Mathematics & Gambling Episode 3: Yet More Sports Betting

(Intro Music Starts) SH: Hello everyone, I’m Sam Hansen SW: And I’m Sadie Witkowski. SH: And you are listening to Carry the Two, a podcast from the Institute for Mathematical and Statistical Innovation aka IMSI. SW: This is the podcast where Sam and I talk about the real world applications of mathematical and statistical research. (Intro music ends) SH: Welcome Back Sadie, ready for… SW: (Interrupting and shouting) Yeeeeeessssss! SH: (Sputtering) Huh, what are you cheering about? SW: I put down $100 bet that you would say welcome back at 3 to 1 odds. You just won me $300! SH: Just a second, you found a bookie that was willing to do a prop bet on how I’d begin an episode? SW: You don’t know about pod book? SH: Nope, and in fact I will hear nothing more about it SW: Me and my $300 are fine with that. Though I do have one question, what is a prop bet? SH: Wait,, just… You managed to place one and yet don’t know what it is? SW: Well I just thought I was placing a bet, what makes it a prop bet? SH: So props, or proposition bets to give them their full legal name, are bets on one off occurrences during an event or game instead of on the outcome. For example some of the prop bets that were on offer for the recent super bowl had to do with the length of the national anthem, which player would score first, which song Bad Bunny (SW vocalizing in the backgroun) would play first, and the one our guide to the world of gambling and mathematics Assistant Vice President at SUNY Erie, mathematician, and author of the book Mathematics of Gambling and Games, an Introduction to Mathematics David Taylor spoke to me about DT: You know, what color gatorade will there be? SW: Ah, or how the commentators greet each other… SH: Exactly SW: I mean sure these are things that happen so I guess you can bet on them, but sports books really like being able to put reasonable odds on their bets so they can cover the payouts. How can they do that with these prop bets DT: But in terms of what the casinos are offering for their payouts, some of these are based in the sort of old school horse racing method of if somebody is betting a lot on a particular color then you probably want to make that harder for somebody to win so that less people bet on it and pick the other colors. So that's a balancing act. You can change those odds in real time so that I'm paying, you know, I'm paying $16 to win $10 and you're paying $22 on the same bets because you did it later and blue seems to be a popular color. SW: Oh, and by making the next people who place the bet wager even more to win the same amount, the sports books and casinos then incentivize more people to pick green because it offers a better payout SH: And then if green starts to have too many bets that they are worried about paying out if it is the gatorade color they would then do the same thing with red and so on SW: So I think I get the sports book side, but what about the gamblers? With the games I get how how they could build up information sources that can help them win, but these prop bets seem less skill and more chance SH: I don’t disagree, and I’m thinking David wouldn’t either given what he said about the gatorade prop bet DT: The only advantage you might have there is knowledge about what colors are possible. SH: And he definitely does not see props as a way to make money DT: The rise of these are it's easy and a lot of these sports apps where you can place a $1 wager or a $5 wager to say if it's worth $5 for the excitement of watching the game and anticipating what color is that Gatorade going to be. Is it going to be neon yellow? Is it going to be blue? Is it going to be clear or white? Yeah, they're there for fun. SH: This isn’t to say that people may never have an informational advantage SW: Really, in what way? SH: Well, at least in the case of the specific prop bet David talked with me, were talking potential insider knowledge DT: There was a wager on who would perform at the halftime for Super Bowl in February. I don’t think…I can't remember up to tell me who got selected, SW: BAD BUNNY! [starts humming DTmF] SH: I know and I have no doubt that he is well aware now and probably bopping along to Nueva Yol like the rest of us. But remember we recorded this weeks before the super bowl was played. Thankfully I did remember and was able to let him know while we were chatting DT: So I don't think they were in the top five in terms of here are the predictions. I think, you know, Taylor Swift was up there. Other people were up there. Yeah, that's where you get into probably concerns of people who have inside knowledge betting, and why there are a lot of disclaimers about some of these things too. SW: Yes, always good to remind people that not only is betting on things with insider knowledge unethical it is also potentially illegal, depending on how the knowledge was obtained and the laws of the jurisdiction you are in SH: Exactly, so no matter how tempting it may be if you are friends with a big time event producer and they let slip who the next halftime performer is going to be you probably shouldn’t place any wagers. And you definitely shouldn’t throw specific pitches, even when it doesn’t impact the game, like a couple of major league pitchers have been charged with doing SW: Definitely not, though I do think it is probably ok to let slip to your event producer friend that you know a great math and stats podcast that would love to open for Radiolab on their next tour SH: Yes, that! Definitely do that! Though I am betting the odds of that happening are even lower than those offered by the final style of sports betting I want to tell you about SW: Hahaha, go on SH: But first, as I am sure everyone would bet that I am about to say, let’s hear about another great podcast from the University of Chicago podcast network (ad music) Have you ever wondered who you are but didn't know who to ask? Well, then join Professor Eric Oliver as he poses the nine most essential questions for knowing yourself to some of humanity's wisest and most interesting people. Nine Questions with Eric Oliver, part of the University of Chicago Podcast Network. (ad music ends) SW: Only one last type of sports betting to share? SH: I know, but it’s a big one SW: Oooooh, bigger than spreads and money lines? SH: Yes, though not in the sense that they are more important than those types of betting. Instead in like, they are literally bigger bets. SW: Gotcha, so like big money bets SH: Mmm, not quite. More like voluminous SW: Ok, enough with the riddles how about you just tell me what this betting style is SH: Spoil sport, but fine. I am talking about parlays SW: Hmm, that is definitely a word I’ve