A roulette wheel is divided into 38 pockets. 18 are numbered red pockets, 18 are numbered black pockets and 2 are green pockets. You can place bets on specific red or black pockets with odds of 35:1. That is, if you are correct you win 35 dollars (plus the dollar you bet), and if you are incorrect, you lose the dollar you bet. A ball is spun into the wheel, and we will assume it lands in all pockets with equal probability. Your friend has developed what he describes as a “foolproof system” for winning. It involves him betting on $1 on 7 red again and again. You try to discourage him, but he is insistent.
What are his expected winnings after 36 spins of the wheel?
Any help would be appreciated. I know it's the probability of red x value of red + probability of not red x value of not red, but don't know how to extend that onto 36 spins.