From my experience i find a lot of the information given on this thread to be incorrect. We all have our experiences and opinions, mine is obviously quite different from some others.
It is possible that any rooster will fight to the death, regardless of size or breed. It is possible that any roosters will work out an accommodation and work together to take care of the flock and be pretty peaceful about it. Some chickens, usually some games, have been bred to fight. Cockerels or roosters from those flocks will often fight to the death. But some flocks of Games have not been bred to fight to the death. The idea that whether they are bantam or not determines if they will automatically fight to the death while no full sized fowl rooster will fight to the death is totally against my experience.
The idea that multiple cockerels will automatically gang bang a pullet does not tie in with my experiences. I raise cockerels and pullets together with the flock every year. Sometimes the ratio of cockerels to pullets is more than 2 to 1 the wrong way. If I see a pullet get gang banged (defined as two cockerels in a row) once every three years that's a lot. Can it happen? Yes. Is it guaranteed to happen? Not at all.
I've seen more problems with overmating and barebacked hens with larger hen to rooster ratios than with small. In my opinion that is not because of a ratio but because of the individuals involved. There is some luck involved with the individual personalities of your chickens. There are plenty of posts on this forum where people have had these problems with a flock of one rooster and over 20 hens when they are out free ranging. It can happen regardless of ratio, age, or space. It is common practice for breeders to keep one rooster penned with one or two hens through out the breeding season and not have these problems. One big but open secret is that those successful breeders use roosters and hens, not cockerels and pullets. There can be a world of difference in behaviors between cockerels and pullets versus roosters and hens which you might be getting ready to find out as yours go through puberty.
One huge factor in chicken behaviors is room. The more you crowd them the more likely you are to have behavior problems. Yours free range for the most part, that gives you a huge advantage. I don't know how big your coop is or how often you leave them locked in there. That might be your Achilles heel. I could maybe see some coop building in your future.
One member of this forum keeps several flocks of Games and Dominique. They are spread out and pretty much free range during the day but he invests a lot in predator management at night, him and his dogs. His Games are not from a line that are bred to fight to the death. It is unlikely your Game is either because it is a bantam but it bears watching. Between your Polish, Cochin, and Game bantams he is the one most likely to cause problems. But it is not guaranteed. He may be low man on the totem pole. He keeps a few rooster with one or two hens to observe interactions but he said when given the choice his flocks tend to sort themselves out into a one rooster - seven hen ratio. Some are higher, some are lower, but 7 to 1 is pretty normal.
There is no magic ratio that stops males from fighting over females. They are as likely to fight over twenty as one. There is no magic ratio that stops overmating or barebacked hens. You just don't get guarantees with living animals and behaviors.
In my experience a male's ability to protect the flock is often overrated. In the predator attacks I've had the rooster survived, he did not give his life to defend the flock. There can be some benefits such as an early warning lookout in certain conditions. A good rooster will often put himself between his flock and some perceived threat while he checks it out, that may be why some die. Some will attack certain predators, such as small hawks. If you want a rooster with your flock go for it, but don't think your flock is safe because there is a rooster with them, especially a Polish that can't see.
So where do you go from here? You could do a bachelor pad and keep two of them housed together. That may solve all your problems. If you want to let them free range I'd get a few more pullets now and integrate them. That is very few pullets for three roosters. How many more? I don't know, I'd think another half dozen minimum. Any more than that is not likely to make any real difference.
You may find that adolescence is pretty rough whether you add another half dozen or another 30. I'd have a pen prepared where you could isolate some cockerels for a while if things get really rough for you.
Good luck!
Our Game has already given warnings out and I got to see him put himself in the middle of his flock to investigate a pigeon. 
It was cool to watch. All the other's ran under the house when he did his warning sound and he ran towards it and then tried to act all cool like he wasn't paying attention when the pigeon didn't even budge. Our Game had even started making indentions in the nests for the pullets and shares or gives his food findings. So far, he hasn't shown any signs of aggression but at 12 weeks it sounds like that could change. 
Right now our roost is plenty big I think for what we have but we are planning on building a bigger one for more pullets. They have their chosen roosts and all is good at night. They are let out first thing in the morning and they put themselves to bed at sundown and we just close it up for protection. So far noone is being aggressive towards anyone so I'm glad I'm getting all this helpful information now so we can plan. Thank you!
