Someone good at math...
 

Okay... so I am a math moron but a bit of a gambler. I heard a discussion this morning of a place that was considering a 12X12 box for a $1 million bucks. That is, you have to get 12 out of 12 games right. I was wondering, what are the total number of possible combinations of 12 games by 12 games?

Anyone?

Re: Someone good at math...
 

Total possible combinations is 12^12 ~= 8.9 trillion.

OK, so I need more clarification to do the math right. I mean, you have to get 12 games right out of how many total number of games you have to select from? What is total number of games you have to choose from?

Re: Someone good at math...
 

i now have a headache

Re: Someone good at math...
 

The answer is ?3

Re: Someone good at math...
 

I have to select 12 games only and get exactly 12 games right. So, I was thinking something like 2^12 ?

Re: Someone good at math...
 

12 games out of how many games? I mean, do you have to select 12 games out of the entire xbox 360 game library? In order to calculate the odds of you getting 12 correct we need to know the total number of games you have to select from. Maybe post a link to the contest itself.

Anywho, the formula for calculating the odds of you picking the right 12 games is:

n!÷(r!*(n−r)!)

Where n is the total number games you have to choose from and r is the number of games you have to get right. So if you have to pick 12 games right out of 100 games your odds are: 1,050,421,051,106,700 to 1. That's a quadrillion to one odds...a runaway star has a better chance of hitting our sun than you getting the right 12 games.

Re: Someone good at math...
 

No, no. (perhaps you are just messing with me)

Each week you look at the NFL games(with the betting line of course). Out of the 16 games available(obviously less during bye weeks) you would select 12 games. To win the million, you would have to get all 12 picks correct.

So, I figured 2^12 = 4096 possible combinations. So, if I was to place 4096 bets at $12.50 per play, I would spend roughly $51,000 but be assured a $1 million payout. Seems like unacceptable risk to the house.

Now, calculating the odds of hitting that without loading up every combination would be a different thing. Each game could fairly be considered to be a 50% chance of winning. Maybe shade that up to 54% or so if you are having a good year and have a good f"feel" for the games. Either way though, the odds of a single play would be pretty tall.

Re: Someone good at math...
 

I total misunderstood...I had video games on my mind. So basically you have to win 12 games you've selected every week to get that million? Or do they give out a million every week?

Re: Someone good at math...
 

i have a headache again

Re: Someone good at math...
 

What if there are 5 ties? Unlikely I know, but it seems as if you would be out of 51K.

Re: Someone good at math...
 

Valid question. My assumption would be that they are all half point games. For example, Denver is favored by 3.5 right now over the Skins. No ties possible.

As a footnote for my fellow degenerates - Washkington is 2-6 against the spread. 0-4 both on the road and as a favorite. So, if you bet the other team, you are making money 75% of the time. Better than the market!

Re: Someone good at math...
 

thats .5^12 then right. If the prob of winning each game is 50 percent.

Re: Someone good at math...
 

[quote=hooskins;624227]thats .5^12 then right. If the prob of winning each game is 50 percent.[/quote]

No. 2 possible outcomes for 12 games. 2^12. .5^12 is a tiny number. ;)

Adding a tie to the mix changes the numbers significantly. You could use your judgment to minimize the risks of a tie, though, but the results wouldn't be a sure thing, obviously. ie, you may lose a ton of money. :)

Re: Someone good at math...
 

The answer is 42, but I don't know what the question is.

Re: Someone good at math...
 

[quote=Hijinx;624398]The answer is 42, but I don't know what the question is.[/quote]

Ask the mice.

Re: Someone good at math...
 

Math nerd to the rescue. The first assumption is that you have a 50% chance of getting a game right against the spread. Over the long haul that's about right.

In any given week, if you pick 12 games and select randomly, you have a 1 in 144 chance of getting all 12 games right (12 games raised to the power of 2, because each game has 2 possible outcomes). That translates to 0.7% chance of succeeding each week.

If you put $12.50 in to play that week, then the expected return is $1800. In other words, if the prize for that week is more than $1800, then the house is losing money, and you could arbitrage the opportunity by buying up all 144 possible combinations. (= 12.50 / 0.7%) If the prize for that week is less than $1800, then you'd lose money by buying up all 144 combinations.

