Does increasing your bet size increase your EV when bonus clearing?

[stephan]

By EV I mean expected value and not $/hour! I need to settle this once and for all. I have this posted at 3 forums and it's split almost evenly the number of people who think both ways.

I'm having a debate with several people over this. Here is the scenario.

Casino x is giving you a $100 bonus for depositing $100 at their site. You have to wager $2000 to clear the $100 bonus and cash out.

Group 1 says that the EV of the bonus is the same no matter how much you bet. If you bet $20 100x then you should expect $2000x.995= (house edge of .5%) $10. Subtract that $10 from the $100 bonus and you net $90. If you bet $1 2000x then it's the same exact result.

Group 2 says Anytime wagering requirements do not carry over, betting
higher increases variance, which increases EV. This reason is very
simple. Over the long run you are wagering a lot less at a negative
expectation game.

Who is right?


EDIT:
This is what the math forum thinks about it

This is what they think about it over at Rx (the discussion starts on page 3)