Double spending is not about doubling, but about using the same UTXO twice. So, you won't gain anything by double spending coins to yourself.
Let me explain you, with a simple example, how double-spending works:
Lets Alice
be an attacker trying to double spend some coins. Alice
goes to Bob
's store to buy some goods. In order to pay for the goods, she create a transaction, TX1
, that spends from an UTXO from a previous transaction, TX0
, and pays to Bob
. Later on, Alice
generates a second transaction, TX2
, that also spends from TX0
but this time pays back all the money to herself. Down bellow you can see the scenario depicted.
Now, Alice
has multiples ways of double-spending the transaction, depending on her hash power and on whether TX1
has been included in the blockchain or not. Since you assumed you have a 51% of the network hash power, we can assume that Alice
can mine a block with a greater probability than anyone else, so we will take it for granted, an analyze only the other factor, what happens with TX1
.
TX1 not confirmed
If we assume that TX1
is still not confirmed, but it has been broadcast and the nodes are aware of it, Alice
can double spend TX1
with TX2
by just including TX2
in the next block she mines. If Bob has accepted the zero-confirmation transaction as a payment and has delivered the good to Alice
before the inclusion of TX1
in the blockchain, Alice
will obtain both the goods and the double-spent amount.
TX1 confirmed
If TX1
gets confirmed, either because, against the odds, another miner has mined a block in which the transaction was included before Alice
mined hers, since Alice
has the greater hash rate she can overcome the previous block by continue mining on the top of the previous block. This will create a blockchain fork, and eventually Alice
branch will be longer than the other, since her hash rate is bigger. Notice that if Alice
does that frequently lots of forks will occur, in which double-spending transaction could be identified, what will undermine the trust on the currency.
Last, being Alice
the most powerful miner, she could just include double-spending transaction without forking the chain, by including a TX2
in the same branch than TX1
was included. Notice that this violates the blockchain inclusion rules, since two transactions can not spend from the same source. Therefore, the rest of the network will not accept this block as valid. However, since Alice
has the greater hash power she can just keep going and mine over that block. In this case two things can happen, either the trust in the currency is lost since more of the 51% of the hash power is devoted to cheating, or the branch that includes both transactions is just ignored by the rest of the network.
In conclusion, no good comes from someone controlling such amount of hash power.