So you have more chances at winning the lottery?
I suppose that depends on the lottery. Different lotteries have different odds. However, any lottery that has the same odds of winning as the odds of generating the same bitcoin address as someone else would be a lottery that nobody would play (since nobody would ever win).
As an example, lets assume that it's after the year 2140 and all the bitcoins that will ever exist have already been mined.
To demonstrate how unlikely it is, lets assume that nobody ever lost any private keys and no bitcoins have ever been permanently lost, so ALL bitcoins are accessible. Then lets assume that all the bitcoins are spread out into the smallest possible outputs. That would result in 2,099,999,997,690,000 addresses each with exactly 0.00000001 BTC in them. This gives you the largest possible set of bitcoin addresses that could ever exist with bitcoins in them.
Given that you are trying to find any one of 2,099,999,997,690,000 different addresses out of a total of approximately 1.46 X 10
48 possible addresses, your odds of "winning" on any given attempt are approximately
1 in 6.96 X 1032Looking at the Mega Millions lottery that is popular in the United States, the odds of winning the jackpot with a single set of 6 numbers are:
1 in 258,890,850If I haven't messed up my math, the odds of winning the Mega Millions lottery jackpot twice in a row with that same set of numbers are therefore:
1 in 6.7 X 10
16The odds of winning the Mega Millions lottery jackpot three times in a row with that same set of numbers are then:
1.7 X 10
25We finally have better odds of finding a bitcoin address that has a balance if we compare to the
odds of winning the Mega Millions lottery jackpot four times in a row with the same exact set of 6 numbers every time: 4.5 X 1033Of course there aren't actually 2,099,999,997,690,000 different addresses that are holding a bitcoin balance (and there never will be due to lost bitcoins and the fact that people will generally store more than 0.00000001 BTC per adddress). If we use a more realistic number (perhaps something like 2,100,000,000 addresses with a balance) we find that:
You have better odds of winning the Mega Millions lottery jackpot all four times on your next four attempts with the exact same set of 6 numbers each time than you will ever have of have of generating a bitcoin address that already exists in a single attempt.