Thanks for doing this because I’ve never understood the way odds are laid out for American sports. In Australia you usually just see the “price” you are betting on. For example if team A had odds to win of $3.00 and you placed a $10 bet, you would get a return of $30 if your bet was successful. I always found that very simple to understand, and never really understood the ways described in the video.
The Australian notation that you describe corresponds pretty much to the decimal notation that's described in the video: the decimal number (2.50 in the video, 3.00 in your example) is the multiplication factor with which you multiply your bet in order to calculate the payout you receive in case your bet wins. I've never heard of moneyline bets before, this is new to me. (I don't live in America though, but in the Netherlands.) I think that "fractional odds" are, just like imperial units, a "leftover" of how betting odds were historically represented and henceforth kept in use. And it's not just in America, but also in use in the UK (at least with non-official bookies).
@@hectorg5809 Decimal odds are based on a $1 bet (or a 1 euro bet, or a bet of 1 unit of whatever your local currency is). For example, if you placed a bet of $1 at decimal odds of 2.5, and your bet wins, then you receive a payout of $2.50 ; if your bet was $100 , then your payout will be 2.5 times $100 = $250 ; if your bet was $200 , then your payout is 2.5 times $200 = $500 etc. Just simply multiply your bet by the factor 2.5 . In other words, if your bet won, and you're going to collect your winnings, then just multiply the bet that you placed by the decimal odds (in this case, the number 2.5) in order to verify that the payout you receive matches the payout that you're owed. So with decimal odds, the calculation just takes one arithmetic operation, one simple step. With American moneyline odds (which is what I assume you're referring to), the calculation takes more than one step. (For example, suppose the bookmaker offered a moneyline of +150 on a certain bet and you placed $58 on that bet, how much should you receive at the payout booth if your bet wins?)
It might also be good to explain some additional differences in wording. Sometimes gambling/betting uses the words "TO" and "FOR". But they mean different things. For example, many people may think that a bet of "6 to 1" and a bet of "6 for 1" mean the same thing, but they do not.
Great video! You should do a follow-up about oddsmakers create money lines to make money. It would also be cool to explore how lines change based on incoming bets.
But it isn’t just the probability of the team winning or losing, it is also the probability of the house losing money should the underdog win and what the house would then have to payout should the underdog win. Thus the lines can change depending on how much has been wagered on one team or another. Seeing how they adjust this, to keep from getting wiped out, would be very interesting.
The bookies are often rather happy when that happens. Yes, they loose a lot of money - but it's also events like that which drive the bets in the first place, and a lot of what they pay out is going to come right back in next week.
Sports betting odds don't teach us anything about probability, because betting odds only tell us how much a bookmaker/the "house" pays out to your bet in each event. It doesn't really tell us anything about the probability of each event.
If you want to calculate the odds from the probability for fractional betting: Say you had an event E with P(E) = 0.8. So 1-P(E) is the probability of it not occuring. The 'Odds On' of the event is P(E)/(1-P(E)) = 0.8/0.2 = 4/1. The 'Odds Against' of the event would be the inverse of that (1-P(E))/P(E) = 1/4. That'd be 'fair odds' but if you see the odds given to you they're almost certainly not fair.
I always liked decimal odds because the probability math is easier. Let's reframe our thinking of expected value. Imagine I placed a $1 bet yesterday, and now the game is about to start. I already placed the bet, so it's not possible for me to lose money. If I win, I get my $2.50. If I lose, I don't get anything. So the expected value is 2.5p. Now, I should expect on average to get my bet back, so we have 2.5p = 1. It would be nice if you could make a followup video on REAL implied probabilities. For example, if payouts are 1.33 and 3, then we take 1/1.33 and find 75% for Team A and 1/3 = 0.333 for team B. If we want to know the bookmaker's probability of Team A winning, we have to normalize by the summed inverse payouts. So we get 0.75/(0.75+0.333) = 3/4 /(3/4+1/3) = 3/4 / (9/12 + 4/12) = 3/4 / 13/12 = 3*12 / 4*13 = 36/ 4*13 = 9/13, which comes to only 69%.
If the decimal odds are 2.5, the "implied probability" is not 40% but a bit less because of the house edge. For example, if you have decimal odds 2.5 and 1.5, the actual implied probabilities can be calculated as follows: 1 / (1 / 2.5 + 1 / 1.5) = 0.9375 0.9375 / 2.5 = 0.375 and 0.9375 / 1.5 = 0.625. So the actual implied probabilities are 0.375 and 0.625.
