I'm currently working on some automated wagering tools. Calculating payouts and such.

However I've hit a little notch which has been eating my brain for the last couple of days.

This notch is the parlay payout function.

By experimenting with some other programs of this nature. I know the following.

There are 3 ways to calculate the payout:

Fixed odds: You multiply the risked amount by the given odd, depending on how many teams are on the parlay.

True odds: You calculate the payout for the first game, the result of that plus the risked amount go as risk on the next game. So on and so forth.

Fixed "True" odds: here's where i have the problem.

I did a graph to know the nature of the function and discovered that it has 2 parts depending on the odds on each game. If the odds are positive (greater than 1:1 ratio) the function shows a linear graph. Ive calculated the inclination of the line (1,8973666) but i still can't figure out how is that calculated from the fixed odd (constant 2.6) and the amount of games in the parlay (Constant 2)

I still haven't started to work on the second part of the function which I know (from the graph) that its y/(x1*x2*...*xn) = z (or something of the sort)

Although I would be very happy to have the answer handed to me. It's best if I could learn a method to deduct formulas from a set of data.

I will post more data if requested.

Thanks in advance.