...an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows[8]:

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Given our assumption that p>q, the probability drops exponentially as the number of blocks the attacker has to catch up with inc reases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.

We now consider how long ...

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>

Given our assumption that p>q, the probability drops exponentially as the number of blocks the attacker has to catch up with inc reases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.

We now consider how long ...