If I use 5KE Bran Stark's ability (kneel to count 6 INI...) for how long does the effect last? Does it end when I reveal my plot card at the beginning of the draw phase or does it last until Bran stands (either during the standing phase or as the result of a card effect) or longer? For example, say I used Bran's ability and then played a plot with zero INI and have no INI modifiers while my opponent has 4 INI total. If Bran is still kneeling during the challenges phase and I want to play Countered Plots to cancel an action by my opponent, do I have the higher INI necessary?
And while I'm at, how would Host of the Bear (ITLP) work under the same scenario (Bran's ability triggered, I have zero INI otherwise)? Would Host of the Bear that I already had in play be kept in play until the next round's Plot phase, at which point I'd need to satisfy the passive ability on the Host of the Bear or lose him, or was there a point after kneeling Bran that my INI would drop down to zero thus forcing Host of the Bear out of play before then?
Keep in mind that there is only one time in the game when you actually COUNT initiative. That's during the plot phase when you determine First Player. At all other times, references to "total initiative" are like STR checks, icon checks, etc. You look at the current board position. It's just the mechanics of the game: you do not count initiative during the plot phase and that becomes your initiative for the entire round. Instead, your "total initiative" is constantly calculated.
Now, the thing to realize about Bran is that he does not MAKE your total initiative 6. Rather, he lets you count 6 total initiative (regardless of what your current plot and modifiers may be). So when determining First Player, your total is 6 no matter what else the board might say. But for every other purpose outside that framework action window, your "total initiative" is what the rules say it is: the current total of your currently revealed plot and all modifiers.
What this means is that the 6 initiative you get from Bran is around for one purpose only: determining First Player. Countered Plots, Host of the Bear, all that other stuff - Bran has no impact on it. You have to have a total initiative higher than your opponent (with Bran being no factor) at the moment you play Countered Plots. For Host of the Bear, you must CONSTANTLY maintain a total initiative above 2 or discard it. (For example, if you have a 2-initiative plot card and someone discards your only initiative bonus from Kingsroad Fiefdom, Host of the Bear goes with it immediately.)