Remember how I said it takes a group of people to open the box? That was a lie. (Actually it was true, but you should treat it as a lie right now)
*Note that I may have misunderstood some stuff, so default to someone who knows more than me if they tell you this is wrong.
Anyone can open the box, and in fact only one person can open the box. So who gets to open the box? Well, the probability of being able to open the box is based on how much computing power you have. The box, hereafter referred to as the block, is designed to make it work this way. Why doesn’t the person who has the most computing power solve the block first? A: Magic B: Lies. Well, B is sort of redundant given A.
So, if only one person solves the block, why don’t they just make it so that they get all the monies?
The answer is that the blocks form a chain, and if the next block solved doesn’t match up with the previous block then the code goes WTF, and throws the old block away like an unwanted child. (Mehh.. close enough)
Depending on the coin, there may be a number of confirms needed before the block is considered canon, (I believe 15 confirms means that 15 blocks have to be solved after that block.)
You can generally assume that after just a few confirms (or even no confirms) the transaction was legitimate, but if you were transferring large sums of money you might want to wait a bit. Confirms are more important to the miners because they don’t get their coins if the block turns out to be bad, as opposed to the average consumer who will still get their money when a good block reads the transaction, as long as the transaction was good.
So, in order to steal money you would either have to:
A: String along a bunch of concurrent blocks (which would be improbable unless you have a lot of the processing power)
B: Solve a phony block at the same time your transaction is processed and leave with your loot before the next block is solved. (Also really hard, and if you are moving large sums the other party is going to wait for a few confirms anyways)
C: Do something else (This one is most likely, but is also very hard. I don’t list it because I don’t understand it yet.)
E: Find a flaw no one has thought of and exploit it (May not exist)
Now remember how I said that you had to work as a group to open a box? Well, it ends up being true. While probability factors into opening the box, it is based on processing power. The computing power of any one person is so small that they have to work in teams to have enough power to get a probability greater than zero. Again, we are treating this as magic for the sake of understanding the basics. If it makes you feel any better think of the block solving probability (as a function of computing power) as having a non-linear component.