I'm not into sports betting, nor experienced in sports betting. But I think the point of "implied probability" is that if for example the decimal odds of a bet is 2.5 , then you as a rational agent should take that bet if you think/know that the probabiity of winning is at least 40% ; that's what "implied probability" is supposed to mean. The calculation of 37.5% is mathematically interesting and correct, but that number is of no use to (the descision-making of) the bettor who looks to make a profit. The calculation of "0.375 vs. 0.625" is correct under the assumption that the bookie/house is unbiased about who pays for the house edge; in other words, if we assume that the house is "charging" both sides the same percentage of their bets as "house edge".
I get the intent, but “profitable gamble” is an oxymoron. Would love to see an analysis of the US state lottery systems. The video used the example of a 5% house edge. Casinos run from a fraction of a percent to maybe 10% or more depending on the game. I believe lotteries would be around 50% or more - a horrendous bet usually made by the folks who can least afford it.
@@Adam-gd6pp I guess the way I think of a profitable gamble is a lottery where odds of winning are 1 in a million. The gamble becomes profitable when the the prize money goes above a million dollars for a one dollar ticket. Not a realistic profit IMO.
The best sort of gambling is investment banking: Not only can you seek investments with good expected payout, but you're gambling with other people's money.
I'm by far not an expert on sports betting, in fact I have pretty much no experience in sports betting, but I guess the offered odds and the math formulas are just the same. For example, if a bookmaker offers you a moneyline of +150 on a tie, it simply means that if you take the bet, you place $100 betting on a tie, and if the game indeed results in a tie, you receive $100 (original wager) + $150 (profit) = $250 payout. The implied probability of a tie is then 100/(100+150) = 40% . So as a rational agent, you should take the bet if you think/know that the probability of a tie is at least 40%, and you should decline the bet if you think/know that the probability of a tie is less than 40% . However, it could be that in practice, (certain) sports betting exchanges have specific payout rules for bettors on "win" (or "lose") if a game ends in a tie (something like: the bettor gets a refund of half or third of their bet, or something like that; they could make up any rules they want), but I don't know about that; because as I just said, I have pretty much no experience in sports betting.
One time in the 80s, I made a sports bet on middle weight boxing champion Marvin Hagler. The money line was -650. So to make $100, I had to bet $650. That's a bad line to have to bet this much just to win $100, but I knew this was a decent bet because he was fighting a relatively unknown fighter, who wasn't that good. Hagler was the best for his weight class. He won, and I won an easy $100.
Is this really a probability? It just looks ratio of win vs. loss. Number is in no way connected to the outcome of the event except for bookmakers expectation of the outcome. And you are betting your expectation of the outcome against the expectation of the house.
The decimal form 2.5 can also be shown as 1:2.5 or 2:5 - for every $1 you bet, you get $2.50 back, which includes your $1 bet, so a profit of $2.50-$1.00=$1.50 A decimal 1.0 or 1:1 odds means that a winning bet only returns your bet. Note that the decimal should never be less than 1 (or the number to the right of the : be less than the number to the left), or even a winning bet will lose money.
Yeah, sorry, but what you wrote is wrong. In mathematics, odds of 1:1 means that there are two events that are equally likely. If those two events are disjunct and exhaustive, either event has a 50% chance of occurring. In a fair gamble, the payout on a bet of 1 on either event would pay out 2 if the event occurs (and 0 if it doesn't occur). In gambling, odds are the ratio between the stake and the (potential) profit. So odds of 1:b on an event means that a bet of 1 on the event, results in a payout of (1+b) if the event occurs (and a payout of 0 if the event doesn't occur). So odds of 1:1 means you receive a payout of 2 (not 1) if your bet wins. And odds of 2:5 would mean that for every $2 you bet, you get ($2 + $5) = $7 back (if you win), so a profit of $7 - $2 = $5 .
How is that the the formula that odds the team wins? Whybisnit 100/100+150..That makes no sense..that's just the money being bet..if two teams are playing, aren't the odds always 50/50? Well okmthem there wouldn't be any point to betting but then it still doesn't explain this..and WHY would expected value be zero of the odds are not 50/50..this sint clear or well explained at all..Why isn't everyone else asking this same question or confused by this???
It's confusing when you say things like "you bet 100 to win a _profit_ of 250." Does that mean you get 250 total or 250 plus your original 100, or 350? By the definition of profit, it's the latter and you receive 350 in return for your bet. But that "feels" wrong, like it should be the former and you get 250 total, for a formal profit of 150. I've never placed a sports bet, so I'm new to this.
