Math Experts - Help with odds

So let's say you have four people in a race: A, B, C and D.

Now this is easy enough. If that's all we know about the race, then each one has 4:1 odds of winning. Meaning they are "four to one" and thus have a one in four chance of winning.

Part I

But let's complicate this. Let's say these same people have raced before - six times. In those six races, the winners were:
A: 3
B: 2
C: 1
D: 0

Now they're going to race again. What are the odds of each of the racers to win?




PART II:

Let's say that there are 8 racers, but which racers are in the race changes each day. So:

A has been in 7 races, and won 3.
B has been in 5 races and won 2.
C has been in 11 races, and won 1.
D has been in 3 races and won 0.
E has been in 12 races and won 4.
F has been in 12 races and won 5.
G has been in 9 races and won 3.
H has been in 7 races and won 1.

Does this change the odds?

Would it matter to the odds if this exact same set of racers (A, B, C and D) had all raced against each other before?

Please explain. I might have follow-up questions.

Fucking Racer D needs to step his game up, or find a new thing to do.

Also, they should all count their lucky stars that they haven't encountered Racer X.

Part 1

A has 50% chance of winning

B has 33%

C has 16.5%

D 0%

That's just the % of wins when working out odds bookies look at weather, ground firmness, lots of other factors

Your expecting to find a math genius on a porn site????

Quote:

Originally posted by Allen_Bradley

Your expecting to find a math genius on a porn site????

People that enjoy maths aren't also able to appreciate the female form?

Quote:

Originally posted by sumo999

Part 1

A has 50% chance of winning

B has 33%

C has 16.5%

D 0%

No, that's the odds that they won one of the previous six races, not the odds they'll win the next race. It's hard for me to say what the actual odds for winning the next race are because of how incomplete the information is because it's been a while since my stats classes, and I'm not sure I remember the conditional probability stuff well enough to speak intelligently about it.

Someone better laugh at my Racer X comment.

Strictly speaking the odds are 3-to-1 against each contestant. There are three losing outcomes and one winning outcome.

As for any sort of subjective wagering scenario, the way most racetracks work (for horse racing) is a system known as pari-mutuel wagering. All of the bets placed on a given race are pooled, a percentage is deducted for the racetrack's operations, another percentage for taxes, and the remaining amount is divided up on a dollar for dollar basis. Each dollar bet on the winner gets an identical fraction of the pool, rounded to the nearest dime (known as "breakage" ) Hence, the odds posted before the race will change as more money is bet, and are not a guarantee of what a given dollar's bet will win.

Quote:

Originally posted by Bangledesh

Also, they should all count their lucky stars that they haven't encountered Racer X.

HA!

Quote:

Originally posted by Bangledesh

Someone better laugh at my Racer X comment.

Only a select few of us have any idea what you're talking about. And yes, your comment was amusing

Quote:

Originally posted by EricLindros

...

It's hard for me to say what the actual odds for winning the next race are because of how incomplete the information is

What other information do you need?

Quote:

Originally posted by ranging

...
People that enjoy maths aren't also able to appreciate the female form?

Yeah but they probably appreciate the female form in Fibonacci ratios instead of fuckability factors....

Quote:

Originally posted by Tarquin

So let's say you have

A homework to do by yourself and you'd like other people to do it for you just for free.

Quote:

Originally posted by Tarquin

… Please explain.

For me it smells like the conditional probability. I may mistake. I had statistics about 20 years ago and condictional probability was just one hour and about six exercises. But I belive that your's statistics/probabliity course is just passing so your head is far more fresh about it than mine.

Quote:

Originally posted by Tarquin

I might have follow-up questions.

No. You just have to sit down on your ass and learn and do the exercises.

Quote:

Originally posted by Tarquin

...

What other information do you need?

Things like race length, margin of victory in the previous races, place in previous races, etc.

For example, compare these race finish scenarios:
Race 1: A, B, C, D
R 2: A, B, C, D
R 3: B, A, C, D
R4: C, A, B, D
R5: B, A, C, D
R6 A, B, C, D

versus

R1: A, D, B, C (5K race)
R2: A, D, C, B (5K race)
R3: C, D, B, A (15K race)
R4: B, D, C, A (10K race)
R5: A, D, B, C (5K race)
R6: B, D, C, A (10K race)

In the first version of the six races D finished dead last in every one. In the second set D finished second, while A either won or finished dead last.

The D placing in last place each race will have lower odds of winning the next race than the D in the second set of races who managed a second place finish against all comers. How much different exactly, and how to precisely calculate it I'm not sure because, like I said, it's been a while and I'd have to go back and look this stuff up again.

The second hypothetical I posed there (with different race lengths) also shows that A would be a great short distance runner but tires out quickly and is unlikely to win any race longer than 5K.

But perhaps I'm getting beyond the scope of the exercise.

wow glad I love women more than numbers and horse racing... it is horse racing you talking about... right... right

Quote:

Originally posted by Bangledesh

Someone better laugh at my Racer X comment.

I did

Nice.

Quote:

Originally posted by kjp_a_man

... A homework to do by yourself and you'd like other people to do it for you just for free.

Not really. I have two bachelor's and a master's. I'm pretty much done with my Ph.D. It happens to be in the behavioral sciences, however. Not math. I'm an expert in human behavior, not mathematics.

I do appreciate the link to the conditional probability calculation. However, this is akin to a math expert trying to understand homogenous political theory in a contemporary society. They might know what each of the words means independent of one-another, but I'd wager most wouldn't know what they meant put together or what the concept being described was.

In other words, not being a math guy, I don't understand that Wiki page.

Quote:

wow glad I love women more than numbers and horse racing... it is horse racing you talking about... right... right

Um... No. Actually. It's a kid's game. In a kid's game that my nieces and nephews play there's a game that has odds for winning contests and they can earn things for their cartoon animal if they correctly predict the outcomes, which will require them to be able to understand odds.

Yeah, I said it. It's for a kid's game. It's not a horse-racing game either. It's a pirate food contest...

Yeah, I'm serious. And yes, I'm embarrassed. Fuck it. You asked, I answered. Fuck it. It's for a pirate eating contest in a cartoon world of fiction.

Quote:

Originally posted by EricLindros

...

Things like race length, margin of victory in the previous races, place in previous races, etc.

Okay, then I'll need to do more research and get back to you. Thank you for telling me what you need.

I don't know the race length, and I don't know the margins of victory, but I can find out the result histories.

Quote:

The second hypothetical I posed there (with different race lengths) also shows that A would be a great short distance runner but tires out quickly and is unlikely to win any race longer than 5K.

But perhaps I'm getting beyond the scope of the exercise.

Well, I do know that fatigue is an issue for the contest in question, but without margins or play-by-play knowledge, I can't tell how much of a factor or who is a sprinter versus who is a marathon runner. All I have are the results and which place they placed in.

I'll try to post a sample of those and see where that gets us.

I do want to learn how to do this myself, so that's the important part. I'll try to get a sample up as soon as I can.

Thank you all for your help.

Okay, so I was able to figure some stuff out. For starters, the game in question doesn't show who placed in what position. All it shows is the winner.

So let's say we have the same four racers in each race, and they come down like this:

1: A
2: A
3: A
4: B
5: B
6: C

All we know is who won between A, B, C and D. Is the odds calculation as simple as I think it is? A is 2:1, B is 3:1, C: 4:1, and D is infinity:1?