Math question ?

Doug · Jan 22, 2005

I'm playing Fishhead head to head in HW contest: 10 games

He's 1-3
I'm 1-2-1

6 games left. Last game our teams played each other. I didn't bet the same as him to preserve my .5 game lead. I had already decided I wanted Detroit to cover the day before. I would definetly do that in game 8 or later.

6 games left, If I go an ordinary 3-3, Fish has to go 4-2 to win.

How does one figure the odds on this. Assume we are both 50% cappers over remaining games. I have an edge, fairly good one, but how good ?

I'm looking for the math to find an exact percentage here. I don't know how to figure that, that's my goal... to find an equation to figure out a situation like this. I can guesstimate I'm 55% or so, maybe a little better, but I can't write an algebraic equation for it.

So lets let the math guys come up with a number, and more importantly the math behind it ! I expect a precise clean number like 57.45 % or something.

daringly · Jan 22, 2005

If you have 6 games left, you have 7 possibilities rangin from 0-6 to 6-0.
Assuming you are a 50/50 coin flipper, you can flip your coin 2^6, or 64 ways.
The odds of any given record (for you and your opponent) are S(6 choose W)/64 where W is the number of wins.

so, for various records:
0-6: 1/64
1-5: 6/64
2-4: 15/64
3-3: 20/64
4-2: 15/64
5-1: 6/64
6-0: 1/64

If I understand correctly, you win the matchup unless your opponent wins more matches then you. So, multiply the above occurrences by the odds that your opponent has an equal or worse record:

By your record:
0-6: 1/64 * 1/64
1-5: 6/64 * 7/64
2-5: 15/64 * 22/64
3-3: 20/64 * 42/64
4-2: 15/64 * 57/64
5-1: 6/64 * 63/64
6-0: 1/64 * 64/64

Factor out the 64^2, and you have
(1 + 42 + 330 + 840 + 855 + 378 + 64 ) / (64^2)
or 2510/64^2 = 61.3%.

Note that if the contest allows you to "lock in" a 3-3 record by betting opposite sides of the same game, you raise your odds of winning to 42/64, or 65.6%.

Doug · Jan 22, 2005

daringly said:
If you have 6 games left, you have 7 possibilities rangin from 0-6 to 6-0.
Assuming you are a 50/50 coin flipper, you can flip your coin 2^6, or 64 ways.
The odds of any given record (for you and your opponent) are S(6 choose W)/64 where W is the number of wins.

so, for various records:
0-6: 1/64
1-5: 6/64
2-4: 15/64
3-3: 20/64
4-2: 15/64
5-1: 6/64
6-0: 1/64

If I understand correctly, you win the matchup unless your opponent wins more matches then you. So, multiply the above occurrences by the odds that your opponent has an equal or worse record:

By your record:
0-6: 1/64 * 1/64
1-5: 6/64 * 7/64
2-5: 15/64 * 22/64
3-3: 20/64 * 42/64
4-2: 15/64 * 57/64
5-1: 6/64 * 63/64
6-0: 1/64 * 64/64

Factor out the 64^2, and you have
(1 + 42 + 330 + 840 + 855 + 378 + 64 ) / (64^2)
or 2510/64^2 = 61.3%.

Note that if the contest allows you to "lock in" a 3-3 record by betting opposite sides of the same game, you raise your odds of winning to 42/64, or 65.6%.

Daringly: Thanks for the math, no lock-in's allowed. Fish picks Milw against spread, I pick Detroit against spread, they don't play each other in next 6 games.

Math is a little heavy, but I think I get it. I guessed 57%, close enough. I'm comfortable enough coming close. Pure math won't beat the books, but at least a basic understanding counts a lot. I think most here couldn't perform this kind of math.

How many of you guys can figure this ?

bigbet1234 · Jan 22, 2005

DougJ said:
Daringly: Thanks for the math, no lock-in's allowed. Fish picks Milw against spread, I pick Detroit against spread, they don't play each other in next 6 games.

Math is a little heavy, but I think I get it. I guessed 57%, close enough. I'm comfortable enough coming close. Pure math won't beat the books, but at least a basic understanding counts a lot. I think most here couldn't perform this kind of math.

How many of you guys can figure this ?

yes it will, trust me.

BB

Doug · Jan 22, 2005

bigbet1234 said:
yes it will, trust me.

BB

Yes, BB a middler can win with math alone, but most guys aren't this math-based.

BlackBart · Jan 22, 2005

True story about how I came to have a degree in math:

I was all set to study english or something like that when, during my junior year of high school, I run into one of the high school math teachers at the dog track (which wasn't difficult, because I was there 6 nights a week). We get to talking and pretty soon I'm going by his classroom and he's teaching me all kinds of probability theory and **** that I could use when playing cards or table games. I'm hooked, I sign up for his classes senior year and then go on to study math in college. I have a minor in business (which I use nearly every day at work), but I only use my degree in my degenerate hobby.

