Betting System Payout Equation

Question

I am currently programming a betting system.

I am a little confused as to the logic for working out the payouts (math is not my strong point)

I will explain this the best i can.

Scenario:

Max Bet = 500 Racers: John, Mark, Lewis, Kate

• Matt Bets 10 on Mark
• Sky Bets 500 on Mark
• Kate Bets 40 on Mark
• Smackie Bets 500 on Lewis
• John Bets 500 on John

Winner = Mark

What i know: ( {} denote variables )

{pot} = 10+500+40+500+500 = 1550

So what i need to know, is how much of the pot Matt, Sky and Kate each win?

Answer 1

The total amount bet on the winner is $550$.

Matt should get $(10/550)\times1550$; Sky, $(500/550)\times1550$; Kate, $(40/550)\times1550$.

Answer 2

You have to define the type of betting game.
The most important question is who is paying to the winners? Imagine that there's only one bet and it wins. Who must pay to the winner? Your example illustrates mix of two appoaches (figuratively speaking, casino-based and wager-based).

If you have casino of some other arbiter which provides payoff ratios regardless of who is betting on whom (however, there ratios may change after a bet of useful information about competitors like "this rider seems to be ill today"), then you (as the casino manager) have to decide a part of each bet you want to keep in average for your mansion in Monte Carlo (it poker it's called rake), calculate a chance of win for each competitor based on your own algorithm and, probably, on the bets placed for them and make the payoff values a bit (or greatly) less than this value according to the rake.

The other appoach is what I called wager-based - in this case you can't just place $X$ for John but you have to find one or more people to form a wager like "Matt bets $20$ on Mark, Kate bets $20$ on Lewis, if Mark wins, Matt gains $40$, if Lewis wins, Kate gain $40$, if someone other wins, Kate marries Matt and they buy puppy for $40$". Rules should be discussed before the wager and there are obviously no restrictions on it if every person taking part in wager aggrees the rules. These rules may consider different winning chances or not but should cover all possible outcomes to avoid conflicts.

Considering all I said, your examples makes no sense without additional information. If it's casino-based game then the payoffs for each competitor are some values from $0$ to $1$ (giving $(1 - rake)$ in total). If it's just a friends' wager, then it should be formed in other way.

For example (just a variant, there could be infinitely many other variants):
$1)$ Matt, Sky and Kate bet $10$ om Mark, Smackie bets $30$ on Lewis, John bets $30$ on John. The rules are: if Kate wins, everyone gains his/her money back; if Mark wins, Matt, Sky and Kate gain $20$ each; if Lewis wins, Smackie gains $90$; if John wins, John gains $90$.

$2)$ Sky and Kate bet $30$ on Mark, Smackie bet $30$ on Lewis, John bet $30$ on John. The rules are: if Kate wins, everyone gains his/her money back; if Mark wins, Sky and Kate gain $60$ each; if Lewis wins, Smackie gains $120$; if John wins, John gains $120$.

$3)$ Sky bets $460$ on Mark, Smackie bets $460$ on Lewis, John bets $460$ on John. The rules are: if Kate wins, everyone gains his/her money back; in other case winner gains $1380$.

These wagers are totally independent of each other and you may simply cancel or change one without affecting another.