Mathy's Math Question of the Day (May 13/2010)

[mathdotcom]

You do not live in the U.S.A., and your local government-run lottery offers lines on sports. They do not, however, allow straight bets - you must bet at least a 2 game parlay. Also suppose they only allow betting on games with spreads, and all you have to do is choose at least two games and decide which team will cover. If you choose these two teams correctly, they pay you 2.5 times the amount of your wager. The spreads are such that you will never push.

a) (easier) How often must you hit the parlay to break even in the long run?

Now suppose the government book puts up their spreads in the morning and never changes them. As you know the spread may fluctuate throughout the day. Suppose by the time the market closes, the market spread is actually x, and if you were to buy points or adjust the spread so that it matches the government spread, the line you would end up betting into is y where for example y could be +115, -120, +170, -250.

[An example. Pretend government spread is such that Team A is -3.5, and market spread is that Team A is -1. Then x is -1 and y would be something like +160.]

b) (harder) Remember you have to bet at least a 2 team parlay, and suppose you do. On average, what is y such that you expect to break even by playing the government game? (Hint: The government does not pay you very well for hitting your parlay, so you know which way the market has to move for you to have a chance at breaking even.)

-mathy

[JohnGalt2341]

28.57%

[Rich Boy]

A) 1/2.5 = 0.4, You must hit 40% of your 2 teamers to break even.

B) sqrt(2.5) = 1.5811

1/1.5811 = .6325

You must hit spreads at a rate of 63.25% (on average) to break even on 2 teamers

[sharpcat]

A) 1/2.5 = 0.4, You must hit 40% of your 2 teamers to break even.

B) sqrt(2.5) = 1.5811

1/1.5811 = .6325

You must hit spreads at a rate of 63.25% (on average) to break even on 2 teamers

A) 1 / (2.5 + 1)=28.5%

B) I am not really sure what the question is asking?????

[mathdotcom]

A) 1/2.5 = 0.4, You must hit 40% of your 2 teamers to break even.

B) sqrt(2.5) = 1.5811

1/1.5811 = .6325

You must hit spreads at a rate of 63.25% (on average) to break even on 2 teamers

[Fishhead]

MATHDOTCOM better be in JJ's top five finalists for POTM

If not, something is missing.

[mathdotcom]

FH I once slipped the coach 2 dimes to name me POTM and he made a point to say he would not be bought and it has hurt my chances ever since.

Bad break

[JohnGalt2341]

How is 40% correct for answer A? Lets walk through this: Suppose I bet $100 100 times. I win 40(40%) times x 2.5 x 100=$10,000 correct? I lost 60(60%) times x 100=$6,000 correct? That's a profit of $4,000. The correct answer is 28.57% If I'm wrong, please show me how.

[mathdotcom]

John, your methodology is right except for one thing:

When you get paid 2.5 to 1, $1 of that $2.5 is what you risked. So your profit is actually 40 x 1.5 x 100 = $6000.

[mathdotcom]

I would like to thank all participants for taking part in Mathy's Math Question of the Day (May 13/2010).

We look forward to your participation next time.

-mathy

[JohnGalt2341]

John, your methodology is right except for one thing: When you get paid 2.5 to 1, $1 of that $2.5 is what you risked. So your profit is actually 40 x 1.5 x 100 = $6000.

Soo... 2.5 to 1=+150? Hmmm... because if that's the case then I am wrong. However if 2.5 to 1=+250 then I am right. I always thought 2.5 to 1 was equal to +250. I guess I have much to learn.