Odds of generating an in-use address vs. odds of winning powerball jackpot

[Moria843]

Does anyone have a comparison of these odds?

What are the odds of using a totally random method of generating a bitcoin address to come up with an address that's already in use vs. the odds of hitting the powerball jackpot?

Which is more likely?

If odds of winning powerball better, would like to see expressed as odds of generating an in-use address with bitcoins the same as winning x powerball lotteries in a row?

I know we would need to know the number of addresses that have funds in them and would need to make some assumptions. Would like to hear educated estimates on odds from math gurus.

[shorena]

Powerball is 1 in 292,201,338[1]
A specific address is 1 in 2¹⁶⁰ = 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976
Any used address[2] 1 in 2¹⁶⁰/0.5*10⁶ ~= 2,923,003,274,661,805,836,407,369,665,432,566,039,311,865

So finding an address with a balance is ~10³⁴ times less likely than winning the jackpot for the powerball lottery.


[1] https://en.wikipedia.org/wiki/Powerball#Prizes_and_odds
[2] https://blockchain.info/charts/n-unique-addresses?timespan=all&showDataPoints=false&daysAverageString=1&show_header=true&scale=0&address=

[DannyHamilton]

EDIT:  Looks like Shorena was faster at the math than me.  Ah well, I'll leave my post here anyhow.

There are 292,201,338 unique ways to choose from the set of Powerball numbers.  There is exactly 1 arrangement of those numbers that will win.  Therefore the odds of winning the powerball with a single $2 set of numbers are a 1 in 292,201,338 of winning approximately $1 billion.

There are 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 unique bitcoin addresses.  There can't possibly be more than 2,099,999,997,690,000 addresses holding a balance at any moment in time (if every potential bitcoin had already been generated, and they were distributed as 1 satoshi in each address).

If I've done the division correctly, that works out to the best possible odds anyone could theoretically ever have are about a 1 in 695,953,161,399,311,771,921,950,012,312,375 chance of "winning" 0.00000001 BTC

Odds would be multiplied for consecutive wins, so for someone who hadn't won the Powerball at all yet to be able to win twice consecutively with only a single $2 set of numbers chosen on each draw you'd be looking at a 1 in 85,381,621,928,990,244 chance of winning approximately $1.04 billion (the prize re-sets back to $40 million after the first win).

For 3 consecutive wins you'd be looking at a 1 in 24,948,624,168,261,090,285,746,472 chance of winning approximately $1.08 billion.

For 4 consecutive wins you'd be looking at a 1 in 7,290,021,363,225,027,714,833,921,447,179,536 chance of winning approximately $1.12 billion.

So, your odds of "winning" 0.00000001 BTC are better than your odds of winning a total of $1.12 billion through 4 consecutive Powerball draws, but not as good as your odds of winning a total of $1.08 billion through 3 consecutive Powerball draws.

Obviously bitcoin isn't spread quite as thinly as 1 satoshi per address, so realistically you're probably looking at better odds of an address collision than winning 5 consecutive Powerball drawings, but better odds of winning 4 consecutive Powerball drawings than encountering an address collision.

Note that this isn't just winning 2, 3, 4, or 5 Powerball draws in a lifetime (which is FAR more likely), this is consecutive draws.

Note also that the odds of "winning" powerball multiple times in a row doesn't change if you choose the same set of numbers every time.  Therefore, another way of looking at those Powerball odds that I stated, is that it is the odds that the powerball draw will come up 1, 2, 3, 4, and 5 with a red ball of 6 that many times in consecutive draws.

[Moria843]

Thanks guys. Such huge numbers it's difficult to fathom, but that really helps put it in perspective.

[cr1776]

Thanks guys. Such huge numbers it's difficult to fathom, but that really helps put it in perspective.

And that is the problem.  It is very difficult to fathom the size of the space even looking at the numbers.

It is easy to think, oh, the number is twice as long, so twice as hard, so I'll just search twice as long when in fact it is nothing like that.  Without consciously thinking about it it is hard to grasp.  Even thinking about it, the scale is just so immense it is hard to appreciate.  Shoot, even looking at the math it is hard to appreciate the enormity of it. 

Glad Shorena and Danny beat me to the math!
 

[Tavos]

Powerball is 1 in 292,201,338[1]
A specific address is 1 in 2¹⁶⁰ = 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976
Any used address[2] 1 in 2¹⁶⁰/0.5*10⁶ ~= 2,923,003,274,661,805,836,407,369,665,432,566,039,311,865

So finding an address with a balance is ~10³⁴ times less likely than winning the jackpot for the powerball lottery.


[1] https://en.wikipedia.org/wiki/Powerball#Prizes_and_odds
[2] https://blockchain.info/charts/n-unique-addresses?timespan=all&showDataPoints=false&daysAverageString=1&show_header=true&scale=0&address=

Wow, that math though. I'm surprised by small the chance is of getting an address in use.

[americanpegasus]

For illustration purposes to people new to Bitcoin, it would be easier to explain using a single Bitcoin address.  We know of a single Bitcoin address with at least a billion dollars in it, right?  For example, the Coinbase cold storage or one of Satoshi's original addresses. 
 
Also, let's assume a computer capable of attempting to brute force a Bitcoin address at a reasonable speed, and running this computer for an hour.  This seems equivalent to going to the convenience store and buying a $2 lottery ticket. 
 
So, how do my chances compare to winning that $1 billion from the Powerball vs. brute forcing a known Bitcoin address with $1 billion of Bitcoin in it?

[DannyHamilton]

We know of a single Bitcoin address with at least a billion dollars in it, right?

Nope.  At the current exchange rate of approximately $450 per bitcoin, there are no bitcoin addresses that currently have $1 billion worth of bitcoins associated with them.

As a matter of fact, there are no bitcoin addresses that even have 10% of that amount.

[americanpegasus]

We know of a single Bitcoin address with at least a billion dollars in it, right?

Nope.  At the current exchange rate of approximately $450 per bitcoin, there are no bitcoin addresses that currently have $1 billion worth of bitcoins associated with them.

As a matter of fact, there are no bitcoin addresses that even have 10% of that amount.

 
 
Shit, sorry.  Bad math.  I guess I was thinking of something else. 
 
Alright, so perhaps let's compare the highest address on the rich list to the average Powerball jackpot (not this record one).  I think the highest address have around $100 million in them, which is comparable to a Powerball jackpot. 
 
Also, it's another reminder of just how big Bitcoin (or a competing financial network) will have to inflate to truly be a world financial network.... a 'bit' will literally need to be worth $1 each.