Mathematics & Gambling Episode

(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: And here we are Sadie at the last episode of our season about the math and stats of gambling SW: Time really does fly doesn’t it SH: Yeah it feels like only an hour and a half, especially when you are having fun talking about math and stats, right? SW: (laughs) Uh huh SH: Ok, let’s try that again with more enthusiasm this time. Especially when you are having fun talking about math and stats, right? SW: RIGHT! SH: There we go! And for this final episode let’s start with talking again about what made me want to talk about gambling in the first place SW: A podcast ad? SH: Well that was the specific thing, but this time I mean all of the online gambling ads on podcasts and YouTube and streaming and radio and everywhere else it seems SW: They are definitely hard to avoid, that’s for sure SH: And one of the things that’s always these ads almost always have are offers of bonus money or matched bets or covered loses SW: Oh yeah, like $1500 in bonus bets if your first bet loses or first 10 $100 bets matched SH: Exactly, and then there’s the very quickly recited fine print about those offers SW: Fine print that makes it clear that they are not all they seem? SH: Now why would you think that? SW: No reason SH: Well reason or not, you’re correct. It turns about that the fine print almost always specifies that the bets must be made within a short time period after signing up, that the matches or bonuses are on non-withdrawable site credit that expires over time, and sometime they even require players to place only certain types of bets SW: Eeesh, that is some fine print. But we are here to talk about mathematics and statistics, not skeezy business practices SH: Ah, but we do often stray into discussions of many different quantitative sciences and this time I want to talk about the economics behind these business practices SW: Fair enough, so where should we start SH: How about with what our guide David Taylor, mathematician, Assistant Vice President at SUNY Erie, and author of the book Mathematics of Gambling and Games, an Introduction to Mathematics said about these offers when I spoke with him DT: At the end of the day, you know, the casino, the sports book is going to make money. This is built into pretty much every wager and it's to the sports book, the casino's benefit to get somebody hooked and addicted or just give them an in to say, you know, your first, you know, if you, your first $200 of wagers are risk-free because if you lose, we will give you $500 back in bonus bets. Now, you know, the, the usual restrictions are there, which are not fun is you don't get your money back. You get your money back in terms of virtual money to use on future bets. If you win those, you get your money, but you know, there's a multiple layer here of I'm encouraging you to stick with them. You have to make another wager. And if your wager loses, you don't get your money back to that level. SW: Ok, so what are the economics here SH: Well the obvious part is that it is not like giving people bonus bets actually means that they’re gonna win, no matter how sure the gamblers themselves may be of that SW: Of course, but they will still win some SH: True, but the more important part is when David is talking about getting the gamblers to stick with them and make another wager SW: Ah, and by getting people to continue to use their gambling platform they become more likely to deposit more money which then makes them more likely to keep betting which makes them more likely to deposit more money SH: And so on and so forth. David likened it to that discounted year of Peacock that I signed up for a year ago or so then definitely forgot to cancel before the next year got charged DT: It's easy to say here's $200 because the long-term value of a customer, you know, they've studied this pretty much the same as any sort of subscription service for streaming sites and whatnot is, you know, how much money do you really get? You can't figure it out based on just somebody paying money. And if you want to figure out how long will somebody stay? Now, you know, if I pay $10 a month for a subscription and I'm expected to stay for for 30 months, my value is $300. How much is the average person going to wager at a sports book before they go somewhere else, try a different site? They have studied this information and know how much to give you back so that you have this money to play with. I think the parlays, you know, hey, you can only use this money on parlays. You know, they want you to have fun. They want you to feel invested. If you're doing a parlay with three or three three things you're invested three times and you're probably not likely to win. So it's easy for them. SW: It was probably a bad idea to let economists and psychologists collaborate wasn’t it? SH: I don’t know if we should go that far, but it does seem that people who want to use those tools to lock people into some platforms