Their was 3 houses but the fight was between 2 of them, The House of Lancaster which was the red roses and The House of York which was the white roses.
Henry and Edward were distant cousins. Henry was with the House of Lancaster and Edward was with the House of York.Edward belives that he should have kingship and he defeats Henry in a firce battle and the kingship passes down to him making Edward IV. But Edward is only king for 10 years and is overthrown and Henry becomes king again in 1470 but is king for a year and is over thrown and Edward is king once more
I think that Richard III didnt kill his nephews becuase he wouldn't have enough time to do the act when he is stuck in the castle.The kids could have gotten lost in the woods were killed to some animal.
The Battle of Bosworth Field was Richard III vs Henry Tutor. Henry gatherd a small rebel armry with support from some of the other houses like from the lancaster and york because they dispised Richard and hated him even more because of the rumors that he killed his nephews.