Interesting course I once took told me that the study of mathematics was begun by degenerate gamblers looking to understand games of chance.

God bless them.

Doug · Jan 22, 2005

Black Bart said:
True story about how I came to have a degree in math:

I was all set to study english or something like that when, during my junior year of high school, I run into one of the high school math teachers at the dog track (which wasn't difficult, because I was there 6 nights a week). We get to talking and pretty soon I'm going by his classroom and he's teaching me all kinds of probability theory and **** that I could use when playing cards or table games. I'm hooked, I sign up for his classes senior year and then go on to study math in college. I have a minor in business (which I use nearly every day at work), but I only use my degree in my degenerate hobby.

Interesting course I once took told me that the study of mathematics was begun by degenerate gamblers looking to understand games of chance.

God bless them.

I don't own a degree. Graduated HS with Honors, might have been High Honors, don't remember ! Took some community college classes much later on, History and economics. I think I pulled an A in economics and a B+ in History. That was back in North Vegas at CCSN, I took tennis back at a community college in north county San Diego, much earlier.

Point is math is good, never will hurt you, but not a panacea.

Doug · Jan 22, 2005

I'm Fishing in a barrel now. ! I must be close to 70% now to beat Fishhead ! Just freaking around.

Good luck FISH. It ain't over, but pressure is on you !

Daringly or math guys re-calculate, the Fish is in trouble !, Doug is now 2-2-1 for a toutable .500

I'm messing with you Fishy, all in fun. Don't lose your next pick ! You don't want to fall 1.5 games behind !

daringly · Jan 22, 2005

Math will crush books on small markets (such as props, or lesser played sports). And I'm not talking rocket science math... But any sports investor really needs to know 3 areas.

1. Algebra (applications in calculating return on risk, value of half-points, and which line is better: Pittsburg +3 -115, or +2 +110)

2. Basic probability/stats (aka pizza problems. How many pizzas can you make with exactly 2 toppings, if your store offers 8 possible toppings?). The main things to know are permutations and selections - how to calculate, and when to use them. Your problem was trivial (though a bit time consuming) if you know selections.

3. Poisson distributions. If I flip a fair coin 100 times, what are the odds that I hit at least 57 heads?

If you can do #2 and #3, small players have no excuse for losing long-term - props are very beatable. Many props on a 30c line have equity on openers, and you can find 10c or 20c lines on props without too much difficulty. If you don't know any of these 3, you are a huge long-shot to winning long-term.

wilheim · Jan 22, 2005

Point is math is good, never will hurt you, but not a panacea.

You will never get that one by Fishhead.

wil.:nono5:

Doug · Jan 23, 2005

wilheim said:
You will never get that one by Fishhead.

wil.:nono5:

I'm up a full game on him ! Fish is dog here !

I'm good favorite to beat Fishhead, can't beat the Math !. He has chance, but I'm favorite, no other way to look at this ! Pressure is on Fish !

Doug · Jan 23, 2005

daringly said:
Math will crush books on small markets (such as props, or lesser played sports). And I'm not talking rocket science math... But any sports investor really needs to know 3 areas.

1. Algebra (applications in calculating return on risk, value of half-points, and which line is better: Pittsburg +3 -115, or +2 +110)

2. Basic probability/stats (aka pizza problems. How many pizzas can you make with exactly 2 toppings, if your store offers 8 possible toppings?). The main things to know are permutations and selections - how to calculate, and when to use them. Your problem was trivial (though a bit time consuming) if you know selections.

3. Poisson distributions. If I flip a fair coin 100 times, what are the odds that I hit at least 57 heads?

If you can do #2 and #3, small players have no excuse for losing long-term - props are very beatable. Many props on a 30c line have equity on openers, and you can find 10c or 20c lines on props without too much difficulty. If you don't know any of these 3, you are a huge long-shot to winning long-term.

#3 is hardest for me. If you ask me the odds of hitting a 10 team parlay ( or any other number of teams), I can do that in my head. I know which line is best...Pitts +3 -115 is slighty better, but not by a bunch, #3 is the hard one.

I'm not ashamed to ask for help ! I knew I had a lead on Fish in first example, was curious to define it. I believe most couldn't put a precise number on it The post got a number of reads before daringly answered it with math.

I believe most here couldn't answer that.

Doug

BlackBart · Jan 23, 2005

Again, I'm no genius, but it's amazing how many people can't use elementary math to determine that a lot of bets--some stuff in Vegas, but mostly things like the state lottery--have the odds clearly stacked against you.

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