Expected Value question / Roulette scenario

Hello, I am trying to explain to someone mathematically why this roulette strategy is a poor idea.

It has been a while since I have calculated more than the simplest probability problems, but I was thinking that demonstrating that this has negative expected value is a way to show that it's a bad bet.

Here's the 'system': You bet $100 on a spin in which there is 12/37 probability of winning and a 2:1 payout. If you lose, you double your initial $100 bet and wager $200 on the following spin... etc. Any time you win, you begin the series again with the initial $100 unit. I'm assuming a max of 12 spins in the series since you are bound by table limits of some sort. Since it is a 2:1 payout, you can win more than your initial $100 betting unit if you are further along in the series of spins.

I think the expected value of spin #1 is:

(12/37) * 200 + (25/37) * -100 = -2.703

I'm trying to figure out what the EV is for the whole game, but I'm having some difficulty. I did a forum search and there was some reference to situations like this, but nothing that fit the bill.

It's my first post, so I hope it's not poor form to start with a question, but any help is greatly appreciated. Thanks!