In a race, an athlete doesn’t must be sooner than 50% of all of the athletes mixed. He simply must be the quickest.
Mining is just not analogous to a race. Racers make progress in the direction of the end line, with the quickest racer finally profitable. There isn’t a progress in bitcoin mining although: with every try (hash) you both discover a right block, or not.
So bitcoin mining is extra akin to a dice-rolling recreation, with a poisson-distributed random probability of success for every try. The extra hashpower you have got, the extra makes an attempt you can also make per second.
If you wish to reliably out-compete the remainder of the community (ie, 51% assault), you will want to have extra hashpower than the remainder of the community (ie, you will want to regulate >50% of the whole hashpower pointed on the community).
So, if there are miners M1, M2, …Mn and mining Swimming pools P1, P2, ..Pm within the community with Pi (1<=i<= m) having the very best hash energy Hello, I as a dishonest miner (or pool) would want to have a mining energy Hx > Hello to finally mine blocks faster than than the remainder of the community if I had been engaged on a sidechain privately.
With a view to 51% assault,
Hx > ((H1 + H2 + H3 + ... + Hm) / 2).
Contemplating provided that
Hx > Hello is inadequate, since
Hello will not be the one different entity mining. Any miner with any quantity of hashpower can win the subsequent block (with a likelihood proportional to their share of the hashpower), so it’s essential to take into account all miners collectively in you calculation.