Combining MLEs question

Hi everyone,

How do you find a combined MLE? As in say you are given data from three different games and you want to work out the MLE of, say, p_A, the probability that team A wins a game. Do you work out the MLEs individually from each game and then do something to them? But what?

Thanks for any help

Identify their individual distributions, find their joint distribution from there and maximize it wrt the unknown parameter(s).