# Chain Race Dynamics
The competition between the honest chain and an attacker's chain can be effectively modeled as a **Binomial Random Walk**. In this model, the success event is characterized by the honest chain being extended by one block, which increases its lead by +1. Conversely, the failure event occurs when the attacker's chain is extended by one block, thereby reducing the gap by -1.
This dynamic can be visualized as follows:
* **Honest Chain**: Each time an honest node successfully mines a block, the lead increases.
* **Attacker's Chain**: Each time the attacker successfully mines a block, the lead decreases.
The block discovery process is inherently random due to the **proof-of-work** mechanism, which means that both honest and dishonest nodes are subject to the probabilities dictated by this process. Each party must engage in a full network proof of work to either extend their chain or reduce the gap.
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