What guarantees that no two address are ever the same ?

[AnonyMint]

If addresses are actually generated using a truly random source, the probability of hitting an address already in use is orders of magnitude smaller than the risk of life on earth being eradicated by an asteroid impact. You can safely ignore that risk.
However, when addresses are generated from "random" passphrases there is a nontrivial risk of collision. If you use "correct horse battery staple" as a passphrase, you might think that you're really clever, but you're certainly wrong...

Onkel Paul

One of the keys to security is the uniform distribution of the hash. This is why if there is any (e.g. cyclical) pattern or any non-uniformity in a random number generator (RNG), then the attacker can potentially crack your Bitcoin.

This is what happened with Mike Hearn's java version of Bitcoin client for Android, because the stock RNG was faulty. Apparently this was quickly fixed.

Many people don't trust the hardware RNG in Intel chips, because they suspect the NSA planted a backdoor in it.

https://www.schneier.com/blog/archives/2012/02/lousy_random_nu.html

[Kluge]

note: DSV refers to the program grue mentioned above. For whatever reason, DSV is castrated by the developer (it only searches for addresses beginning with 1DSV). This assumes there is a non-castrated, optimized DSV which may include botnets or NSA super computers (really, super-duper theoretical computers from the land of Oz).

Assuming 500K addresses which either have funds or will have funds within next three months,
0.0000000000000000000000000000000000000000034211388289180104270598866779539% chance per check (or address creation).

Assuming average computer can do 250 optimized DSV-like checks per second,
0.00000000000000000000000000000000000000085528470722950260676497166948848% chance per second.

Assuming a "theft pool" is formed, and 500 of these computers averaging the above click/s,
0.00000000000000000000000000000000000042764235361475130338248583474424% chance per second.

Assuming each theft pool is one botnet, and 20 botnets, exactly the same, exist in these theft pools,
0.0000000000000000000000000000000000085528470722950260676497166948848% chance per second.

Per minute,
0.00000000000000000000000000000000051317082433770156405898300169309%

Per hour,
0.000000000000000000000000000000030790249460262093843538980101585%

Per day,
0.00000000000000000000000000000073896598704629025224493552243804%

Per month (30D),
0.000000000000000000000000000022168979611388707567348065673141%

Per year,
0.00000000000000000000000000026972258527189594206940146568988%


Assume worst-case scenario, DSV-like software can check 5000 addresses (10M of which are funded or will be funded within 6 months) per second, and 100 botnets of 50,000 computers each...
Per day,
0.000000000000000000000000014779319740925805044898710448761%

Per month,
0.00000000000000000000000044337959222777415134696131346283%

Per year,
0.0000000000000000000000053944517054379188413880293137978%

Per century,
0.00000000000000000000053944517054379188413880293137978%


ETA: Worse-than-worst case scenario. NSA can check 1T addresses per second, 1T addresses are funded.
Per century,
0.0000000000000021577806821751675365552117255191%

Per billion centuries,
0.0000021577806821751675365552117255191%

[DeathAndTaxes]

note: DSV refers to the program grue mentioned above. For whatever reason, DSV is castrated by the developer (it only searches for addresses beginning with 1DSV). This assumes there is a non-castrated, optimized DSV which may include botnets or NSA super computers (really, super-duper theoretical computers from the land of Oz).

Assuming 500K addresses which either have funds or will have funds within next three months,
0.0000000000000000000000000000000000000000034211388289180104270598866779539% chance per check (or address creation).

Assuming average computer can do 250 optimized DSV-like checks per second,
0.00000000000000000000000000000000000000085528470722950260676497166948848% chance per second.

Assuming a "theft pool" is formed, and 500 of these computers averaging the above click/s,
0.00000000000000000000000000000000000042764235361475130338248583474424% chance per second.

Assuming each theft pool is one botnet, and 20 botnets, exactly the same, exist in these theft pools,
0.0000000000000000000000000000000000085528470722950260676497166948848% chance per second.

Per minute,
0.00000000000000000000000000000000051317082433770156405898300169309%

Per hour,
0.000000000000000000000000000000030790249460262093843538980101585%

Per day,
0.00000000000000000000000000000073896598704629025224493552243804%

Per month (30D),
0.000000000000000000000000000022168979611388707567348065673141%

Per year,
0.00000000000000000000000000026972258527189594206940146568988%


Assume worst-case scenario, DSV-like software can check 5000 addresses (10M of which are funded or will be funded within 6 months) per second, and 100 botnets of 50,000 computers each...
Per day,
0.000000000000000000000000014779319740925805044898710448761%

Per month,
0.00000000000000000000000044337959222777415134696131346283%

Per year,
0.0000000000000000000000053944517054379188413880293137978%

Per century,
0.00000000000000000000053944517054379188413880293137978%


ETA: Worse-than-worst case scenario. NSA can check 1T addresses per second, 1T addresses are funded.
Per century,
0.0000000000000021577806821751675365552117255191%

Per billion centuries,
0.0000021577806821751675365552117255191%

[jellies]

great image.
maybe in future that can be the first post to topics like this!

[AnonyMint]

D&T that is perfect.