How many nodes need to collude to harm Casper or Sharded Eth?

How many and can you explain why? (I’m familiar with big O notation) Thanks!

2/3+1 of 128 i.e., 86 validators, of 32 ETH each.

How committee size for shards is determined:

How to bribe said committee:

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Thanks! And and are the validators chosen pusdo randomly? And how often are they rotated out?

They are rotated once per epoch, with a lookahead period of one epoch.