# What are the best odds?

## What is the best system for odds?

• ### Malay

• Total voters
19

#### Samson

##### Deity
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.

Spoiler Odds description :
DECIMAL ODDS
Decimal (or European) odds are most popular among the bookmakers online. They’re simple to understand and easy to calculate the return. That’s what the decimal odds represent – the return of your bet. For example, if the decimal odds are 1.5 and your stake is \$10, you get \$15 (\$5 profit + \$10 stake).

FRACTIONAL ODDS
Fractional (or British) odds are popular in the United Kingdom. They represent the profit, not the return. For example, if the fractional odds are 2/1 and your stake is \$10, you’d get \$20 profit in case of a win (plus, \$10 stake back).

MONEYLINE/AMERICAN ODDS
Moneyline (or American) odds are popular among the United States bookmakers. The Moneyline odds show how much you need to bet to win \$100 (if Moneyline is negative) or how much you would earn if your stake were \$100 (if Moneyline is positive). For example, if the Moneyline odds are -150, you need to bet \$150 to win \$100; if the odds are +150, you need to bet \$100 to win \$150.

HONG KONG ODDS
Hong Kong (or HK) odds are standard among the bookmakers in China. They are similar to fractional odds, except written not in a fractional but decimal form instead. For example, if the Hong Kong odds are 0.25 and your stake is \$10, you’d get \$2.5 profit in case of a win (plus, \$10 stake back).

INDONESIAN ODDS
The Indonesian odds are popular among bookmakers available in Indonesia. They are similar to Moneyline odds, except instead of taking \$100 stake/profit into account, they consider 1 unit. For example, if Indonesian odds are -1.5, you need to bet \$1.50 to win \$1; if the odds are +1.5, you need to bet \$1 to earn \$1.50.

MALAY ODDS
The Malay odds are similar to American and Indonesian odds. The positive odds show the 1 unit profit while the negative odds show how much you need to bet to win 1 unit. For example, if Malay odds are -0.25, you need to bet \$0.25 to win \$1; if the odds are +0.25, you need to bet \$1 to earn \$0.25.

IMPLIED PROBABILITY
Implied probability converts the odds to probabilities. In other words, it shows what the chances of that particular bet to win are. For example, if your bet has an implied probability of 80%, it’s more likely that the bet will result in a win.

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 :

I have put \$100 on Trump to win, if he does, I will have X money (Trump Wins | 8/13 | 1.61 | -163 | 0.61):
• 8/13 * 100 + 100 = \$161
• 1.61 * 100 = \$161 ## WINNER
• 1 - (100 / (-163)) = \$161.34 ## LOSER
• 0.61 * 100 + 100 = \$161
If I put \$100 on Harris to win, if she does I will win X (Harris Wins | 23/10 | 3.3 | 230 | 2.3):
• 23/10 * 100 = \$230
• (3.3 - 1) * 100 = \$230 ## LOSER
• 230 = \$230 ## WINNER
• 2.3 * 100 = \$230
What chance would I need to think Obama has to be worth putting money on her (Obama Wins | 26 | 27 | 2600 | 26)
• One in 26 ## Joint WINNER
• One in (27 - 1) ## Joint LOSER
• One in (2600 / 100) ## Joint LOSER
• One in 26 ## Joint WINNER
What is the minimum chance I need to give the republicans at winning to be worth betting on them (Republicans Win | 1/2 | 1.5 | -200 | 0.5) [EDIT] Rereading it I think this effectively a repeat of the above?
• 1/(1+1/2) = 0.66
• 1/1.5 = 0.66 ## WINNER
• -(-200)/(-(-200-100)) = 0.66 ## LOSER
• 1/(1+0.5) = 0.66
Friends are betting on the result of two coin flips. What should the odds be on two heads, p = 0.25?
• 1/0.25 = 4 ## Joint WINNER
• 1/0.25 + 1 = 5 ## Joint LOSER
• 1/0.25 * 100 = 400 ## Joint LOSER
• 1/0.25 = 4 ## Joint WINNER
How much less likely is Clinton to get the nomination than Obama (Clinton Nominated | 40 | 41 | 4000 | 40, Obama Nominated | 167/10 | 17.7 | 1670 | 16.7) (note these are actually reciprocals, but that cancels out)
• (40+1)/(167/10+1) = 2.316384
• (41)/(17.7) = 2.316384 ## WINNER
• 1670/4000 = 2.316384 ## LOSER
• (16.7+1)/(40+1) = 2.316384
What do the relative Nominated/Winning odds imply of the relative chances of Obama compared to Harris vs. Trump
• ((26+1)/(16.7+1)) / ((2.3+1)/(0.15+1)) = 0.5315871
• (27/17.7) / (3.3/1.15) = 0.5315871 ## WINNER
• I am not even trying ## LOSER
• ((26+1)/(16.7+1)) / ((2.3+1)/(0.15+1)) = 0.5315871
Spoiler Relevant bit of the table and working for decimal :

 Bet Fraction Decimal American Hong Kong Harris Wins 23/10 3.3 230 2.3 Obama Wins 26 27 2600 26 Harris Nominated 2/13 1.15 -667 0.15 Obama Nominated 167/10 17.7 1670 16.7

Harris Wins = Harris Nominated * (Dems win | Harris)
Obama Wins = Obama Nominated * (Dems win | Obama)

3.3 = 1.15 * (Dems win | Harris)
27 = 17.7 * (Dems win | Obama)

3.3/1.15 = (Dems win | Harris)
27/17.7 = (Dems win | Obama)

(Dems win | Obama) / (Dems win | Harris) = (27/17.7) / (3.35/1.15)

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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Interesting, never thought about that there might be differences.
I'm looking at that American system, and it completely breaks my mind. That's unintuitive as hell.