But I'm pretty sure a 12x12 box means you need to get 12 games right every week for [B]12 weeks in a row[/B]. Odds of that happening are 1 in 20,736 ( = (12 * 12)^2). That translates to a percentage chance of winning: 0.0048%.

If you pay $12.50 per week to play for 12 weeks, so a total of $150, the expected return would be $3.1 million (= $150 / 0.0048%). So if the house is giving away $1 million as a prize, they're making out real well on the deal. Assuming they can drum up enough participants to cover it. By buying up all 20,736 combinations, and thus guaranteeing yourself a win, you would lose $2.1 million.

Not to mention the possibility of someone else lucking into a winning combination. What if you have to split that million dollar prize with someone?

There was a prominent company that tried to arbitrage the Mega Millions lottery. They did the math and figured that if they bought every combination possible, they'd make out on the deal. The math was right, and they did win, but they forgot to factor in both the taxes they'd have to pay and the possibility that they'd split the pot. There was one other winner, and then they had a tax bill. The people who made this decision were fired. Wish I could remember who and when it was, but my statistics professor loved to tell that story.

Re: Someone good at math...
 

If you need me to change the assumptions in any way, I can adjust the calculation easily. Perhaps the entry fee is different, or I'm not understanding the rules of the game, or whatever. Correct me if I'm making the wrong assumptions.

Re: Someone good at math...
 

[quote=Schneed10;624462]Math nerd to the rescue. The first assumption is that you have a 50% chance of getting a game right against the spread. Over the long haul that's about right.

In any given week, if you pick 12 games and select randomly, you have a 1 in 144 chance of getting all 12 games right (12 games raised to the power of 2, because each game has 2 possible outcomes). That translates to 0.7% chance of succeeding each week.

If you put $12.50 in to play that week, then the expected return is $1800. In other words, if the prize for that week is more than $1800, then the house is losing money, and you could arbitrage the opportunity by buying up all 144 possible combinations. (= 12.50 / 0.7%) If the prize for that week is less than $1800, then you'd lose money by buying up all 144 combinations.

But I'm pretty sure a 12x12 box means you need to get 12 games right every week for [B]12 weeks in a row[/B]. Odds of that happening are 1 in 20,736 ( = (12 * 12)^2). That translates to a percentage chance of winning: 0.0048%.

If you pay $12.50 per week to play for 12 weeks, so a total of $150, the expected return would be $3.1 million (= $150 / 0.0048%). So if the house is giving away $1 million as a prize, they're making out real well on the deal. Assuming they can drum up enough participants to cover it. By buying up all 20,736 combinations, and thus guaranteeing yourself a win, you would lose $2.1 million.

Not to mention the possibility of someone else lucking into a winning combination. What if you have to split that million dollar prize with someone?

There was a prominent company that tried to arbitrage the Mega Millions lottery. They did the math and figured that if they bought every combination possible, they'd make out on the deal. The math was right, and they did win, but they forgot to factor in both the taxes they'd have to pay and the possibility that they'd split the pot. There was one other winner, and then they had a tax bill. The people who made this decision were fired. Wish I could remember who and when it was, but my statistics professor loved to tell that story.[/quote]

What does a "guess" consist of? My assumption is...

You have 12, and only 12, spots to play in each guess. Each spot can have 2 results. The number of unique "guesses" is 2^12.

Re: Someone good at math...
 

[quote=cpayne5;624481]What does a "guess" consist of? My assumption is...

You have 12, and only 12, spots to play in each guess. Each spot can have 2 results. The number of unique "guesses" is 2^12.[/quote]

Oh jeez, you're right. Me = fail. Not one in 144 like I said, it's one in 4096.

Pay in $12.50 for that week, the expected payoff for that week is $51,200.

!q
 

[quote=Schneed10;624520]Oh jeez, you're right. Me = fail. Not one in 144 like I said, it's one in 4096.

Pay in $12.50 for that week, the expected payoff for that week is $51,200.[/quote]

See? Give yourself more credit! You just thought you were a nerd!