Generating the last block

[amazingrando]

I was looking at a pending payout from mining on Eligius that said the coins would be generated in XX blocks.

Suppose that the last block has been found, such that there are now 21 million coins.  How would coin generation work given that no more blocks would be found.  Or, am I totally misunderstanding??

[slush]

Number of coins is limited, but number of blocks isn't. There simply won't be any block reward from blocks once all coins will be mined. Miners will live from transaction fees then.

[amazingrando]

Interesting.  Thanks Slush

[ElectricMucus]

It will take 32 block reward reduction till we get to ~1 satoshi per block. That's a looong time, and if there isn't any revolutionary life extending technology coming up it is likely you won't live to tell them about the first reduction

[amazingrando]

So it will go down to 25 and then 12.5, etc.?  I assume that it does not need to be whole coins found per block (can be fractions).  Is there an easy way to calculate when we will hit the first reward reduction?  I am guessing late next year.

[ElectricMucus]

That is difficult to exactly estimate because of luck. Every 210000 blocks the reward drops in half and the time between blocks *should* be around 10 minutes on average, but will never be exactly 10 minutes on average.

To calculate the next adjustment you could take 2100000 minutes - current block*10 - block of the last block reward reduction*10 (in our case 0, the genesis block)
The resulting number would be the number of minutes it should take under ideal conditions. To arrive at a better estimate you would have to do some cumbersome heuristics on the lag behind difficulty and actual hashrate which would only work if you know a better way to estimate it than the diffuclty adjustment algorithm does in the first place.

My uneducated guess for the 25 block reward reduction is the end of the maya calender 

[amazingrando]

Luck shouldn't be a factor, right?  The law of large numbers should mean that over time things will average out to 10 mins.

So if we take 2,100,000 minutes - 1,524,610 = 575,390 minutes.  Which would put us sometime around 400 days from now, or around December 16, 2012.  Just in time for the apocalypse!  Maybe the reward reduction will unleash a super stuxnet type virus that will cause skynet to become self aware and thereby bring out the end of days. 

[ElectricMucus]

Well the difficulty adjustment lags behind the actual hashrate so if difficulty is falling most of the time and since miners are motivated by prices the hashrate follows prices. Also there is luck involved but of course the longer the period the lesser it depends on it.
So if we have higher prices on average the event will take place sooner, and verse visa.

[amazingrando]

Should have added that caveat that difficulty could affect things