have definitely had some luck. Though we are at the University of Chicago, which as you may have heard has a rather famous economics department SW: Hahaha, yeah - so we’ve been told . . . SH: Which means that if you want to know more about economics it would probably be quite useful for you to listen to one of our University of Chicago Podcast network shows that focus on that exact topic SW: One that you are about to tell our listeners about? SH: Yep! (ad music starts) If you’re enjoying the discussions we’re having on this program, here’s another University of Chicago podcast network show you should check out. It’s called The Pie. Economists are always talking about The Pie – how it grows and shrinks, how it’s sliced, and who gets the biggest share. Join host Tess Vigeland [VIG-lund] as she talks with leading economists about their cutting-edge research and key events of the day. Hear how the economic pie is at the heart of issues like the aftermath of a global pandemic, jobs, energy policy, gambling, and much more. (ad music ends) SW: I do believe you promised to cover one last area where mathematics and statistics intersects with gambling SH: I did, and that topic is betting systems SW: And these are strategies about how to bet to make sure you win money? SH: That is often the implication, but no strategy can claim that. In fact there is a theorem from game theorist Richard Epstein that makes it rather clear that any and all strategies for fixed probability games of chance will lead, over time, to the same expected value SW: If that is the case, why would people bother SH: There’s a couple of reasons. First, and most obvious, this is about games of chance. So for games of skill like blackjack, as we discussed three episodes ago, there are strategies that can lead to better outcomes provided that you play at tables where you are reasonably able to count cards SW: And the second reason? SH: The phrase over time. SW: Ah, so there are some strategies that could help over the shorter term SH: Help may be too strong a word. More that they offer the chance of winning on the short term provided you know when to stop SW: That is always the trick, isn’t it SH: It is. So, would you like to hear more about one of these systems SW: I definitely would SH: Great, let’s talk about a famous one that has been around since at least 18th C France, the Martingale system DT: So, you think about any even money wager game, whether it's casino, whether it's over or under sports betting, if I bet $5 and I lose, the next time I double my wager and I bet $10, if I win, I've made back enough money to recoup my original. bets my second bet and to win whatever the minimum prize was so i will be five dollars richer and it's going to happen most of the time because you're going not going to lose twice in a row other than 25% of the time SW: Sure, but 25% chance things happen all the time. What do you do then? DT: Well, what happens if you lose that 25%? Well, then you double your bet again. So now instead of betting $10, you're betting $20. You've got 20 plus 10 plus five invested. You're only gonna win 40 at the end. So you're still gonna be up $5. And it seems a very surefire way to win is to just keep doubling, doubling, doubling until you win. In which case you reset, you've made the original minimum bet back you've made a little profit and you can continue SW: Wow, that is so simple and it does seem rather guaranteed to work eventually. It is not like you would keep losing a 50/50 game forever SH: True SW: But I thought you said that over time no system would work over a long period of time SH: That’s not quite right, I said that no system can change the expected value and this system doesn’t either as the chance of win or loss each time is still 50% which means the expected value is zero. But no matter what, the expected value isn’t the reason this system fails anyway DT: Works great other than most casino games have a limit. Most people don't want to wager you know 10 20 30 40 50 times losing and waiting to pay SH: To illustrate this David laid out what would happen if we were playing a coin flip game with an initial bet of a dollar and I was using the martingale system having lost the first 15 tosses DT: 16 times, 2 to the 16 is 65,536. You're betting a lot of money to win a dollar. Now granted, you're getting your money back and it may happen, but if the casino's table limit is $10,000, you've maxed that at some point. I don't think a casino sportsbook is going to let you wager, you know, million dollars on a single bet after you've lost so many wagers just to try to get your original $5 bet SW: Not to mention there isn’t infinite time either SH: No there’s not. So, while theoretically with infinite time and wealth the martingale system would mean you make your money back, but, and I hate to say this, that is way too mathematical a way of thinking to really work in the real world SW: Saying that really hurt you didn’t it SH: It did, so let’s