I'm not confident enough with statistical tools, but I'm looking for suitable statistical test. As there are many profound people here, I ask for advice.
My original problem is different from the one below, but I will use the game of roulette to give an accurate example of what test I'm looking for.
So, let's say I have a roulette game where I believe the wheel is biased, and the bias will depend on an external parameter A. I cannot control this parameter which is different each time, but I can observe the parameter before each acting on each spin. (Such a parameter could be the the wheel's last result, the choice of ball or whatever).
Let's also say that I have a model for the roulette game incorporating this parameter A, and it will give me probabilities of each result depending on this parameter.
My question would be: How can I test whether my model does in fact produce the correct probabilities for this game, depending on the observation of both the external parameter and the outcome of the game ?
Let's say a first test of simple correlation between the parameter and the outcome turned positive significantly. But how do I quantify the quality of the model ?
My original problem is different from the one below, but I will use the game of roulette to give an accurate example of what test I'm looking for.
So, let's say I have a roulette game where I believe the wheel is biased, and the bias will depend on an external parameter A. I cannot control this parameter which is different each time, but I can observe the parameter before each acting on each spin. (Such a parameter could be the the wheel's last result, the choice of ball or whatever).
Let's also say that I have a model for the roulette game incorporating this parameter A, and it will give me probabilities of each result depending on this parameter.
My question would be: How can I test whether my model does in fact produce the correct probabilities for this game, depending on the observation of both the external parameter and the outcome of the game ?
Let's say a first test of simple correlation between the parameter and the outcome turned positive significantly. But how do I quantify the quality of the model ?