# Thread: Sports betting related math question

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## Sports betting related math question

If you’ll allow another sports betting post. Some of you math nerds love this stuff though . Promo offers a “risk free” 1st score basketball bet. You bet \$25 and receive it back in free bets if it loses. Most of these odds start at +400 or +500 for the favorite and step up from there. I work through 5 accounts. So, question is how can I figure the odds that one of the 5 favorites is the one who makes the 1st basket? For simplicity sake, let’s assume it’s +500, +600, +700, etc. Thanks

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What odds you get when the bet wins has nothing to do with the question you're asking. They're separate concepts. For NONE of the five favorites to make the first basket, is about one chance in 32. No matter which is the better team, making the first basket is somewhat of a tossup. So, in five games, at LEAST one of the five favorites will make a first basket 96.9% of the time.

Don

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Originally Posted by DSchles
What odds you get when the bet wins has nothing to do with the question you're asking. They're separate concepts. For NONE of the five favorites to make the first basket, is about one chance in 32. No matter which is the better team, making the first basket is somewhat of a tossup. So, in five games, at LEAST one of the five favorites will make a first basket 96.9% of the time.

Don
Sorry, apparently I did a terrible job articulating what I was asking. What I would be doing would be betting on the same game, across 5 accounts. In each account, I would pick a different one of the top 5 favorites to make the first basket. So, I’m trying to find out how to calculate the odds that one of those 5 players would score first. What are the odds I win one of those bets? If I knew those odds, in conjunction with the \$25 free bet return on the losing bets, I believe I could figure out whether or not it was a positive EV situation. Thanks

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Originally Posted by Old new guy
Sorry, apparently I did a terrible job articulating what I was asking. What I would be doing would be betting on the same game, across 5 accounts. In each account, I would pick a different one of the top 5 favorites to make the first basket. So, I’m trying to find out how to calculate the odds that one of those 5 players would score first. What are the odds I win one of those bets? If I knew those odds, in conjunction with the \$25 free bet return on the losing bets, I believe I could figure out whether or not it was a positive EV situation. Thanks
Oh, so you're betting on individual players to score the first basket, and you'd like to know the odds that one wins, assuming they're ALL +500, +600, or +700? Or, do you assume different odds for each of the five bets? Answer the above question, and I'll let you know. (It would be much easier if the odds stay the same for all five players, regardless if they're all +500, +600, or whatever.)

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If what you ask is the implied probability for the different odds, that is easiest calculated by converting the odds to European decimal odds, and divide those odds by one. For +400 the decimal odds are 5 and the implied odds are 1/5. For +500 the decimal odds are 6 and the implied odds are 1/6 and so forth. Hope this helps. The true probability is of course lower than this, because of the wig.

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Originally Posted by DSchles
Oh, so you're betting on individual players to score the first basket, and you'd like to know the odds that one wins, assuming they're ALL +500, +600, or +700? Or, do you assume different odds for each of the five bets? Answer the above question, and I'll let you know. (It would be much easier if the odds stay the same for all five players, regardless if they're all +500, +600, or whatever.)
Yes..the bets are on individual players to score the first basket of the game. The odds are all different, as you would expect some players to be more likely than others to score first. An example of the top five for tonight’s GS/Minn game is Curry +450, Towns +550, Russell +600, Wiggins +600, Edwards +650. So, I would pick each one of these guys in each of my 5 accounts. Any one of them winning covers my losses in the other 4. Plus, I get 4 \$25 free bets. So, that is positive AV for sure. But..one of them has to win. So, I would like to know the odds that any one of them would win, given these odds. If you’d like to teach me to fish, how could I figure it out for any example of odds? (Assuming the math is a few steps below your level . ) Thanks

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So you want to know the odds of one of the top 5 players in a basketball game scoring the first basket?....hmmmm....assuming that they all start the game and there are 10 players total, I say 50%

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Originally Posted by Sharky
So you want to know the odds of one of the top 5 players in a basketball game scoring the first basket?....hmmmm....assuming that they all start the game and there are 10 players total, I say 50%
Also: "If you’d like to teach me to fish, how could I figure it out for any example of odds? (Assuming the math is a few steps below your level . ) Thanks"

Well, it's not exactly 50% just because you have five of the 10 starters, because you may have the best five, the worst five, or the middle five. You can't just say you have half the players, so it's 50%. With the stated odds, you have to calculate that none of the five will win, and then the probability that one of them will win is 100% minus that calculated value. Actually, you have to invoke that concept twice.

So, first you change each of the odds to win to fractions: 2/11, 2/13, 1/7, 1/7, and 2/15. Those are the chances of each winning. So the chances that each of them loses are: 9/11, 11/13, 6/7, 6/7, and 13/15. The chance of all five losing is the product of those fractions: 9/11 x 11/13 x 6/7 x 6/7 x 13/15 = 0.441. So, the probability that one of them wins is 100% - 44.1% = 55.9%.

If you bet \$25 five times (total of \$125), your e.v. is 0.559 x \$125 = \$69.88. In addition, you get four free \$25 bets, or \$100 in free bets. It matters, of course, how you bet that, but if you were to make four straight point-spread bets at -110 each, that e.v. would be an additional 100/210 x \$100 = \$47.62. Together, your total e.v. is \$117.50. Sadly, you're \$7.50 short of your \$125 outlay, so you lose 6%.

