There are 10 types of people-- those who understand binary, and those who don't.

At one point in time-- and that point actually lasted for a very long period of time-- oddsmakers at the horse (or dog) tracks listed the "odds" of an animal winning a race as a fraction. Some odds, like 4 to 1, were shown simply as "4", but there were other less apparent odds, too. Instead of using decimals, something like 1.5 to 1 odds was written as "3/2". Things could get crazy, quickly though, and the fraction used could be expressed as "5/4", or "13/10", for example.

On race day, your 5 - 1 odds horse could get a lot of attention and the organizers would lower the odds before the race, to allow for the extra money that they would lose should everyone suddenly decide to bet on the 'favorite', or even raise them to encourage others to take a chance on a bet on a less-likely winner. The guys who were writing the odds out normally used chalk and a board, so they could erase and show the current odds more easily to the bettors.

With computers becoming more common in the '80s, all of the bigger tracks went to a system that had a large tote board that calculated the exact payout, based on a $2 ticket instead of simply the odds. Decimals were employed, and you could see-- right to the penny-- how much your potential winner would be worth, and the old fractional system went out of fashion in a hurry.

So then. Go back in time, and let's see how you would do with the "old" system of fractions.

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Seems straightforward to me...

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9/5 means you get 9/5 of your initial bid (plus you get your bid back) if you win. So, $2 * 9/5 + $2 = $5.60.

At least that's the way that I recall betting odds working. As of now, most people are guessing $3.60, which means either I'm mis-remembering or else they are forgetting that a winner always gets their bid back in addition to the prize.

I have to admit that where things can get a little confusing that different websites will use the phrase "odds" and "payout" interchangeably when they really mean different things. So when Mabby is using the phrase "collect" it isn't clear if he is talking about player winnings versus the redemption value of the ticket. Still, I would have got this wrong. I have a vague recollection of this being taught in one paragraph of my algebra book back in 1988, but I've never used it since then. I'm not aware of any industry who actually uses odds outside of gambling. The "real world" talks about things in terms of probabilities.

Gambling always comes with disappointments, Mabby! Gambling is not playing. Gambling is gambling. An appeal to greed. Be like me, be sensible. I admit it is a boring life, but with more money in your pocket.

So here it is a beautiful Monday morning and Mabby is asking for math. Can you tell us exactly what happened to you over the weekend that pissed you off this much?

So here it is a not-so-beautiful Monday morning (overcast, drizzly, kinda dreary really) and Mabby is asking for math. A simple math question is like a day at sunny Churchill Downs, designed to make us carefree, happy, and willing to take a crazy chance...

Aren't you glad they moved to the new system, now you only have to multiply what you gambled, times the winning $2 ticket, and bang, you have the payout. Most people gamble in increments of your typical bills, in the U.S., one, five, ten, twenty, fifty, or one hundred. So it makes the math fairly easy.

If the odds of the horse winning are 9/5, that's better than 1 which means the horse is likely to win, so the amount won should be less than the amount bet if the racetrack wants to stay in business.

I believe in this example the odds of the horse winning are actually 5/9.

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Yes, I really am that awesome.

jbrecken wrote:

If the odds of the horse winning are 9/5, that's better than 1 which means the horse is likely to win, so the amount won should be less than the amount bet if the racetrack wants to stay in business.

I believe in this example the odds of the horse winning are actually 5/9.

?

The odds aren't the odds of the horse winning. It's the payoff odds. 9/5 odds means that the chance of the horse winning is a little bit under 35.7%. The "a little bit under" gives the track their profit margin.

Edit: I did my math wrong originally. I'm pretty sure that 35.7% is the right value.

There are 10 types of people-- those who understand binary, and those who don't.

jbrecken wrote:

If the odds of the horse winning are 9/5, that's better than 1 which means the horse is likely to win, so the amount won should be less than the amount bet if the racetrack wants to stay in business.

I believe in this example the odds of the horse winning are actually 5/9.

9 to 5 odds is better than one, so that merely means that the horse is a longshot. The favorite might be paying closer to 1:1 odds, but the track makes money on every failed bet, so they make the odds for the bad horses higher to encourage bad money on them to follow.

5/9 odds means that for every 9 dollars you wager, you can win five. Plus your $9 back. Weird numbers, in fractional form, but possible. And, while this isn't a great way to make money for the gambler, it still works if they want to take the risk on a heavy favorite.

At 5/9, you'd bet $2.00, and you'd win $1.10 (2 x 5/9) + $2.00 = $3.10

The desperate guy who put his $2 on a 100 - 1 longshot would win $202, but that isn't going to happen enough times to make the track worry about it. In fact they'd clean up, since all of the failed bets on the favorite are theirs now and there's only a handful of people to pay the big prize to.

If the odds of the horse winning are 9/5, that's better than 1 which means the horse is likely to win, so the amount won should be less than the amount bet if the racetrack wants to stay in business.

I believe in this example the odds of the horse winning are actually 5/9.

9 to 5 odds is better than one, so that merely means that the horse is a longshot. The favorite might be paying closer to 1:1 odds, but the track makes money on every failed bet, so they make the odds for the bad horses higher to encourage bad money on them to follow.

Then your introductory paragraph is wrong, where you said

MABBY wrote:

At one point in time-- and that point actually lasted for a very long period of time-- oddsmakers at the horse (or dog) tracks listed the "odds" of an animal winning a race as a fraction.

9/5 in your example is not the odds the horse will win the race. If it was, it would mean if this horse runs 5 races, it will win 9 of them.

9/5 means you get 9/5 of your initial bid (plus you get your bid back) if you win. So, $2 * 9/5 + $2 = $5.60.

At least that's the way that I recall betting odds working. As of now, most people are guessing $3.60, which means either I'm mis-remembering or else they are forgetting that a winner always gets their bid back in addition to the prize.

Never having had any interest or involvement, no I was not aware of that, so naturally worked it out just as most other people did.

Just shows that it was a rigged question that does not contain all the information necessary to correctly answer it.

I would like to know, though, if this is the case everywhere.

Science without religion is lame, religion without science is blind—Einstein

I think that's how it's always done in horse racing. I've been to several tracks in the U.S. and one in Singapore.

For sports betting the odds are often stated differently....But the amount you get back if you win is still the payoff plus the initial wager. For example, in the UK if you're betting on soccer, odds expressed as 3/7 mean for every £7 that you bet you get £3 if you win (plus your £7 back).*

*From the book I'm currently reading -- Soccermatics: Mathematical Adventures in the Beautiful Game

I have to admit that where things can get a little confusing that different websites will use the phrase "odds" and "payout" interchangeably when they really mean different things. So when Mabby is using the phrase "collect" it isn't clear if he is talking about player winnings versus the redemption value of the ticket. Still, I would have got this wrong. I have a vague recollection of this being taught in one paragraph of my algebra book back in 1988, but I've never used it since then. I'm not aware of any industry who actually uses odds outside of gambling. The "real world" talks about things in terms of probabilities.

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Good points, well put. I, personally, can't get enough of game gaming that is for sure.