Typically in Roulette you bet on (say) red and if it isn't red you lose. The 1/37 shot goes to the house. So, the probability of -1 is 19/37.
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
A few questions:
- random walk is a sequence of independent random variables, a (stochastic) process in time; roulette is a one-off shot, ie one random variable, not a sequence - so, are you looking to model a repeated sequence of roulette spins?
- the 'time' connection: do you want to model expected winnings over a period of time?
I would love to hear what the experts have to say, as I am just a learner.