Richard's personality is so shallow thought that after Mowbray had left, one look at Gaunt's face and he "plucks" four years away from Bolingbroke's sentence. Although Richard does have ultimate power, he seems to use it for minor, insignificant things, or isn't sure how to use it properly.
Once again, Richard has one of his mood swings, and turns on Gaunt, whom he respected at the duel at Coventry. Richard has gone from "Why! uncle, thou hast many years to live." to "The linings of his (Gaunt's) coffers shall make coats / To deck our soldiers.......Pray God we may make haste and come too late!"
Richard has his heart set on inheriting Gaunt's land and money ahead of Bolingbroke, and even comments that if Gaunt weren't his uncle, he would have him executed.
Richard is on a one track mind on taking Bolingbroke's inheritance, and ignores York's prophecy that Bolingbroke will return and claim what is rightfully his.
If Richard was balanced and listened to the wise advice from Gaunt and York, he would have certainly kept his crown after this episode.
Despite being seen as the ’good guy' in the first two acts, Bolingbroke also comes in for condemnation. At the start of Act 3, he has Bushy and Green "dispatched" by Northumberland, simply because they are "Near to the King in blood, and near in love" . This is a harsh, brutal side to Bolingbroke that has not been seen before, but becomes more apparent throughout the rest of the play. An interesting contrast appears in Bolingbroke as soon as Bushy and Green leave. The word 'dispatched' is used in its normal sense again by York (Bolingbroke's uncle), whom Bolingbroke is desperate to please after York had recently announced "I am no traitor's uncle".
Bolingbroke is also guilty of having an ulterior motive for returning to England. If he was genuinely coming back to make sure he received his inheritance, than he wouldn't have needed to murder Bushey and Green. On the way to Berkley, Bolingbroke says to his entourage "I wot your love pursues / A banished traitor. All my treasury / Is yet but unfelt".
This reason may be legitimate, but when York asks "Why have those banished and forbidden legs / Dared once to touch a dust of England's ground?" Bolingbroke replies with "I was banished Hereford, / But as I come, I come for Lancaster." This may have been enough to satisfy York, but Bolingbroke continues; "my rights and royalties / Plucked from my arms perforce, and given away / To upstart unthrifts? Wherefore was I born? / If that my cousin king be King in England"
This must convince York that Bolingbroke is returning for far more than his inheritance, and Richard's throne is in danger.
Despite both having such dark characters, Bolingbroke and Richard also deserve some sympathy during the play, Richard more than Bolingbroke in my opinion.
Of course, Bolingbroke had his estate taken away from him when he was exiled perhaps a little unfairly, and he seemed to be the only man of real power that could see the faults in Richard as a king.
Richard however just seems to be a little unfortunate to be in some of the situations he is in. It was his fault that Bolingbroke returned to England looking for vengeance, but the audience may feel genuinely sorry for him by the end of the play.
He believes in the Divine Right of Kings, that he had been appointed by God to be King of England, and only his own son could replace him. However, this may have added to his selfish attitude, thinking that there was no-one good enough to replace him on the throne.
He is married to his French wife, and they have a very emotional seen through the streets of London as he is lead to the Tower. This would surely provoke sympathy from the audience, compared to the cold calculated Bolingbroke, who is hell-bent on seeking revenge for being robbed of his inheritance. The audience will understand more with a married character, rather than someone so driven and focused on one prize to miss out on settling down with a family.
Finally, if Richard's army of Welshmen (Act II Sc. iv) had not left on a tip off that the king was dead, then they would have easily overpowered Bolingbroke's small force. This evokes sympathy from the audience, as they will all know what it is like to be so tantalisingly close to something, but still see it slip through their fingers.