For a roulette wheel i have P(red)=18/37, P(blue)=18/37 and P(other)=1/37

Now in order to modell this as a random walk if 1 dollar is one for red and 1 dollar lost for blue, if i take the values:

y= 1 for red 18/37

-1 for blues 18/37

however i thought for a random walk the probability has to sum to one, or does it suffice if there are two possibilities and the expectation is zero.

If i include y=0 for other 1/37 then this has three possibilities and is no longer a simple random walk which by definition should only take two possibilities