In an event with a set of n possible single-winner outcomes, with wagers W1, W2, W3, ..., Wn the total pool of money on the event is:
Wt = W1 + W2 + W3 + … + Wn
After the ecosystem deducts the vig of r from the pool, the amount remaining to be distributed between the successful players for a successful outcome m is:
Wr = (WT – Wm) * (1 − r)
Those who bet on the successful outcome m will receive a payout of Wr / Wm for every dollar they bet on it. Wm is the wager which the outcome favors.
When there are k possible winners the total amount to be distributed WR is first divided into k equal shares. If m is one of the k winners, those who bet on outcome m will receive a payout of (Wr / k) / Wm for every dollar they bet on it.