One problem of filling blocks is that transactions with too-low fees will get "stuck"; I've read about such things happening on Reddit.  Then one of my coworkers told me that those he looked at were simply never broadcast properly, and broadcasting them manually fixed it.  Which lead both of us to wonder how often it's really happening...

My approach is to look at the last 2 years of block data, and make a simple model:

1. I assume the tx is not a priority tx (some miners reserve space for these; default 50k).
2. I judge the "minimum feerate to get into a block" as the smallest feerate for any transaction after the first 50k beyond the coinbase (this is an artifact of how bitcoin core builds transactions; priority area first).
3. I assume the tx won't be included in "empty" blocks with only a coinbase or a single non-coinbase tx (SPV mining); their feerate is "infinite".

Now, what feerate do we assume?  The default "dumb wallet" fee is 10000 satoshi per kilobyte: bitcoin-core doesn't do this pro-rata, so a median 300-byte transaction still pays 10000 satoshi by default (fee-per-byte 33.33).  The worse case is a transaction of exactly 1000 bytes (or, a wallet which does pro-rata fees), which would have a fee-per-byte of 10.

So let's consider the last two years (since block 277918).  How many blocks in a row we see with a fee-per-byte > 33.33, and how many we see with a feerate of > 10:

## Conclusion

In the last two years you would never have experienced a delay of more than 10 blocks for a median-size transaction with a 10,000 satoshi fee.

For a 1000-byte transaction paying the same fee, you would have experienced a 10 block delay 0.7% of the time, with a 20+ block delay on eight occasions: the worse being a 26 block delay at block 382918 (just under 5 hours).  But note that this fee is insufficient to be included in 40% of blocks during the last two years, too; if your wallet is generating such things without warning you, it's time to switch wallets!

Stuck low-fee transactions are not a real user problem yet.  It's good to see adoption of smarter wallets, though, because it's expected that they will be in the near future...