Sports betting related math question

**Old new guy** · 11-10-2021, 01:34 PM

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

**DSchles** · 11-10-2021, 04:09 PM

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

**Old new guy** · 11-10-2021, 04:34 PM

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

**DSchles** · 11-10-2021, 05:02 PM

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.)

**Old new guy** · 11-10-2021, 06:28 PM

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

**Sharky** · 11-10-2021, 07:03 PM

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%

**DSchles** · 11-10-2021, 07:29 PM

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

**Old new guy** · 11-10-2021, 08:15 PM

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.

**Sharky** · 11-11-2021, 07:29 PM

Originally Posted by Old new guy

.... Of course, it’s no surprise that the sports book comes out ahead, even with the bonus offer. Thanks for your time.

That's because Don used the SB odds to calculate "ev"....handicapping is calculating your own ev based on data and comparing that to the SB odd to find value

I do not know exactly what to look at,, ...but a start is to examine each of the 10 players average points per second (as opposed to just points per game where everyone's minutes per game, of course varies)....then also factor in "intangibles" such as player #3 has a 7-4 center who on 5 otf their 10 games this year directed the opening tipoff to my player for an easy 1st basket, etc

**DSchles** · 11-12-2021, 05:50 AM

Originally Posted by DSchles

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%.

In answering another question about a roulette free bet a moment ago, I realized that I made a mistake here in the value of the four free $25 sports bets. I apologize. Unfortunately, this makes the promo worth even less than I said it was. If you make a $100 sports bet and have to lay $110 to win $100, then it means that if you lay $100, you win only 100/110 x $100 = $90.91. Since you win that half of the time (better, of course, if you can handicap better than 50%!), the value of the bet(s) is only $45.45. In essence, before, I multiplied by 100/210, but it should have been 100/220.

So now, the promo is worth $45.45 + $69.88 = $115.33, leaving you short $9.67 on your $125 basketball bets, for a shortfall of 7.74%.

Don

**mike235** · 11-10-2021, 06:25 PM

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.

**DSchles** · 11-11-2021, 09:02 AM

Since you like fields of 7, 8, or 9, harness racing would seem to be ideal for you, since almost all races fit that numerical category. Have you looked at the trotters?

Don

**DSchles** · 11-11-2021, 09:34 AM

Originally Posted by drunk

maybe I'm a wimp but I couldn't stand the way they whip those horses
their whip is very heavy and the driver has a lot of leverage - when it hits the horse it makes a horrible loud cracking sound - it just seems really abusive to me

They don't whip the horse!! They whip the saddle blanket with the horse's number! USTA would never stand for actually whipping the animals. Surprised you don't know that.

Don