Interesting, never thought about that there might be differences.
I'm looking at that American system, and it completely breaks my mind. That's unintuitive as hell.
It is completely different depending on if it is above or below evens. It just makes no sense.

Interesting, never thought about that there might be differences.
I'm looking at that American system, and it completely breaks my mind. That's unintuitive as hell.
Glad that i picked it for my Civ4 AI Survivor "contest", then
I have no problems with it tbh..
163 to win 100 (-163) or 100 to win 230 (+230).
And once you know that, it works out for all numbers.

Glad that i picked it for my Civ4 AI Survivor "contest", then
I have no problems with it tbh..
163 to win 100 (-163) or 100 to win 230 (+230).
And once you know that, it works out for all numbers.
This is only answering one question, and a different question depending on the odds. If it is better than evens, and you want to know how much you will win it is convenient, especially if you are betting around \$100. Any other question is more difficult, and when you would be asking the optimum question for the worse than evens odds I do not know.

Why not just %?

Well it's not easy to know what % chance -163 really stands for (62%), but you could use an odds converter for that (i just did).
But 8/13 or 1.61 wouldn't tell me that either as newbie

When playing around with that converter, i can see that american odds are the most accurate.
The other systems don't even react to all small changes in "Implied Probability".

Why not just %?
Because it is not clear % of what? In a fair coin flip, your probability is 50%, your profit 100% and your return 200%.
Well it's not easy to know what % chance -163 really stands for (62%), but you could use an odds converter for that (i just did).
But 8/13 or 1.61 wouldn't tell me that either as newbie

When playing around with that converter, i can see that american odds are the most accurate.
The other systems don't even react to all small changes in "Implied Probability".
That converter does some odd things with rounding. They are all as accurate as each other, it is maths.

If you think it is good, can you do the calculation I chickened out of?

Spoiler The sum :

What do the relative Nominated/Winning odds imply of the relative chances of Obama compared to Harris vs. Trump (note these are actually reciprocals, but that cancels out)
• ((26+1)/(16.7+1)) / ((2.3+1)/(0.15+1)) = 0.5315871
• (27/17.7) / (3.3/1.15) = 0.5315871 ## WINNER
• I am not even trying ## LOSER
• ((26+1)/(16.7+1)) / ((2.3+1)/(0.15+1)) = 0.5315871
Spoiler Relevant bit of the table and working for decimal :

 Bet Fraction Decimal American Hong Kong Harris Wins 23/10 3.3 230 2.3 Obama Wins 26 27 2600 26 Harris Nominated 2/13 1.15 -667 0.15 Obama Nominated 167/10 17.7 1670 16.7

Harris Wins = Harris Nominated * (Dems win | Harris)
Obama Wins = Obama Nominated * (Dems win | Obama)

3.3 = 1.15 * (Dems win | Harris)
27 = 17.7 * (Dems win | Obama)

3.3/1.15 = (Dems win | Harris)
27/17.7 = (Dems win | Obama)

(Dems win | Obama) / (Dems win | Harris) = (27/17.7) / (3.35/1.15)

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So the point of the types was:
Fraction: to calculate if it makes sense to bet when looking to gain at the least x
Decimal: to have the return a multiplication away
USian: [snip] Moderator Action: Edited

Last edited:
Decimal: to have the return a multiplication away
The return a multiplication away and the probability a reciprocal away. It is quite elegant.

Yup it's all a ripoff anyways..
you would always bet with worse than you should get, and i imagine that professionals who can identify rare advantages are more or less gently shown the door out.

The return a multiplication away and the probability a reciprocal away. It is quite elegant.
And betting Trump's return be dollars by the golden ratio.

They all suck. Han Solo gets it. “Never tell me the odds.”

I have no idea what's going on with the American system at all, but if 2.3 = 230, 26 = 2600 and 16.7 = 1670... why does 40 = 4100? Is that last one a mistake?

For those who gamble for money with regularity, some systems are better than others. If one is more about predicting outcomes, then implied probability is more useful.

Everything here except decimal is completely unhinged

Why not just %?
Because betting odds aren't actually a prediction of the probability of an event. They're an attempt to lure people into putting money on the whichever side doesn't yet have enough money on it, for the book to make the maximum profit. Getting the projections right is only a means to an end. The "implied probability" column in the chart only applies when the initial odds on an event are released. After that, the odds are adjusted based on how much money is coming in on one side or the other and the "implied probability" becomes a function of the popularity of the two sides, against one another. (In the case of a "prop bet" the two sides are "this thing will happen" vs. "this thing will not happen", or an "over-under", or a point-spread, or whatever.)

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