Been working on this for a few hours with no luck.
The context: I'm setting up a formula for dividing up a betting kitty to bet on 5 favourites across multiple games that all occur in the same competition.
What i want to know:
How do I calculate what percentage of my total kitty to bet on each favourite (across 5 games) if the odds of each win is different, assuming that i want the same return from each win. Meaning, i want the value of the winnings per game to be equal. That way the weighting of betting on a heavier favourite that pays less takes up more percentage of the kitty but results in an equal fifth of the return (assuming all games win).
For example, lets say the odds of each game, one to five, are: 1.12, 1.33, 1.45, 1.60 and 1.89. These are made up but common odds for this bet. Let's say i start with $200. How do I calculate what proportion of total kitty to place on each bet so that the winning (bet + profit) are equal?
Formulas would be great of course so that I can play around with numbers.
If this question is structured badly and you need more infornation - please let me know.
Thanks in advance!
Not sure if I actually understood the question. Here is a try.
Let your budget be $B$. And the odds be $o_i$ for each game $i$. You bet $b_i$ on each game $i \in \{1,...,5\}$ such that in case of winning you get $b_i o_i$ as a return. In case you lose you get 0. The actual probabilities of winning are not observable from the odds. No one knows these true probabilites and even the odds are not the bookmakers true guesses as they want some profit.
Is your question that, given $B$ and all five $o_i$, you want to find the five $b_i$ such that
$b_i o_i = x$ for all $i$ and $\sum b_i \leq B$ with the maximal $x$?
If you spend the entire budget, you have $B = \sum b_i = \sum \frac{x}{o_i}$ which you can solve for $x$ (you have all the other numbers). Then you have some $x$ which you plug into $b_i = x /o_i$ so you know how much to bet on each game $i$.