There are multiple ways of representing odds around the world. Before today I thought there were two, then I easily learnt that Decimal and American are different, and they googling for an image of who uses what system I came across the table below. I have grabbed descriptions of all of them from here, in the spoiler below the image.
After thinking about it for a few minutes, the list of questions/calculations/algorithms I want to use odds to answer are:
We can examine the simplicity of the calculations with some examples. We could use the current US political odds, here are some. I have had to calculate American with an online converter, and the Hong Kong myself (as Decimal - 1).
For each question above I have done an example sum and given a winner and loser in my opinion:
A way to count them is 1 for win, -1 lose, 0.5 if joint:
I think I agree with the outcome, if not the method. Decimal does very easily convert to and from probabilities. I think Fraction and Hong Kong work well for the sort of profit/lose calculations that you should be doing when gambling, with each having pluses and minus's (though I think I do prefer Hong Kong now I know about it).
American is awful. Why have two different systems depending on the odds, that are so hard to compare? I wonder if it is just to make it harder for the punters to give the bookies an advantage.
Spoiler Odds description :
After thinking about it for a few minutes, the list of questions/calculations/algorithms I want to use odds to answer are:
- How much money will I get if I win the bet, aka. the return from the odds
- "I have made the bet and have no money, if I win, I will have X money"
- How much money do I gain by making and winning the bet, aka. the profit from the odds
- "If take the bet and win, I will be X better off than if I did not take the bet"
- In business speak I think this would be the "return on investment" on a successful project
- In game theory terms this would be one value in your outcome matrix (the other being the value of the bet as a loss)
- What probability of winning would make it so the bet is "fair", aka. implied probability from the odds
- "I need to think the probability of an event happening is X for it to be worth taking the bet"
- What are the "fair" odds, aka. odds from the implied probability
- "I think the true probability of an event is Y, I should take odds over X"
- "We are betting with friends, and the probability of the outcome is Y, we should make the odds X"
- Given two odds, what can we say about their relative likelihood?
- "How much less likely is Obama than Clinton to get the nomination?"
- Given multiple odds, what can we say about the odds of the difference between them?
- "What do the odds of Harris/Obama for the nomination/presidency say about their expected chances?"
We can examine the simplicity of the calculations with some examples. We could use the current US political odds, here are some. I have had to calculate American with an online converter, and the Hong Kong myself (as Decimal - 1).
| Bet | Fraction | Decimal | American | Hong Kong |
| Trump Wins | 8/13 | 1.61 | -163 | 0.61 |
| Harris Wins | 23/10 | 3.3 | 230 | 2.3 |
| Obama Wins | 26 | 27 | 2600 | 26 |
| Republicans Win | 1/2 | 1.5 | -200 | 0.5 |
| Harris Nominated | 2/13 | 1.15 | -667 | 0.15 |
| Obama Nominated | 167/10 | 17.7 | 1670 | 16.7 |
| Clinton Nominated | 40 | 41 | 4000 | 40 |
For each question above I have done an example sum and given a winner and loser in my opinion:
Spoiler Some example maths worked out :
A way to count them is 1 for win, -1 lose, 0.5 if joint:
| Fraction | 0.5 |
| Decimal | 2 |
| American | -3.5 |
| Hong Kong | 0.5 |
I think I agree with the outcome, if not the method. Decimal does very easily convert to and from probabilities. I think Fraction and Hong Kong work well for the sort of profit/lose calculations that you should be doing when gambling, with each having pluses and minus's (though I think I do prefer Hong Kong now I know about it).
American is awful. Why have two different systems depending on the odds, that are so hard to compare? I wonder if it is just to make it harder for the punters to give the bookies an advantage.
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