In a problem of finding the probability that an even number of games (even S) not being lost in $l$ games, I read the following explanation :
"We form the equation, $x^2 - 4rx + 2r^2 = 0$, and that the roots of that equation be $m$ and $p$, and then make $A = \frac{1-p} {m-p}$, $B = \frac{1-m} {p-m}$"..."the two terms alone $Am^{\frac{1}{2}l} + Bp^{\frac{1}{2}l}$ will then determine the probability" ..."if $l$ is the number of games given, it is evident that the probability for an event occuring in the $l$th game is distant from an event occurig in the 0th game by $\frac{1}{2}l$" ... "the odd number being omitted,since it is impossible an even number of games to be won or lost exactly in an odd number of games"
Why would you want to create A and B as such ?