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moneyline without the juice?
How would you convert the moneyline to true odds without the juice. Say two friends wanted to bet using the moneyline. The favorite is -650 and the underdog is +450. Is there an acurate way to take the juice out so both betters get the true odds?
Calculation of probability
Here is how we, based on the odds of a bookmaker,calculates the probabilities behind the posted odds.The calculations are done for an event with three outcomes, like a football match ending with either 1 (home win), X (draw), or 2 (visitors win), but can be used quite generally.The only condition is, that the outcomes, for which odds are given, are mutually exclusive and jointly cover all possible outcomes of the event.
Step 1 - Calculating the bookmaker's profit indicator
First we calculate what could be termed as the bookmaker's profit indicator. It shows how much the bookmaker receives in stakes whenever he makes a payment of $1. If odds is the (European) odds for a home win, the payout from a $1 bet, then 1/odds is the bookmakers price for a payout of $1 in case of a victory for the home team.The price for paying out $1 irrespective of the outcome of the outcome of the game (where you play all three outcomes) is thus:
Profit indicator = (1/odds) + (1/odds[X]) + (1/odds)
1 Brazil 1.40
X Draw 3.75
2 England 5.00
Profit indicator = (1/1.40) + (1/3.75) + (1/5.00)
= 0.7143 + 0.2667 + 0.2
In this case the profit indicator shows that the bookmaker recevies a stake of $1.181 for every $1 paid out.
Step 2 - Calculating the bookmaker's payout share
If the bookmaker receives the bets in the right proportions, then the payout share (as part of total stakes for that match) for the customers will be
Payout share = 100% x 1 / Profit indicator
From the payout share, you'll have the profit share for the bookmaker as 100% - payout share.
Payout share = 100% x 1 / 1.181
Step 3 - Calculating the probability for each outcome
For the final step, multiply the bookmaker's price for each of the three outcomes by the payoutshare. This removes the part of the price, which is the bookmaker's profit, and leaves only the pure probability element of the price..
The probabilities are thus calculated like this:
Probability = (1/odds) x Payout share
Probability[X] = (1/odds[X]) x Payout share
Probability = (1/odds) x Payout share
Probability[1 - Brazil]: 0.7142 x 84.67% = 60.47%
Probability[X - Draw]: 0.2667 x 84.67% = 22.58%
Probability[2 - England]: 0.2 x 84.67% = 16.93%
Sum rounded to 100.00%
The calculations above show how to obtain the probabilities intrinsic in the odds of the bookmaker. The bookmaker's probabilities may of course not be correct estimates.When you judge the probabilities to be different, is when you have a good opportunity to make money on a bet.
I am almost with you drunkguy. Your formula shows me how to get from odds to perctages without the juice, I am just a little shaky on the terms. How did you covert the moneyline to odds to profit indicator. I am trying to get the true percentages on a boxing match. The favorite is -650 and the underdog is 450. So if one bets on the favorite ($650 trying to win $100) and then someone else bets on the underdog ($100 trying to win $450) and the underdog wins, the house walks away with $250 in profit. If the favorite wins, I guess the house breaks even? Can you show me how to use your formula to convert the published moneyline to acutal percentages that would add up to 100% with the house taking nothing???
I think what might be your problem is that they are using decimal moneylines instead of american
you can get info on the conversion from Mansion:
just following the instructions in my last post:
profit indicator = (1/1.15) + (1/5.50) = .870 + .182 = 1.052
payout share = 100% x (1/1.052) = 95.1%
now you can figure the probabilities:
for the favorite: (1/1.15) x 95.1% = 82.7%
for the underdog: (1/5.50) x 95.1% = 17.3%
so that right there is the % on each team without the "juice" - it adds up to exactly 100%.
Now you can convert that back to a fair moneyline, which will give you +/- 478, which would be the "no juice" line
hope that clears things up, but if not feel free to ask some questions...
Those formulas work fine but I do this a slightly different way as follows:
+450 = 100/(450+100) = 0.182 or 18.2%
-650 = 650/(650+100) = 0.867 or 86.7%
Total above equals 0.182 + 0.867 = 1.049 or 104.9%
For no juice you want the % to equal 100% so divide each value by 1.049
0.182/1.049 = 0.173 or 17.3%
0.867/1.049 = 0.827 or 82.7%
Now convert either % back to a Moneyline (for example):
(0.827/(1-0.827)) x 100 = 478
I also use these formulas to calculate the house hold % which is especially important with 3 way lines. The above shows the house hold % is 4.9% which is similar to a game with -110 lines both ways. I don't like to bet into lines with a house hold % above 5% unless they are props or I have a strong opinion.
Here is a great calculator that will do all the work for you with the click of a mouse. You can convert win probability into moneyline or moneyline into win probability Moneyline Coverter - Converting Moneyline Odds into Win Probability
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