ch10: changes to the analogy of a dice game

ch10.asciidoc

@@ -887,7 +887,7 @@ Successful blocks pay the reward to a pool bitcoin address, rather than individu
 
 Pools are open to any miner, big or small, professional or amateur. A pool will therefore have some participants with a single small mining machine, and others with a garage full of high-end mining hardware. Some will be mining with a few tens of a kilowatt of electricity, others will be running a data center consuming a megawatt of power. How does a mining pool measure the individual contributions, so as to fairly distribute the rewards, without the possibility of cheating? The answer is to use bitcoin's Proof-of-Work algorithm to measure each pool miner's contribution, but set at a lower difficulty so that even the smallest pool miners win a share frequently enough to make it worthwhile to contribute to the pool. By setting a lower difficulty for earning shares, the pool measures the amount of work done by each miner. Each time a pool miner finds a block header hash that is equal to or less than the pool target, she proves she has done the hashing work to find that result. More importantly, the work to find shares contributes, in a statistically measurable way, to the overall effort to find a hash lower than the bitcoin network's target. Thousands of miners trying to find low-value hashes will eventually find one low enough to satisfy the bitcoin network target.
 
-Let's return to the analogy of a dice game. If the dice players are throwing dice with a goal of throwing equal to or less than four (the overall network difficulty), a pool would set an easier target, counting how many times the pool players managed to throw equal to or less than eight. When pool players throw equal to or less than eight (the pool share target), they earn shares, but they don't win the game because they don't achieve the game target (equal to or less than four). The pool players will achieve the easier pool target much more often, earning them shares very regularly, even when they don't achieve the harder target of winning the game. Every now and then, one of the pool players will throw a combined dice throw of equal to or less than four and the pool wins. Then, the earnings can be distributed to the pool players based on the shares they earned. Even though the target of eight-or-less wasn't winning, it was a fair way to measure dice throws for the players, and it occasionally produces a four-or-less throw.
+Let's return to the analogy of a dice game. If the dice players are throwing dice with a goal of throwing equal to or less than four (the overall network difficulty), a pool would set an easier target, counting how many times the pool players managed to throw equal to or less than eight. When pool players throw equal to or less than eight (the pool share target) but higher than four (higher than the overall network difficulty), they earn shares, but neither they nor the pool win the game because they don't achieve the game target (equal to or less than four). The pool players will achieve the easier pool target much more often, earning them shares very regularly, even when they don't achieve the harder target of winning the game. Every now and then, one of the pool players will throw a combined dice throw of equal to or less than four, the pool player wins a share and the whole pool wins the game. Then, the earnings can be distributed to the pool players based on the amount of shares each one has earned. Even though the target of eight-or-less wasn't winning, it was a fair way to measure dice throws for the players, and it occasionally produces a four-or-less throw.
 
 Similarly, a mining pool will set a (higher and easier) pool target that will ensure that an individual pool miner can find block header hashes that are equal to or less than the pool target often, earning shares. Every now and then, one of these attempts will produce a block header hash that is equal to or less than the bitcoin network target, making it a valid block and the whole pool wins.