That's much more complicated, but I can try to sum it up for you. You take players' or teams' ranking and look how teams on these levels performed. Let's say 1st team in the standings plays average team. Then it depends on the sport, because in NFL the best teams are like 12-3 (they win 80% of the matches), but in MLB the best teams are 100-62 (they win only about 60% of the games). Then you have to approximate other factors, such as home advantage, key player injured, last 5 matches, some tennis players prefer clay over hard and vica versa, have their favourite tournament, somebody may be underrated after an injury, last game of the season and one team has nothing to gain and so on and so on.
@@mr.schloopka1124All true, but you forgot the two most important factors: the market and risk management. You do not want to offer odds that stray too far from what other exchanges and bookies are offering. Then players can get a surewin betting on the outcome you have high odds on and and hedging at the other bookie. This will also get you lots of risk on one outcome, you want bets on both sides to make a secure win whatever happens.
Two ways. One is to do lots of math, which is conveniently automated now - you can feed in heaps of data about the players performance and do statistical modeling. The other way is to let the gamblers themselves do the estimation, by counting how much is being bet on different outcomes and taking that into account in revising the odds throughout a game. If a lot of players suddenly start betting on X happening, then it's a sign that some event has occured that makes X seem likely - so the computers can quickly raise the odds.
How dies this make sense..if expected value is zero doesn't that imply odds are even so its fifty/fifty..or itd because the amounts are different since it's conditional..otherwise if the amount you win wquals the amount you would loae i see p wpuld equal 1/2..but wasn't everyone else confused by this?
Thanks for doing this because I’ve never understood the way odds are laid out for American sports. In Australia you usually just see the “price” you are betting on. For example if team A had odds to win of $3.00 and you placed a $10 bet, you would get a return of $30 if your bet was successful. I always found that very simple to understand, and never really understood the ways described in the video.
The Australian notation that you describe corresponds pretty much to the decimal notation that's described in the video: the decimal number (2.50 in the video, 3.00 in your example) is the multiplication factor with which you multiply your bet in order to calculate the payout you receive in case your bet wins.
I've never heard of moneyline bets before, this is new to me. (I don't live in America though, but in the Netherlands.)
I think that "fractional odds" are, just like imperial units, a "leftover" of how betting odds were historically represented and henceforth kept in use. And it's not just in America, but also in use in the UK (at least with non-official bookies).
American odds are really easy to me because everything is based on a $100 bet. I don't understand decimal odds!
@@hectorg5809 Decimal odds are based on a $1 bet (or a 1 euro bet, or a bet of 1 unit of whatever your local currency is). For example, if you placed a bet of $1 at decimal odds of 2.5, and your bet wins, then you receive a payout of $2.50 ; if your bet was $100 , then your payout will be 2.5 times $100 = $250 ; if your bet was $200 , then your payout is 2.5 times $200 = $500 etc. Just simply multiply your bet by the factor 2.5 .
In other words, if your bet won, and you're going to collect your winnings, then just multiply the bet that you placed by the decimal odds (in this case, the number 2.5) in order to verify that the payout you receive matches the payout that you're owed.
So with decimal odds, the calculation just takes one arithmetic operation, one simple step. With American moneyline odds (which is what I assume you're referring to), the calculation takes more than one step. (For example, suppose the bookmaker offered a moneyline of +150 on a certain bet and you placed $58 on that bet, how much should you receive at the payout booth if your bet wins?)
6/4 is always reduced to 3/2
was never that interested in sports nor betting, but this itself seems pretty interesting!
It might also be good to explain some additional differences in wording. Sometimes gambling/betting uses the words "TO" and "FOR". But they mean different things. For example, many people may think that a bet of "6 to 1" and a bet of "6 for 1" mean the same thing, but they do not.
Great video! You should do a follow-up about oddsmakers create money lines to make money. It would also be cool to explore how lines change based on incoming bets.
But it isn’t just the probability of the team winning or losing, it is also the probability of the house losing money should the underdog win and what the house would then have to payout should the underdog win. Thus the lines can change depending on how much has been wagered on one team or another. Seeing how they adjust this, to keep from getting wiped out, would be very interesting.
The bookies are often rather happy when that happens. Yes, they loose a lot of money - but it's also events like that which drive the bets in the first place, and a lot of what they pay out is going to come right back in next week.
Wow, I understand more about probability by watching this video.
Sports betting odds don't teach us anything about probability, because betting odds only tell us how much a bookmaker/the "house" pays out to your bet in each event. It doesn't really tell us anything about the probability of each event.
If you want to calculate the odds from the probability for fractional betting:
Say you had an event E with P(E) = 0.8.
So 1-P(E) is the probability of it not occuring.
The 'Odds On' of the event is P(E)/(1-P(E)) = 0.8/0.2 = 4/1.
