1. I keep seeing here at this site that you cannot make money mining on your own. It also seems that you cannot pay for mining as the cost will not allow you to earn money. Given all of that, why are so many people still mining and trying to mine, etc? It would seem that if you are unlikely to make your money back, why is there so many people trying to mine?
Mining can still be profitable if you have access to cheap electricity and manage to acquire ASIC without overpaying.
On the other hand, there are many people who are mining at a loss. While some may do it as a hobby, or for educational purposes, I suspect many continue to mine at a loss simply because they are not very good at figuring out the math to know if they are truly profitable or not.
If the bitcoin exchange rate continues to increase, it is possible to spend money mining, and end up at the end with bitcoins that are worth more than the amount spent on equipment and power. However, often the miner would have been better off if they had simply exchanged their local currency for bitcoins instead of mining.
Hypothetical Example:
When bitcoin is exchanging at $200 per bitcoin, a user spends $1000 on mining equipment, then waits 6 months for delivery. Once the equipment is delivered, the user starts spending $100 per month during the next 3 months mining. During mining month 1, the exchange rate is $400. During month 2 it is $600, and during month 3 it is $800. By the end of 3 months of mining the difficulty has gotten so high that the user is mining less than 0.0000001 BTC mer month, and the exchange rate is $1000. The miner manages to mine a total of 1.4 bitcoins and sells them all at the end of month 3 for $1400.
It would appear that this miner made a profit (They spent $1300 to acquire 1.4 bitcoins and sold them for $1400). However, on closer inspection we see that if the miner had simply bought bitcoins in the beginning they'd have acquired 5 bitcoins. If they spent the $100 per month on bitcoins during the 3 months of mining, then they'd have purchased another 0.25 + 0.1666 + 0.125 = 0.5416. They could have sold this 5.5416 BTC at the same time they sold the 1.4 bitcoins and they'd have ended up with $5,541.60. That's $4,041.60 more than they got by mining. Even if they could find someone to buy the now useless mining equipment back from them at the full price they paid, they'd still be short $3,041.60.
When you buy mining equipment and mining power, all you're really doing is indirectly buying the bitcoins that the mining will get you. If you believe that those bitcoins will hold enough value to turn a profit, then you are often better off just buying the bitcoins.
2. Does luck have anything to do with finding a bitcoin through mining? If I start two identical mining rigs up at the exact time, what are the odds that one will find the bitcoin before the other?
If you are solo mining with both machines (and if the machines have enough hashing power to actually solve a block in the next 3 years), then it is guaranteed that one machine will be awarded at least 25 BTC before the other machine gets any at all. If you are mining in a pool, then the 2 machines should earn bitcoins at nearly the same rate.
In other words, if we are trying to solve a mathematical equation to earn a bitcoin,
This is not what mining does.
would both mining rigs take the same path to earn the coin
Generally? No.
But again, it depends a bit on whether you are talking about solo mining or mining in a pool,
or would they go separate paths to get to the bitcoin? Hopefully this makes sense.
It doesn't really. If you are mining in a pool, then each machine will receive different work from the mining pool. If you are solo mining, then each machine will be communicating with a different client and will therefore be working on slightly different transaction order.
The analogy I can think of is if three people were driving from Michigan to Florida and left at the same time. They each take a different route, but will eventually all get to Florida. The person that takes the shortest/quickest route should get their fastest. Would mining be like that? Depending on which route they take, will that allow one to get there faster. Or would the analogy be better as 3 cars leave Michigan and the fastest car who can drive the fastest gets there first?
No, there is only one route.
If you are looking for an analogy that you can wrap your head around, think of a mining machine more like a person rolling five 6-sided dice. They keep re-rolling all 5 dice until they get a Yahtzee (all five dice land on the same number). Once they roll a Yahtzee, they get 25 BTC and start all over. If a second person starts rolling their own set of dice at the eaxct same speed, will they get a Yahtzee at the same time? Is there a shorter path that they can use when rolling those 5 dice? If the second person rolls their dice twice as fast are they guaranteed to get a Yahtzee in half the time, or do they just have a better likely hood to do so?
Now, think of a pool as a group of people that agree to roll their dice as a team. Everyone in the group has their own 5 dice to roll. Everyone agrees that if any one of them gets a Yahtzee, then they will split up the 25 BTC among them all. To keep the split fair (so one guy doesn't just roll his dice once or twice, and then wait for the group to win), they agree that the total number of rolls will be added up for each of them, and their share of the 25 BTC will be proportional to the number of times that they roll. This means that someone who rolls their dice twice as fast as everyone else will receive twice as much of the 25 BTC as everyone else (and that someone who only rolls once or twice while the rest of the group rolls thousands of time will barely get anything at all).