The stats for each player-character in BF are generated via the hatreds of the other player-characters, with a hatred being the reason why they are jealous or resentful of someone else. For example, Alice hates Brian because she is jealous of how much Cooler he is than her, but in return Brian hates Alice because he resents how much Richer she is than him. As each player assigns one hatred to each other player-character, and there are five stats to hate the other PCs for, the game works best with exactly six players: you get five points spread across your five stats and an instant basis for your relationship with each other PC. The system still works with more PCs, so everyone gets their five stat points and five relationships, but there will also be some undefined relationships between some PCs and these might be uneven, e.g. Alice hates Brian for being Cooler but Brian doesn't hate Alice for anything.
With less than six players, the rules advise you to 'double-up' on your hatreds, so each player actually picks two or three other PCs to hate, each for a different reason. This means everyone still has five stat points in total, but now they also have two reasons for hating some other PCs but still only one reason for others. It's a system that works well, but I'm now going to suggest an alternative that will tighten up the relationships between PCs in games with only three or four players and more closely link the stats to the setting. This is also totally compatible with the GMless optional rules that will follow.
The crux of this hack is that, instead of using the stats out of the rulebook, you create you own set, custom built to fit the game you want to play. You might come to the table with a pitch and the stats already decided or you might have a brainstorming session, with everyone discussing the sort of game they want to play and which stats would suit it best. Customising stats has two great benefits when playing BF: you change the assumptions of the setting & tone of the game, but you can also change the number of stats you use. If you only have four players, then whittle it down to just three stats; if you have three players, use only two stats.
For three players and two stats, do what Gregor Hutton does in 3:16 Carnage Among the Stars. In this game of space marine combat, the only two stats are Fighting Ability and Non-Fighting Ability, i.e. everything else. If you want to have a heroic action-adventure game, then your stats could be Bold/Gritty for combat and stunts, while Calm/Cool could cover all the other stuff like hacking computers, spotting trouble, talking to bystanders and so on. If you're going for investigative horror, then Spooky or Weird could cover all the ghost hunting, vampire slaying, seance holding business while Steady or Earthy would be used for dealing with day-to-day problems.
If you've got four players and three stats, try dividing things into a classic triumvirate, like the generic Physical, Mental and Social, but flavour them for your specific setting, e.g. Tough, Smart and Mean for something with a military or Wild West theme; maybe Quicker, Slicker and Trickier for a noir detective story or a heist thriller.
With five players and four stats, it's easiest to take the basic stats from BF and agree which one you won't need or which isn't very important for the story you want to tell: being Richer probably doesn't count for much if you're all stranded on a desert island and being Prettier might not make a lot of difference during the zombie apocalypse.
Even if you have six players, you can still choose a different set of stats that better fits the game you're pitching; in a game about the classic Universal Monsters (mummy, werewolf, mad scientist, etc) sharing a house, I created some custom character sheets with the stats being Scary, Strong, Smart, Stealthy and Smooth. I've also created a 'blank' version of the BF character sheet to use for this sort of situation, allowing everyone to discuss and fill in the stats they agree on.
One last twist on re-theming stats to think about: what about embedding comic tropes in the narrative by inverting their intent? As is, the stats represent each PC's competence in a field, from a base-line zero 'Can't do anything' to a maxed out three or more 'Best in the world,' but what if you change what the stats mean? Try replacing Pretty, Cool, Smart, Tough and Rich with Homely, Dweeby, Stupid, Weak and Poor, so the hatreds aren't jealousies but resentments or pity, because you can forgive a friend for being really bad at one particular thing. This sets up the game as a sitcom, with characters having exaggerated, cartoon-like flaws and they exploit how bad they are at them to succeed in absurdly amusing ways, e.g. the character with Homely of 3 can frighten animals and peel paint just by looking at it, whereas one with Stupid of 3 is too ignorant to notice that they're on fire and so takes no damage from it.
To lift an idea from PbtA games and others besides, instead of just saying that you hate another PC for being more whatever than your PC at something, you can add details and histories. With only three or four players in the game, you've got time to flesh out the reasoning behind each hatred. Try rephrasing your hatreds as "I hate [PC's name] for being [stattier] than me because..." and then completing the sentence with a memory or feeling about them, e.g. "I hate Alice for being Richer than me because she bought the exact car that I've always wanted." Flesh out the content of these reasoned hatreds and add them as Stuff & Nonsense, so in the example above, Alice add's Brian's dream car under her Stuff.
