Answer to question isn't right maybe?

Hey guys, so I saw this on the website/linkdin. And I didn't know how to put a comment on it. But I think the answer here is wrong. In two scenarios. Firstly, if it is a roulette, than you get double your money each time you win. So the caculation would be: 

• 0.45 * 2 (because you double your money when you win) = $0.90.

So, for every dollar you bet, on average, you will get back $0.90. This means you're losing $0.10 on every dollar bet.

If you bet a total of $2000:

• Expected returns from bets = $2000 * $0.90 = $1800.

Now, you started with $1000 and you bet all of it, and then you received and bet an additional $1000. This means that out of your initial $1000, you now have:

• $1000 + ($1000 - $2000) + $1800 = $800.  And then you add in the 200. It would thus break even. 

Another scenario would be if you would get 45% on your money when you win. This would give the following caculation: 

• If you win (which happens 45% of the time), you get $0.45.
• If you lose (which happens 55% of the time), you lose $1.

So, the expected value for every dollar you bet is:

• $0.45 * 0.45 (because you win 45% of the time) - $1 * 0.55 (because you lose 55% of the time) = -$0.2025.

This means that for every dollar you bet, on average, you will lose $0.2025.

If you bet a total of $2000:

• Expected losses = $2000 * $0.2025 = -$405.

Now, you started with $1000. After betting a total of $2000, you will lose $405 from this, leaving you with:

• $1000 - $405 = $595.

Finally, adding in the $200 bonus:

• $595 + $200 = $795.

So, with these conditions, after all the betting and considering the bonus, you would be left with $795, so a net loss of $205.

Correct me if I 'm wrong guys. I just wanted to figure out what the right answer is. 

Thanx in advance