[greenfish6]

The first example has a miscalculation; if you invest 1k and the EV is 900, then your choice has negative ROI, not positive.

[breischl]

He's calculating EV above cost. If you look at the calculation, the first term is -1000 to account for the initial investment. So the final value is tell you that you got back the initial money plus 900 more.

[neom]

However, the article is technically inconsistent in framing.

[quirino]

The calculation that arrives at 900 has already subtracted the 1000 from the start.

[postflopclarity]

it's correct. the EV is 900 after accounting for the 90% probability of -$1000. that's what the first term in the sum is for.