You have to purchase something from the lottery runner, to participate in that lottery. That is what "Consideration" is.
Incorrect. "Purchase" is most definitely not legally required and is not synonymous with "consideration". See for example this legal definition (pg 3 at
http://www.revenue.pa.gov/FormsandPublications/PAPersonalIncomeTaxGuide/Documents/pitguide_chapter_15.pdf:
"
Consideration in this context means any valuable advantage or benefit that the person conducting a competition, contest of chance or lottery expects to realize as a result of conducting such competition, contest of chance or lottery.
The term, therefore, may include, but is not limited to, bets or wagers of cash or property, making a purchase, being present at a drawing, giving a testimonial for a product of the donor of the prize, filling in an application or contest blank,
following any rules; or expending time or personal effort."
This legal definition includes expending time and personal effort and resources to come up with a crypto block that, when added to the Bitcoin blockchain, allows the multi-billion-dollar Bitcoin juggernaut to continue functioning for another ten minutes.
when did the miner pay the entrance fee into that lottery?
When he first spent money to acquire a computer and electricity / bandwidth to take a chance at calculating a "winning" crypto block.
You are saying that as soon as the Miner "finds a block", its Consideration.
Incorrect. When a miner "finds a block", that's the moment he is awarded a "prize". He gives "consideration" to the Bitcoin community BEFORE he finds a block and BEFORE he wins a prize by chance.
So, an unsuccessful Miner is mining, equals no lottery, since there is no consideration...But when a Miner "finds a block", and gets a "prize", finding the block is the consideration?
Incorrect. The "consideration" is the computer purchase money and electricity the miner dedicates to trying to finding a block whether he succeeds or not.
Who is running this lottery?
Everybody who participates as a Bitcoin miner. Bitcoin is a decentralized group consensus lottery that uses the internet to allow participation among consenting members. That consent doesn't make it legal.
Your legal reasoning is bad faith interpretation, but the US Federal Government has been known to play those games.
Your definition and case law that you are citing is dated 1940, 1954, 1976. Those opinions and definition can not adequately answer many questions with new tech.
If a new technology, uses "Game Theory", to make fair an (unfair) decentralized confirmation network, that does not make itself an illegal lottery.
But is using aspects of a lottery, or "Game Theory" to make the unfeasible (a nontrusted system becomes trustable through nontrust), thus feasible.
There is no caselaw or current US Rulings that would lead one to think the US Attorney General would claim Bitcoin mining is a lottery, thus illegal.
This is new law and only the Supreme Court of the US will be able to rule on this matter.
At the end of the day, if the US Government receives tax revenue from bitcoiners buy/selling bitcoin (like the IRS now mandates), why would they make parts of it illegal?