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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!

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  • $\begingroup$ When you say the odds are $1.12$, if you bet one dollar do you get back $2.12$ (your dollar plus $1.12$) or $1.12$ (your dollar plus $0.12$ $\endgroup$ – Ross Millikan Dec 27 '16 at 1:05
  • $\begingroup$ Odds are 1.12 to the dollar so for betting $1 you get back $1.12. These are the most extreme favourites odds that I have seen for situations where an undefeated team might be playing someone in 10th placd for example. $\endgroup$ – Jordan Mackenzie Dec 27 '16 at 1:47
  • $\begingroup$ Bayesian has shown how to allocate your bets so that each successful bet gives you the same return. I don't understand why you are asking this question. Each bet is independent of the others. In your example, you lose unless you win four of the five, and even then you win very little. I can understand trying to figure out how much to bet on each competitor in the same game to see if you can assure a profit, but you won't be able to do so here. $\endgroup$ – Ross Millikan Dec 27 '16 at 4:46
  • $\begingroup$ You're definitely right, the idea is this (and i could be completely wrong! Im just having fun and brainstorming). I've been betting on League of Legends esports for NA and LCS where the odds are usually quite good and the matches are head to head with no chance of a draw. MOST games are reasonably obvious of who the clear favourite is. As the industry develops I assume this will become less and less. Im still looking into research from the past few seasons to see how often the betting favourite actually wins their match but from my viewing experience it is very often. $\endgroup$ – Jordan Mackenzie Dec 27 '16 at 8:59
  • $\begingroup$ Will update if i lose all my money 👍 $\endgroup$ – Jordan Mackenzie Dec 27 '16 at 9:06
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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 $i$.

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  • $\begingroup$ So for your example, you should get $x=200/(1/1.12+...+1/1.89)=57.33$. Then you bet $57.33/1.12$ on game 1 and $57.33/1.33$ on game two and so on such that for every single bet won you get 57.33. Is that what you were after? $\endgroup$ – Bayesian Dec 27 '16 at 1:28
  • $\begingroup$ Wow you are a genius. I'm only just keeping up with the math but I'll go over it with pen and paper and confirm but I'm pretty sure this is exactly what I meant. Thank you. $\endgroup$ – Jordan Mackenzie Dec 27 '16 at 1:49
  • $\begingroup$ If youre interested at all, The theory of course being betting on the favourite from each match for a certain week but obviously betting more on a favourite that pays less but is more likely to win - proportionate to your current kitty size. $\endgroup$ – Jordan Mackenzie Dec 27 '16 at 1:50
  • $\begingroup$ So that each bet brings in an equal win but favourites that are riskier have a lower total kitty for potential loss. The average odds for a round (5 games) is usually abour 1.55. Next step is looking up what percentage of the time in the past favourites have won their match. $\endgroup$ – Jordan Mackenzie Dec 27 '16 at 2:01

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