August 12th, 2018, 09:16 AM  #1 
Newbie Joined: Feb 2018 From: Ocala Posts: 7 Thanks: 0  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. Last edited by skipjack; August 13th, 2018 at 07:06 AM. 
August 13th, 2018, 07:10 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
You asked something similar in February. There's no way to do it.

August 13th, 2018, 07:22 AM  #3 
Senior Member Joined: May 2016 From: USA Posts: 1,245 Thanks: 515 
I find this a remarkably silly question. Define "winning" as beating the average time. Anyone who bets on the racer to win will lose. 
August 13th, 2018, 08:03 AM  #4 
Newbie Joined: Feb 2018 From: Ocala Posts: 7 Thanks: 0 
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.

August 13th, 2018, 08:55 AM  #5  
Senior Member Joined: Aug 2012 Posts: 2,126 Thanks: 618  Quote:
In horse racing, you are not betting against the house, you're betting against the other players. This is called parimutuel 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 oneperson 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. Last edited by skipjack; October 3rd, 2018 at 02:04 AM.  
August 13th, 2018, 08:49 PM  #6 
Newbie Joined: Feb 2018 From: Ocala Posts: 7 Thanks: 0 
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. Last edited by skipjack; August 14th, 2018 at 12:30 AM. 
August 14th, 2018, 12:38 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,089 Thanks: 1902 
Retrieve your original stakes, explaining that you're entitled to them, as you were merely pretending to bet.

August 14th, 2018, 12:55 AM  #8 
Newbie Joined: Feb 2018 From: Ocala Posts: 7 Thanks: 0 
Serious replies only please.

August 14th, 2018, 02:30 AM  #9  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,133 Thanks: 719 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
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.  
August 14th, 2018, 03:47 AM  #10 
Newbie Joined: Feb 2018 From: Ocala Posts: 7 Thanks: 0 
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. 

Tags 
impossible, mathematics, solve 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Near impossible to solve, mathematical pattern  astronomical  Number Theory  8  December 24th, 2016 08:47 AM 
how do I solve this impossible thing?  matisolla  Calculus  1  June 16th, 2015 08:19 PM 
impossible :(  Ole Daniel  Algebra  3  January 13th, 2015 01:50 AM 
Solve mathematics problems  lebnitz  Academic Guidance  1  September 28th, 2011 04:38 PM 
Trinagle Problem. Math Award Winner Can't Solve, IMPOSSIBLE?  nqavisid  Algebra  4  November 14th, 2008 01:28 PM 