The 'Odds Against' of the event would be the inverse of that (1-P(E))/P(E) = 1/4.
That'd be 'fair odds' but if you see the odds given to you they're almost certainly not fair.
Can someone define "profit"
If I bet 4, the profit is 6... do I make 2 or 10?
You make 10, and your profit is 10-4=6
That's what I thought.
Thank you
Wonderful explanation.
Parimutuel betting (i.e. for horse races) helps ensure the house always wins.
Things i wish i learned in school 🤔
There are more important things to teach at school, than sports betting.
I always liked decimal odds because the probability math is easier.
Let's reframe our thinking of expected value. Imagine I placed a $1 bet yesterday, and now the game is about to start. I already placed the bet, so it's not possible for me to lose money. If I win, I get my $2.50. If I lose, I don't get anything. So the expected value is 2.5p. Now, I should expect on average to get my bet back, so we have 2.5p = 1.
It would be nice if you could make a followup video on REAL implied probabilities. For example, if payouts are 1.33 and 3, then we take 1/1.33 and find 75% for Team A and 1/3 = 0.333 for team B. If we want to know the bookmaker's probability of Team A winning, we have to normalize by the summed inverse payouts. So we get 0.75/(0.75+0.333) = 3/4 /(3/4+1/3) = 3/4 / (9/12 + 4/12) = 3/4 / 13/12 = 3*12 / 4*13 = 36/ 4*13 = 9/13, which comes to only 69%.
If the decimal odds are 2.5, the "implied probability" is not 40% but a bit less because of the house edge.
For example, if you have decimal odds 2.5 and 1.5, the actual implied probabilities can be calculated as follows:
1 / (1 / 2.5 + 1 / 1.5) = 0.9375
0.9375 / 2.5 = 0.375 and 0.9375 / 1.5 = 0.625.
So the actual implied probabilities are 0.375 and 0.625.
I'm not into sports betting, nor experienced in sports betting. But I think the point of "implied probability" is that if for example the decimal odds of a bet is 2.5 , then you as a rational agent should take that bet if you think/know that the probabiity of winning is at least 40% ; that's what "implied probability" is supposed to mean. The calculation of 37.5% is mathematically interesting and correct, but that number is of no use to (the descision-making of) the bettor who looks to make a profit.
The calculation of "0.375 vs. 0.625" is correct under the assumption that the bookie/house is unbiased about who pays for the house edge; in other words, if we assume that the house is "charging" both sides the same percentage of their bets as "house edge".
I get the intent, but “profitable gamble” is an oxymoron. Would love to see an analysis of the US state lottery systems. The video used the example of a 5% house edge. Casinos run from a fraction of a percent to maybe 10% or more depending on the game. I believe lotteries would be around 50% or more - a horrendous bet usually made by the folks who can least afford it.
There is such a thing as a profitable gamble in sports betting, as sportsbooks sometimes mis-estimate the probability of an event.
@@Adam-gd6pp I guess the way I think of a profitable gamble is a lottery where odds of winning are 1 in a million. The gamble becomes profitable when the the prize money goes above a million dollars for a one dollar ticket. Not a realistic profit IMO.
The best sort of gambling is investment banking: Not only can you seek investments with good expected payout, but you're gambling with other people's money.
@@vylbird8014 Yeah, like LeChiffre (Mads Mikkelsen) did in that movie, Casino Royale (2006).
@MindYourDecisions How about games where there can be a tie?
What formulas to use for those?
I'm by far not an expert on sports betting, in fact I have pretty much no experience in sports betting, but I guess the offered odds and the math formulas are just the same.
For example, if a bookmaker offers you a moneyline of +150 on a tie, it simply means that if you take the bet, you place $100 betting on a tie, and if the game indeed results in a tie, you receive $100 (original wager) + $150 (profit) = $250 payout. The implied probability of a tie is then 100/(100+150) = 40% . So as a rational agent, you should take the bet if you think/know that the probability of a tie is at least 40%, and you should decline the bet if you think/know that the probability of a tie is less than 40% .
However, it could be that in practice, (certain) sports betting exchanges have specific payout rules for bettors on "win" (or "lose") if a game ends in a tie (something like: the bettor gets a refund of half or third of their bet, or something like that; they could make up any rules they want), but I don't know about that; because as I just said, I have pretty much no experience in sports betting.
One time in the 80s, I made a sports bet on middle weight boxing champion Marvin Hagler. The money line was -650. So to make $100, I had to bet $650. That's a bad line to have to bet this much just to win $100, but I knew this was a decent bet because he was fighting a relatively unknown fighter, who wasn't that good. Hagler was the best for his weight class. He won, and I won an easy $100.
