CH02::mining: replace sudoku example with accurate description

This takes up the same amount of space and is (I think) just as easy to
understand, but avoids the indirection of a metaphorical example and
some of the confusions it can create, e.g. that mining is a race to
complete a puzzle rather than a memoryless lottery.

We also remove a later desciption of PoW which is now redundant.

ch02.asciidoc

@@ -542,41 +542,45 @@ and diminishes with time, following a fixed issuance schedule.
 
 
 Mining achieves a fine balance between cost and reward. Mining uses
-electricity to solve a mathematical problem. A successful miner will
+electricity to solve a computational problem. A successful miner will
 collect a _reward_ in the form of new bitcoin and transaction fees.
 However, the reward will only be collected if the miner has correctly
 validated all the transactions, to the satisfaction of the rules of
 _consensus_. This delicate balance provides security for bitcoin without
 a central authority.
 
-A good way to describe mining is like a giant competitive game of sudoku
+Mining is designed to be a decentralized lottery.  Each miner can create
-that resets every time someone finds a solution and whose difficulty
+their own lottery ticket by creating a _block template_ that includes
-automatically adjusts so that it takes approximately 10 minutes to find
+the new transactions they want to mine plus some additional data fields.
-a solution. Imagine a giant sudoku puzzle, several thousand rows and
+The miner inputs their template into a specially-designed algorithm that
-columns in size. If I show you a completed puzzle you can verify it
+scrambles (or "hashes") the data, producing output that looks nothing
-quite quickly. However, if the puzzle has a few squares filled and the
+like the input data.  This _hash_ function will always produce the same
-rest are empty, it takes a lot of work to solve! The difficulty of the
+output for the same input--but nobody can predict what the output will
-sudoku can be adjusted by changing its size (more or fewer rows and
+look like for a new input, even if it is only slighly different from a
-columns), but it can still be verified quite easily even if it is very
+previous input.  If the output of hash function matches a template
-large. The "puzzle" used in bitcoin is based on a cryptographic hash and
+determined by the Bitcoin protocol, the miner wins the lottery and
-exhibits similar characteristics: it is asymmetrically hard to solve but
+Bitcoin users will accept the block template with its transactions as a
-easy to verify, and its difficulty can be adjusted.
+valid block.  If the output doesn't match the template, the miner makes
+a small change to their block template and tries again.  As of this
+writing, the number of block templates miners need to try before finding
+a winning combination is about 168 billion trillions.  That's also how
+many times the hash function needs to be run.
+
+However, once a winning combination has been found, anyone can verify
+the block is valid by running the hash function just once.  That makes a
+valid block something that requires an incredible amount of work to
+create but only a trivial amount of work to verify.  The simple
+verification process is able to probabalistically prove the work was
+done, so the data necessary to generate that proof--in this case, the
+block--is called Proof-of-Work (PoW).
 
 ((("mining and consensus", "mining farms and pools")))In
 <<user-stories>>, we introduced ((("use cases", "mining for
 bitcoin")))Jing, an entrepreneur in Shanghai. Jing runs a _mining farm_,
 which is a business that runs thousands of specialized mining computers,
-competing for the reward. Every 10 minutes or so, Jing's mining
+competing for the block reward. Jing's mining
-computers compete against thousands of similar systems in a global race
+computers compete against thousands of similar systems in the global
-to find a solution to a block of transactions. ((("Proof-of-Work
+lottery to create the next block.
-algorithm")))((("mining and consensus", "Proof-of-Work
-algorithm")))Finding such a solution, the so-called _Proof-of-Work_
-(PoW), requires quadrillions of hashing operations per second across the
-entire Bitcoin network. The algorithm for Proof-of-Work involves
-repeatedly hashing the header of the block and a random number with the
-SHA256 cryptographic algorithm until a solution matching a predetermined
-pattern emerges. The first miner to find such a solution wins the round
-of competition and publishes that block into the blockchain.
 
 Jing started mining in 2010 using a very fast desktop computer to find a
 suitable Proof-of-Work for new blocks. As more miners started joining
@@ -628,14 +632,14 @@ round.
 
 ((("candidate blocks")))((("blocks", "candidate blocks")))Alice's
 transaction was picked up by the network and included in the pool of
-unverified transactions. Once validated by the mining software it was
+unverified transactions. Once validated by a full node, it was
-included in a new block, called a _candidate block_, generated by Jing's
+included in a block template generated by Jing's
 mining pool. All the miners participating in that mining pool
-immediately start computing Proof-of-Work for the candidate block.
+immediately start trying to generate a Proof-of-Work for the block template.
 Approximately five minutes after the transaction was first transmitted
 by Alice's wallet, one of Jing's ASIC miners found a solution for the
-candidate block and announced it to the network. Once other miners
+block and announced it to the network. After other miners
-validated the winning block they started the race to generate the next
+validated the winning block, they started a new lottery to generate the next
 block.
 
 Jing's winning block became part of the blockchain as block #277316,