51% Attack & Double-Spend Race

Attack Parameters

Attacker hashrate 30%

Confirmations required 6

Mining pace 2.0 blk/s

Races run

Double-spends won

Actual success rate

–

Theoretical P(success)

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Honest chain

Attacker's secret fork

How it works

A merchant accepts a payment once it is buried under k confirmations on the honest chain. A dishonest miner who controls a share q of total network hashrate can instead spend the coins, then secretly mine an alternative fork starting one block earlier. If that private fork ever overtakes the public honest chain in length, the attacker broadcasts it — the network reorganizes onto the longer chain, the merchant's payment block is discarded, and the coins can be re-spent elsewhere. This is Satoshi's original double-spend race from the Bitcoin whitepaper.

each block: honest wins w.p. p = 1−q, attacker wins w.p. q
attacker must be ≥ honest length once honest reaches k blocks
P(success) ≈ (q / p)^k        for q < p   (Nakamoto race)
P(success) = 1                for q ≥ p   (true 51% attack)

Attacker hashrate — the fraction of total mining power the attacker secretly controls; above 50% the attacker eventually wins every race no matter how many confirmations are required.
Confirmations required — how many blocks the merchant waits before releasing goods; each extra confirmation multiplies the attacker's odds down by roughly q/p, which is why exchanges demand more confirmations for larger payments.
Mining pace — how fast the animation plays out block discovery; it does not change the odds, only how quickly you see the statistics converge.

Watch the "Actual success rate" converge toward "Theoretical P(success)" as more races accumulate — a live demonstration of why blockchain security is fundamentally probabilistic, not absolute.

Honest chain block Attacker's secret block Confirmation threshold Orphaned (discarded)

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