People would bet on Mayweather at over -1000 because he wasn't going to lose
So which team do I bet on..?
Most important rule. Don’t bet against Vegas. I don’t care if you’re going into the 4th quarter up 10 on +20 spread. Vegas will likely hit
Which sports you talking about dude?
I'll give you two to one odds that he left something out.
Is this really a probability? It just looks ratio of win vs. loss. Number is in no way connected to the outcome of the event except for bookmakers expectation of the outcome. And you are betting your expectation of the outcome against the expectation of the house.
The decimal form 2.5 can also be shown as 1:2.5 or 2:5 - for every $1 you bet, you get $2.50 back, which includes your $1 bet, so a profit of $2.50-$1.00=$1.50
A decimal 1.0 or 1:1 odds means that a winning bet only returns your bet.
Note that the decimal should never be less than 1 (or the number to the right of the : be less than the number to the left), or even a winning bet will lose money.
Yeah, sorry, but what you wrote is wrong.
In mathematics, odds of 1:1 means that there are two events that are equally likely. If those two events are disjunct and exhaustive, either event has a 50% chance of occurring. In a fair gamble, the payout on a bet of 1 on either event would pay out 2 if the event occurs (and 0 if it doesn't occur).
In gambling, odds are the ratio between the stake and the (potential) profit. So odds of 1:b on an event means that a bet of 1 on the event, results in a payout of (1+b) if the event occurs (and a payout of 0 if the event doesn't occur). So odds of 1:1 means you receive a payout of 2 (not 1) if your bet wins. And odds of 2:5 would mean that for every $2 you bet, you get ($2 + $5) = $7 back (if you win), so a profit of $7 - $2 = $5 .
Fun subject! Now do odds against the spread.😉
Is is just me or moneyli e dosent really make sense
How is that the the formula that odds the team wins? Whybisnit 100/100+150..That makes no sense..that's just the money being bet..if two teams are playing, aren't the odds always 50/50? Well okmthem there wouldn't be any point to betting but then it still doesn't explain this..and WHY would expected value be zero of the odds are not 50/50..this sint clear or well explained at all..Why isn't everyone else asking this same question or confused by this???
It's confusing when you say things like "you bet 100 to win a _profit_ of 250." Does that mean you get 250 total or 250 plus your original 100, or 350? By the definition of profit, it's the latter and you receive 350 in return for your bet. But that "feels" wrong, like it should be the former and you get 250 total, for a formal profit of 150.
I've never placed a sports bet, so I'm new to this.
At the beginning of the video he says Chicago +150. This gives you a total return of $250 if the bet wins: $100 initial risk and $150 for winning
@@hectorg5809 OK, thanks. So "profit" here is the difference between the bet and the return, which follows the definition.
Very useful
Thanks!
Decimal FTW. :)
Can you do one on how the odds are set? How does one decide there’s a 40% chance of a win?
That's much more complicated, but I can try to sum it up for you.
You take players' or teams' ranking and look how teams on these levels performed. Let's say 1st team in the standings plays average team. Then it depends on the sport, because in NFL the best teams are like 12-3 (they win 80% of the matches), but in MLB the best teams are 100-62 (they win only about 60% of the games). Then you have to approximate other factors, such as home advantage, key player injured, last 5 matches, some tennis players prefer clay over hard and vica versa, have their favourite tournament, somebody may be underrated after an injury, last game of the season and one team has nothing to gain and so on and so on.
@@mr.schloopka1124All true, but you forgot the two most important factors: the market and risk management. You do not want to offer odds that stray too far from what other exchanges and bookies are offering. Then players can get a surewin betting on the outcome you have high odds on and and hedging at the other bookie. This will also get you lots of risk on one outcome, you want bets on both sides to make a secure win whatever happens.
Two ways. One is to do lots of math, which is conveniently automated now - you can feed in heaps of data about the players performance and do statistical modeling. The other way is to let the gamblers themselves do the estimation, by counting how much is being bet on different outcomes and taking that into account in revising the odds throughout a game. If a lot of players suddenly start betting on X happening, then it's a sign that some event has occured that makes X seem likely - so the computers can quickly raise the odds.
How dies this make sense..if expected value is zero doesn't that imply odds are even so its fifty/fifty..or itd because the amounts are different since it's conditional..otherwise if the amount you win wquals the amount you would loae i see p wpuld equal 1/2..but wasn't everyone else confused by this?
How is the 150 odds chosen though..he does not explain that at all
Japanese dub ki quality bekar hai matlab action ke sath sync nahi hai