tactics Broker ability be lost.