Tying a hatred to a specific past event or a general behaviour that's been repeated many times gives you more meat to chew on in the story that follows: Alice's car, instead of just being a convenient prop, now becomes a bone of contention for Brian. The same goes for rivalry over careers, lovers and success in life, as well as coping with failures and disappointments, e.g. "I hate Brian for being Cooler than me because he talked his way out of trouble with the police and left me to face the music alone." A detail of the history shared by each pair of PCs will often create a plot or at least a sub-plot all by itself, encouraging personal motivations and quests for each character that will add depth to your portrayal of them.
The GM's Role
With fewer players, you're going to get more bang for your buck by having everyone take on a PC role and do without a separate GM. I've done this informally with experienced story gamers who were happy to make up content and roll with the direction the story was pointed in by group consensus, but here are some solid, mechanical suggestions for handling it.
The simplest non-traditional GMing style is to hot seat that role, so anyone can play the GM for a scene or two: if you're happy with a scene-framing style of play, you can just all take turns to be the GM for the other players. This works well for a drama using the framework of a TV episode, with acts and scenes breaking the narrative into manageable chunks. Everyone gets a turn in the spotlight, saying what their character is doing, where and who with, then someone whose PC is not involved in the scene plays the supporting roles and pushes the scene towards a dramatic resolution, invoking the mechanics to do so. Go around the table, giving every PC a scene; one round of scenes completes an act and three to five acts completes an episode.
For a slightly more dynamic version of the above, add a Dictator-chip to the pool of Friend-chip tokens: the Dictator-chip is a differently coloured token from the Friend-chips and replaces one of them. Put all the tokens in a bag or other container at the start of the game, then have everyone draw from the pool one token at a time until each player has three: one of you will have the Dictator-chip, so they are in the hot seat to begin with. The Dictator plays their character as well as serving the GM's role of playing supporting characters and pushing the narrative towards dramatic conflicts, but their PC cannot resolve any challenge in the current scene as long as they are Dictator, e.g. if you create a confrontation with some hostile locals in your Dictator role, then your PC cannot be the one to fight, charm, bribe or otherwise deal with them.
When using the Dictator role, PCs can still challenge and confront each other, so even though your PC can't face challenges that you have created as the Dictator, you can still get involved in conflicts and exchanges with the other PCs as normal. The Dictator-chip is just like a Friend-chip in this respect, so you can push to win a conflict by passing it to another player who then immediately becomes the Dictator. This form of fluid hot-seating lets you adopt a looser approach to framing the narrative, creating something more like a novel or a found-footage piece, with more natural segues between scenes instead of forced, televisual-type shifts. Since the focus of each scene can change just as fluidly as the Dictator changes, you can get a less predictable, more naturalistic-seeming story and as long as you aren't currently the Dictator, your PC can take on any challenge in the story.
This is my preferred technique for dealing with a player getting five Friend-chips at any time and it's what I advise whenever I run the game, but I'm going to present it here in an expanded form to complement the hot seating rules above. The basic form is that whenever you have five Friend-chips, you have to immediately interrupt the drama with something awesome, in the form of an unexpected twist or shock: this can be in-character, pushing as usual to do something outrageous ("I steal Alice's
If the Dictator-chip is one of the five chips you have at any time, then you must push it to another player, you can't push a Friend-chip to them instead: in this way, players can tactically maneuver a Dictator out of the hot seat by pushing Friend-chips to them until they have five, if they want to do that. This can be a democratic way of letting someone know that they've had enough time in the hot seat or just a fun side-game of vying for the Dictator-chip. Either way, it makes sure that no-one can hold onto the Dictator-chip forever: you can control the scene while in the hot seat, but you can't control what the other PCs do, so they can always engage in challenges that channel chips to you until you reach five and are ousted from the hot seat.
When you're hot seating or otherwise sharing the GM's duties, don't be tempted to abuse your position: remember that the point is to create an enjoyable, entertaining story together, not to have your PC win at all costs, crushing all opposition. Don't set unreasonable stakes for failure ("If you fail to find your front door key, you house blows up!") and do accept the consensus when determining the need to push a chip or not (finding your own front door key probably doesn't even need a push unless the PC in question has a Smart stat of zero.) Bear in mind that, at some point, someone else is going to take the hot seat and have just as much authority over your character as you had over theirs, so don't invite petty, tit-for-tat one-upmanship. Be respectful, be kind and most of all, have fun.