Suppose a match can be completed in three ways: win, loose or draw. A bookmaker provide the following coefficients (including spread) for each case respectivelly: $c_1, c_2, c_3$. That is, if a player predicts result of the match correctly he is rewarded by his bet multiplied by respective coefficient; otherwise, he looses his bet. The spread is a fraction of the player's bet that the bookmaker "wins" on average.
There are two questions: how much is the spread for given coefficients and how coefficients $c_1, c_2, c_3$ would change if we increase spread by $x$.
My suggestions: let $p_1, p_2, p_3$ be a probabilities of the respective event. Then the expectation for each result will be: $$E_i = (1 - p_i)\cdot 1 - p_i\cdot (c_i - 1),\, i=1, 2, 3$$ On the other hand all $E_i$ must be equal to spread $s$. That is, we got a system of linear (in $p_1, p_2, s$, since $p_3 = 1 - p_1 - p_2$) equations which can be easily solved. This would be an answer to the first question. The second question is answered by solving the same system of linear (now in $c_1, c_2, c_3$) equations substituting $s:= s + x$.
Am I right?