This document in super short is about:
Keeping found blocks secret, to perform calculations on them so that others cannot, thereby giving a racing adventage. They "secretivers" will have a head start.
When "publicers" announce their block quickly publish the "secret" block to create a tieing situation.
Currently the first block that arrives is picked by miners so the "secretives" have incencitive to "delay public blocks", an incentive to listen in on other mining pools "detect early public block announcement to quick react to it" and to try and inject/publish their secretive block as fast as possible towards other miners that have not yet received a new block.
If the random picking solution is implemented, 50% of "publicers" will choose the "publicer" block, 50% will choose the "secretivers" blocks, while 100% of the "secrectives" pick the "secritive" block. 150% will therefore try and continue on "secretive" block and only 50% on "publicer" block, increasing the likelyhood of "secrective" block to win out, thereby injecting the secretive block into the blockchain, either the next block will be found be a publicer or by a secretiver, the more secretivers there are the more likely it will be found by them especially because of the headstart, leading to an incentive for others to join the "secretivers" also known as "(a)head-starters"
(actual percentages will depend on the size of the pools).
The conditions above describe the secretives being ahead 1 block.
The document continues with being 2 blocks ahead. (now it gets longer and fudgy for me at least):
I am not sure but I think in this case it will publish both secretive blocks if the publicers announce their block, immediatly invalidating their progress, this could also cause other self-ish miners to be in trouble, they could also publish their second block creating a new tie, or perhaps even a third.
These situations could be easy to detect, the second block would be announced immediatly ? perhaps the algorithm can be refined somewehat by introducing a believable delay of a few minutes, though risky if another selfish pool announces it sooner, though keeping the second block secret could also be an option and try and rely on tieing only. Though for many this would not be statisfactory and would probably try the third block strategy and so forth and thus keep immediatly publishing any found blocks immediatly to try and win over the main network.
This last line of thought is described in the last else statement.
If more than 2 blocks ahead, publish all of them to solidify the gains. If this is truely the longest chain then they'll win and be garantueed of the rewards, if this is not truely the longest chain then they will be superseeded/defeatede by another selfish mining pool... so I am in doubt that this last else statement is smart in case of multiple selfish mining pools.
Eventually they would be defeated by another selfish mining pool that may delay their +1 block to try and defeat the other selfish mining pool into wasting their processing time on their private blocks which they hope would be the new public chain... eventually the longer selfish mining pool may win out by delaying their publication of their found blocks.
So I do think the algorithm can be refined somewhat by building in delays to try and defeat other selfish mining pools. Thus if this does get implemented we'll be seeing some kind of time wars... publish to late and one may be superseeded, publish too soon and one may be superseeded, however in this case one would always be superseeded so it makes no sense, and thus always publishing beyond two makes sense... either you truely have most processing power or not, however this does not include luck and by chance...
Perhaps the document describes these lines of thoughts and explains how to handle it or maybe not... maybe it was too difficult to analyze how the algorithm would perform against itself.
For now I shall give it a rest until further notice
Some points to sum up:
+ Find a block and keep it secret.
+ Find the next block for the secret block.
+ Publish the secret block if a public block is published.
+ Try to get the secret block published sooner.
+ Some honest nodes may work on the published secret block and if they find the next block the secret block wins.
+ Secret block has more chance of winning if random selection is implemented (this could be the true motive for the document, implementors of bitcoin beware !
+ Currently fastest announced block seems to win.
+ Incentive to keep public blocks delayed.
+ Incentive to spy on other pools to detect early block announcement.
+ Incentive to detect traitors by selective announcing private blocks found by pool maintainer.
+ Spying on selfish pools is a potential counter-strategy if done in secret somehow.