Selfish mining changes publication strategy, not block validity. Outcomes depend on hashrate, propagation, tie handling and others' behavior; no single universal threshold guarantees profit.
After finding a valid block, the miner starts a private branch rather than announcing it immediately. Others keep working on the public tip without knowing that block. [Eyal and Sirer — Majority is not Enough]
The strategy tracks the gap between private and public branches. Depending on subsequent discoveries it extends the lead, releases blocks or abandons its private branch. [Eyal and Sirer — Majority is not Enough] [Sapirshtein, Sompolinsky & Zohar — Optimal Selfish Mining Strategies in Bitcoin]
Selective publication when branches draw level can trigger a race between two valid branches. Which branch other miners extend helps determine the outcome. [Eyal and Sirer — Majority is not Enough] [Bitcoin Developer Guide — Block Chain]
Blocks on the losing branch remain outside accepted history and their rewards do not apply. The aim is for honest miners to waste proportionally more work than the attacker. [Eyal and Sirer — Majority is not Enough] [Satoshi Nakamoto — Bitcoin whitepaper]
Eyal and Sirer's model compares the share of rewards for accepted blocks with the share of hashrate. A larger relative share is not automatically greater net hourly profit; difficulty, time and costs also matter. [Eyal and Sirer — Majority is not Enough] [Sapirshtein, Sompolinsky & Zohar — Optimal Selfish Mining Strategies in Bitcoin]
In the basic model α is the attacker's hashrate share and γ the fraction of honest hashrate that mines on its branch during a tie. Changing γ changes the advantage threshold, so hashrate percentage alone is insufficient. [Eyal and Sirer — Majority is not Enough] [Sapirshtein, Sompolinsky & Zohar — Optimal Selfish Mining Strategies in Bitcoin]
Relay speed and relationships between pools can change tie advantage. Model parameters are neither universal measurements of the real network nor proof of a particular pool's behavior. [Eyal and Sirer — Majority is not Enough] [Sapirshtein, Sompolinsky & Zohar — Optimal Selfish Mining Strategies in Bitcoin]
Withholding is risky: the public branch can overtake the private one and the attacker loses its block rewards. Merely starting the strategy does not guarantee success. [Eyal and Sirer — Majority is not Enough]
A Full Node still rejects invalid transactions and excess issuance. Selfish mining exploits competition between valid branches and grants no authority to spend others' coins. [Satoshi Nakamoto — Bitcoin whitepaper] [The Bitcoin Backbone Protocol] [Bitcoin Core v29.0 — validation]
Defense research examines block propagation, tie handling, incentives and detection. A stale block alone is not evidence of an attack: natural concurrent discoveries produce a similar outcome. [Eyal and Sirer — Majority is not Enough] [Bitcoin Developer Guide — Block Chain] [Sapirshtein, Sompolinsky & Zohar — Optimal Selfish Mining Strategies in Bitcoin]
For the clearest picture, read this entry together with Block propagation, Compact block relay, Nakamoto consensus, Sybil attack. The reverse links also lead from Block withholding attack.