Did I teach you how to fish?

Don

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Originally Posted by DSchles
Also: "If you’d like to teach me to fish, how could I figure it out for any example of odds? (Assuming the math is a few steps below your level . ) Thanks"

Well, it's not exactly 50% just because you have five of the 10 starters, because you may have the best five, the worst five, or the middle five. You can't just say you have half the players, so it's 50%. With the stated odds, you have to calculate that none of the five will win, and then the probability that one of them will win is 100% minus that calculated value. Actually, you have to invoke that concept twice.

So, first you change each of the odds to win to fractions: 2/11, 2/13, 1/7, 1/7, and 2/15. Those are the chances of each winning. So the chances that each of them loses are: 9/11, 11/13, 6/7, 6/7, and 13/15. The chance of all five losing is the product of those fractions: 9/11 x 11/13 x 6/7 x 6/7 x 13/15 = 0.441. So, the probability that one of them wins is 100% - 44.1% = 55.9%.

If you bet \$25 five times (total of \$125), your e.v. is 0.559 x \$125 = \$69.88. In addition, you get four free \$25 bets, or \$100 in free bets. It matters, of course, how you bet that, but if you were to make four straight point line bets at -110 each, that e.v. would be an additional 100/210 x \$100 = \$47.62. Together, your total e.v. is \$117.50. Sadly, you're \$7.50 short of your \$125 outlay, so you lose 6%.

Did I teach you how to fish?

Don
Thanks Don..this is exactly the answer I was looking for. And, upon 4th reading, I believe you’ve taught me how to fish . Of course, it’s no surprise that the sports book comes out ahead, even with the bonus offer. Thanks for your time.

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___________

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I did something involving math that I use in betting horses. I used to post about this subject a few years ago and there were a few guys that were interested. I don't know if anybody here now is interested - but anyway -

this is just a few examples - of course I'm aware it's not a proof - but there are so many and they are so easy to find that I believe it's significant - here we go:

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EXACTA OVERLAY

it's been my admittedly unscientific but nonetheless compelling (to me) observation/speculation that exacta payouts on the low odds horses are often very generous

the accepted way to calculate a fair exacta payout after the takeout is considered is this:

(odds on the winning horse) times (odds on the 2nd place finisher + 1)______this will give you a fair payout on a \$1.00 bet after the takeout

throughout racing, in the long run, the favorite or 2nd fave wins about 55% of all races

here is a look at some \$2.00 exacta payouts at Churchill from 11/6

please note that as far as I know all tracks will allow a \$1.00 exacta bet as long as it is a box or wheel - unlike win bets

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Race 2_________2.50/1.40__________fair payout__________12.00__________actual payout_________23.40

Race 4_________2.00/2.30__________fair payout__________13.20__________actual payout_________20.60

Race 10________3.70/2.60__________fair payout__________ 26.64__________actual payout_________37.60

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why does this happen?
because typical horseplayers are longshot lovers
they overbet the shots causing them to get less than a fair payout on them_________and underbet the low odds horses causing them to get more than a fair payout

here are 2 payouts from Churchill where longshots came in the 1st and 2nd positions
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11/6____Race 5__________7.40/14.10___________fair payout___________223.48___________actual payout__________125.00

11/5____Race 8__________21.10/7.70___________fair payout___________367.14___________actual payout__________288.20

actually, horses priced at 7.40 and 7.70 are not true longshots
generally longshots are considered to be horses priced at 10/1 or more

I didn't want to spend a lot of time looking for that - it doesn't happen too often
but in those instances when it does happen - the payouts are usually even worse than shown

of course, when a longshot lover gets a \$288 payout for a \$2.00 bet he's hardly going to care if it's short of what would be fair

but he's never ever going to be a long run winner playing that way

all of this is considering that no handicapping at all is done

if a player is an excellent handicapper than these longshot payouts may be more than fair - meaning that he may see a horse priced at 14/1 as having true odds of 8/1

if he's a poor handicapper - which is often the case - he's really going to get creamed in the long run

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a further observation/speculation on the exacta pools re the big tracks only
I don't trust the little tracks

those that bet NYRA (Belmont, Saratoga and Aqueduct) are sharper than those that bet in the Midwest/South pools - Churchill and Keeneland

although anyone can bet anywhere due to technology - still I believe there are different characters to the different locales

I couldn't find anything this extreme at Belmont - but I could easily find it at Churchill

I believe that NYRA bettors don't fall for the longshot sucker bets anywhere near as much as they do at Churchill and Keeneland

CA (Santa Anita & Del Mar) seems to me to be in between the 2 - but IMHO the NYRA pools are the hardest to beat

I don't consider the Gulfstream bettors to be as sharp as NYRA bettors - but their pools are hard to beat too

Woodbine is also a good track to use this as well as Laurel - Laurel is not a big track and I wasn't going to bet there - but I looked into their payouts and quite a few looked generous

my personal way to play this angle is this:

I won't bet when the fave is odds on - the payouts get depressed - even though they still may seem generous when calculated

I won't play the fave over the 2nd fave - the payouts again get depressed - even though they still may calculate as being generous

I will only bet when the field is 7, 8 or 9 horses

this is just personal preference - I don't like the very small payouts in small fields - and I don't like the increased risk in large fields

for me it's like Goldilox who said "this porridge is too hot and this porridge is too cold but this porridge is just right"___________________________(-:\

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