In September, 2014, a collective experiment began in the bitcoin
ecosystem.  Available block space (1MB) began to sometimes fall short of
the space required to mine all of the transactions that would otherwise
have been included.

This chart, posted earlier, shows the onset of the
some-blocks-at-maximum era.

Although the average block is only about 400K, real blocks are bigger or
smaller due to the random length of time between blocks (and other
factors).  I look at how often this is predicted to happen.

Recently, transactions have been confirmed at a rate of about
100000/day*.  The average transaction size for the past 6000 blocks has
been 545 bytes.  Using these values,

txesPerMinute = 100000 / 24 / 60 = 69.4
txesInMaxBlock = 999977 / 545 = 1834
minutesToFillBlock = txesInMaxBlock/txesPerMinute = 26.4

Using the theoretical formula for the time before an inter-block
interval of at least a given length **

blockChickenMinutes[x] := 10 (exp(x/10) - x/10 - 1)

we obtain

minutesBetweenFullBlocks = blockChickenMinutes[minutesToFillBlock] = 104

We currently expect a maximum-size block every 1 hour + 44 minutes, on
average.  If the transaction rate doubles, we should expect a
maximum-size block every 14 minutes, on average.  The non-linearity
makes sense, because doubling the average without raising the maximum
requires disproportionately more maximum-size blocks.

This estimate is understated because transaction size and submission
rate have their own distributions.  Using the averages of 545 bytes and
100000/day ignores the fact that for some blocks, there are unusually
big and/or numerous transactions, which increases the block size
variance and causes blocks over the threshold to be encountered more

These calculations are confirmed by empirical observation of the most
recent 6000 blocks:

In many cases, the miner chose to create a 750KB block, which is
unusually likely to be followed by another 750KB or 1MB block, because
the next interval starts off with a 250KB backlog.  Some backlog
transactions may experience more than 1 block delay in these cases.


** This is a chicken-crossing-the-road problem. Wait time = (exp(λx) −
λx - 1) / λ
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