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-   -   This seems impossible. Can mathematics solve it? (http://mymathforum.com/number-theory/344664-seems-impossible-can-mathematics-solve.html)

 Jumbo August 12th, 2018 08:16 AM

This seems impossible. Can mathematics solve it?

Here's a very simple scenario: There is a 1 person foot race of 10 yards length. Therefore there can be only 1 winner.

A bookmaker then takes one bet on the outcome, a \\$1 bet & if the bet wins (which it must) the bookmaker payout dividend is 90 cents. These odds are agreed upon by the bookmaker & gambler. Therefore the person making the bet is guaranteed to lose 10 cents on his winning bet.

So it's....

Bet \\$1 to win 90 cents (yes, yes I realize nobody would take these odds in a "real" one person event .... this is a "theoretical" example).

Here's the math question: Is there any way using mathematics that the 10 cent loss can be turned into a profit via the use of complex, imaginative, mathematical formulas? In other words, constructing the bet with the 90 cent return, in an imaginative way to return at least \\$1.01 instead of the 90 cents (whilst at the same time the return is still "officially" listed at 90 cents).

Yes your first thought would be "that's 100% impossible to achieve". I suspect there's a way to achieve it though, likely via a very involved & complex series of mathematical formulas & inventive ways to construct the bet.

Can anyone here do it successfully?

Thanks.

 skipjack August 13th, 2018 06:10 AM

You asked something similar in February. There's no way to do it.

 JeffM1 August 13th, 2018 06:22 AM

I find this a remarkably silly question.

Define "winning" as beating the average time. Anyone who bets on the racer to win will lose.

 Jumbo August 13th, 2018 07:03 AM

I reckon there IS a way to achieve at least a \$1.01 return. Use your imagination, use mathematical formulae, use utterly unconventional ways of constructing the bet via mathematical computation that the average person would never, ever consider or is capable of.

 Maschke August 13th, 2018 07:55 AM

Quote:
 Originally Posted by Jumbo (Post 597583) I reckon there IS a way to achieve at least a \$1.01 return. Use your imagination, use mathematical formulae, use utterly unconventional ways of constructing the bet via mathematical computation that the average person would never, ever consider or is capable of.
There actually is one example I know of where the house is required to pay out more than they took in.

In horse racing, you are not betting against the house, you're betting against the other players. This is called pari-mutuel betting. All the money paid for tickets is put into a pool. After the race, the pool is divided out among everyone with a winning ticket. So if the favorite wins, the payout to each individual is smaller because a lot of people bought ticket. But if a longshot comes in, it pays more because there were fewer players buying tickets on that horse.

Now, 100% of the pool is not paid back to bettors. The state, the county, the racing association, the track, and various other government and private agencies get a cut, around 17% or so in the US on average if memory serves.

So it's possible that if everyone bets on a particular horse, and that horse wins, then after the cut is taken off the top, each winning bettor gets back less than they put in. That doesn't seem fair. So the law generally requires a \\$2 bet to pay off at least \\$2.20. In the case where the pool is too small to pay everyone off, the track actually loses money. They have to pay out more than the win pool contained.

In your case of a one-person race, everyone will bet on that one person, who will of course win. If there is a law in effect that requires, say, at least \\$2.20 to be paid on a \\$2.00 bet, the house will indeed lose money and each bettor will win a small amount.

 Jumbo August 13th, 2018 07:49 PM

Here's a marginally different scenario (based on exactly the same principle) that will enable mathematicians here to get more creative......

We have a coin toss scenario. This coin does not have heads/tails, it has 2 heads, therefore you must pick "heads" for every toss to win. So you'll win with every toss. The coin will be tossed 100 times. For each toss you bet \\$1. Your wife will act as the pretend bookmaker, and she will pay you 90 cents for each \\$1 bet you make with her. So you make 100 bets, win 100 times, and each time you win you get 90 cents return for your 1 dollar bet. So your total outlay will be \\$100 and your total return will be \\$90.

Here's the mathematical challenge: Can you, via the use of advanced mathematical computation in this real time scenario, find a way to end up with a return of a minimum of \\$100.01 instead of the \\$90 (even though the return for each \\$1 bet is 90 cents)?

There's mathematical principles involved with this. "On the surface" it appears that a profit return can't be made, however I suspect there are creative mathematical formulas that can be applied over the 100 bet series that are uncommon, unknown to 99.99999% of people & can produce a minimum of a 1 cent overall profit instead of the usual \$10 overall loss.

I'm using a gambling example because that's the easiest scenario for people to comprehend. The same mathematical principles could cover hundreds of different scenarios in other subject matter.

It's all about "mathematics" done in creative, uncommon and effective ways. What "appears" to be an impossible mathematical task is not always an impossible mathematical task.

 skipjack August 13th, 2018 11:38 PM

Retrieve your original stakes, explaining that you're entitled to them, as you were merely pretending to bet.

 Jumbo August 13th, 2018 11:55 PM

Serious replies only please.

 Benit13 August 14th, 2018 01:30 AM

Quote:
 Originally Posted by Jumbo (Post 597519) ...the person making the bet is guaranteed to lose 10 cents on his winning bet. ... Is there any way using mathematics that the 10 cent loss can be turned into a profit via the use of complex, imaginative, mathematical formulas? ...
No, since you stated in your premise that anyone who makes a bet is guaranteed to lose some money.

If you already have an answer in mind, chances are there is either a flaw in your solution or there is something you are not telling us about the betting system.

 Jumbo August 14th, 2018 02:47 AM

Benit13: Yes, the person is "guaranteed" to lose .... but only "if" they make standard bet computations in the standard way. Basically I'm asking people to think outside of the box and approach it via creative & ingenious mathematics. The "gambling" examples are mere simplified examples of one particular application; the same mathematical principles I'm seeking could also apply to complex mathematical computation in physics, biology, astronomy etc. And no, I don't already have an answer in mind.

Remember, a mathematical computation doesn't "always" have 1 logical result ..... depending on how & why it's approached there can sometimes be numerous results that are all 100% correct & logical but not always obvious.

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