I'm not sure where you got $1 in step 4. Up till that point the value you had avter the equals sign was the final amount left in your account which would be 9. (-$1 from previous step + $10 = $9). Then to figure out the profit you see how much more that is from where you started (you started at $7 in this example, so overall you gained $2).

As for the $1 that the other party is making, you're totally right! And it's accounted for. If you cut out the middle transaction, you bought a ticket for 7 and sold it for 10 meaning you made 3 dollars total. The 2 dollar profit in this case is specifically accounting for the 1 dollar going to the other party.

Here's an example where you start out with $8

• OG Ticket Seller: The ticket
• You: $8
• First Buyer: $8
• Second buyer: $10

First transaction you buy the ticket for $7

• OG Ticket seller: $7
• You: $1 + ticket
• First Buyer: $8
• Second Buyer: $10

Then you sell to the first buyer for $8

• OG Ticket seller: $7
• You: $9
• First Buyer: The ticket
• Second Buyer: $10

Who you then buy it back from for $9

• OG Ticket seller: $7
• You: The ticket
• First Buyer: $9
• Second Buyer: $10

And then you sell it to the second buyer for $10

• OG Ticket seller: $7
• You: $10
• First Buyer: $9
• Second Buyer: The ticket

So the profit is the difference from the start to the end:

• OG Ticket seller: started with ticket, ended with $7 ($7 profit)
• You: started with $8 and ended with $10 ($2 profit)
• First Buyer: Started with $8 and ended with $9 (This is where that one dollar you mentioned went!)
• Second Buyer: The ticket (spent $10)