heard on some of the gambling ads, but I honestly think of Pirates of the Carribean and have no idea what they are SH: Well sadly Captain Jack isn’t involved but, I guarantee you have heard of them on those ads because sports books love when people bet parlays. SW: Why is that? SH: Well, parlays are effectively a way to combine a bunch of bets all together into one single bet which pays off only when you get all of those bets correct. David used a racetrack example when he was explaining them to me DT: You can bet on a horse to win. You can bet on a single horse to win, plays or show, and all these things, but the horse tracks, the equivalent of a parlay, is the trifecta or the exacta, where you're trying to say, "I'm not only going to tell you which horses are going to win, I'm going to tell you the top three horses and pick the correct order." SW: That sounds super hard to do SH: It is, and so are winning parlays DT: The mathematician looking at this is saying, I can feel confident that if I do three baseball wagers that, you know, two of them might pay off and I'll be fine. But I don't feel confident enough to say that I'm going to pick these three and all three are going to win. They pay off much better, but also you're much higher risk at, you know, losing them. SW: What does he mean they pay off much better? SH: Well, let’s use the simple game of flipping a coin SW: Ok so the odds for choosing right are 50/50 SH: Which if we were going to talk about ½ probability in moneyline terms would be -100. So you were to wager $100 and you would win $100 for a total payout of $200 (not counting whatever the sports book fees are). Then for a parlay you would be betting on picking the right outcome three times in a row SW: And I know the probability of that would be ½ * ½ *½ or ⅛ or 12.5% SH: Which translates to +700 in moneyline terms. Which means a $100 bet would get a $700 return, and a $800 total payout. So like the bet on ½ chance leads to a 2*$100 or $200 payout. The bet on a ⅛ chance leads to a 8*$100 or $800 payout SW: Oh, so you essentially multiple the probability of getting each throw right together? SH: Precisely, and for sports betting parlays you do the same thing DT: So think your three favorite weekend Sunday NFL games, parlay them together, and you have a roughly one in eight chance of calling all three of them correctly, assuming that your information is not much better. than what you did when you placed the major. You know, it's exciting when it pays off. It pays off roughly eight times what you would have won. SW: But, with the assumption of a coin flip probability of choosing the winner correctly that also means that 7 out of 8 times you lose the bet. Which would not have been true if the bettor had wagered on each game individually SH: Ding, ding, ding. So let’s look at all 8 possibilities that a gambler who had $300 to bet on three +100 games would be if they either bet on them individually or spent $300 on a three game parlay instead SW: Well the parlay is easy the gambler would walk away with Nothing 7 times for every time they walked away with $2100 in winnings or $2400 total SH: The individual bets are a bit harder to calculate. There is one case where the gambler walks away with nothing, where all three bets are wrong, 3 cases where only one bet is right and they walk away with $200, another three where two bets are right and they leave with $400, and if all three bets are right they walk out with $600 SW: I mean I get why people would be tempted on the parlay, $2400 is a lot more than $600 if all three bets are correct, but nothing at all is also less than $200 SH: Or $400 or $600, one of which would occur 7 out of 8 times the gambler played at 50/50 odds SW: So just like props do it for fun only? SH: That seems like a good idea, oh and of course never bet what you can’t afford to lose SW: Oh, of course. That is always good advice SH: Though you mentioning prop bets reminds me of something else David told me about DT: What modern sports betting has done with websites has really made it easy to make a parlay out of anything. You know, traditional parlay would have been, pick your games, cover the spread and that's pretty simple. But now you can go anywhere, you can parlay, you know, who's gonna get the next touchdown in this game? What's gonna happen with the first pitch in the baseball game in the next hour? And then who's going to win the presidency in 2028? SW: Ooof, prop bet parlays? SH: Yeah, and that silliness is just one of the methods that the online betting and casino apps have used to get people playing. In the next, and final episode, of this season we will dig into the economics behind a more subtle and deceptive method, as well as discuss the mathematics behind why one of the more well known gamblings systems may work on paper but not in the real world SW: Mmm, I can’t wait (outro music) SH: If you or someone you know is struggling with a gambling problem, help is available. The National Council on Problem Gambling provides a range of resources, including the National Problem Gambling Helpline™ which is at (1-800-MY-RESET) and helps connect you with local resources. SH: Don’t forget to check out our show notes in the podcast description for more about David’s work and a link to his book SW: And if you like the show, give us a review on apple podcast or spotify or wherever you listen. By rating and reviewing the show, you really help us spread the word about Carry the Two so that other listeners can discover us. SH: And for more on the math research being shared at IMSI, be sure to check us out online at our homepage: IMSI dot institute. We’re also on Bluesky and on instagram both at IMSI dot institute! That’s IMSI, spelled I M S I. SW: And do you have a burning math question? Maybe you have an idea for a story on how mathematics and statistics connect with the world around us. Send us an email with your idea! SH: You can send your feedback, ideas, and more to sam AT IMSI dot institute. That’s S A M at I M S I dot institute. SW: We’d also like to thank Blue Dot Sessions for the music we use in Carry the Two. SH: Lastly, Carry the Two is made possible by the Institute for Mathematical and Statistical Innovation, located on the gorgeous campus of the University of Chicago. We are supported by the US National Science Foundation and the University of Chicago. SW: My friend calls him my big son Shohei Ohtani, and I’m like he does give big boy energy (laughs) SH: Yeah, he really does SH: Don’t bet on pod book. Stupid pod book SW: (Laughing) Don’t bet on pod book SH: Have you ever wondered who you…What? SW: Laughs SH: Money li..Money lime, money lime SW: Money lemon, money lime SH: Vocalizes (Shave and a haircut)