skip right on past it please to the Kelly Criterion SW: Sure sure, I’ll let you repress that but don’t blame me if it surfaces later tonight ok? And what is the Kelly Criterion SH: Well the Kelly Criterion was developed by Bell Labs researcher John Larry Kelly Jr and it’s a formula that takes into account the probability of winning and the win loss ratio to calculate the percentage of your total money that you should be bet in order to maximize the total possible payout overtime DT: It really is probably the most mathematical version of a betting system you have and I think it really made news. probably about 10-15 years ago, especially in sports betting, because it does give you sort of this more economics theory about when it makes sense to make a bet. SH: This tracks very well with the reporting that investors like Warren Buffet and Larry Gross have been reported as using modified versions of the Kelly Criterion in their investment work. But famous proponents or not, just because it maximizes your potential payout overtime, it doesn’t mean that it increases your probability of actually winning anything SW: That is a good point. Now, I have a final question for you Sam. After six episodes of talking about the math and stats of gambling what do you think, will you be heading to a casino or scratching off a ticket any time soon? SH: I mean I could answer, but don’t you think David’s answer would be much more interesting than mine? SW: You know, you are right about that SH: You didn’t have to say it like you were so sure SW: (Laughing) DT: I will play the lottery when it gets large enough, just for fun. I like to put a $20 bill on the slot machine and pay the penny slots, and see the bells and whistles.I think for me, that's more enjoyable sometimes than watching a movie. And sometimes you win money back. Otherwise, I will do a sports bet now and then. But usually it's a version of, hey, this Phillies team has a -300 to win. And it's worth me paying $30 to maybe win 10 because it's almost a surefire thing. SH: And his experience focusing on these topics over the years has given him an important insight DT: Having taught about this, having written a textbook, having talked with a lot of people about this topic is, us as humans don't really have a good sense of probabilities when it involves either long term or small chance rare events. SH: For example, let’s talk about coin flipping one last time DT: You know, if you flip a coin 10 times and it always comes up heads, that that coin must be not fair or something. Well, that's one outcome. The other outcome is that, you know, two to the 10th is, can we do that? 1024, you know, among everybody flipping coins on this planet, every 1024 times, you will flip a coin 10 times and it will come up heads every single time. It is an unlikely rare event, but rare unlikely events to happen. SW: That really is such a hard thing to internalize. I mean I can know logically that there are probably many cases today alone of 10 heads coming up in row, but I have also never seen it happen myself so I also mostly think of it as an impossible thing SH: Me too, and at less than a .1% chance of happening it sort of an impossible thing for a given person, since there probably are not that many people out there who are regularly throwing a coin 10 times in a row and noting down the results. This is why it’s so important to remember that any specific series of 10 heads and tails coming up is just as likely as any other specific series of 10 heads and tails, even if you are much more likely to see a total of 5 heads than 10 SW: Yet I am never going to fully internalize that am I? SH: Probably not, just like I probably won’t either. Which is why it’s imperative to bring the right perspective to gambling if you decide to do it DT: If you find it entertaining and it's something that's not going to make you go broke, then I think as long as it's bringing you joy, it's not causing problems, go for it, have fun. Try to beat the system, casinos want you to. It's really not going to happen very often. If you find something they'll fix it but I mean it is also a place where it's easy to, you know, get into a place where you don't have much money and it is a… You can bet all your money on black and almost half the time you're going to double it but more than half the time you're not going to SH: Now that we are at the end of the season Sadie, I want to thank you so much for taking this journey through the math and stats and gambling with me SW: You are very welcome, it was a pleasure SH: And I also have an announcement that I want to share with you and, most importantly, with our audience. This will be my last show hosting and producing Carry the Two SW: Oh no, that’s really is sad to hear SH: It’s sad to announce, but I’m moving on to a new job and will no longer be able to talk about the real world applications of mathematical and statistical research with you or our audience. Making Carry the Two with you has been a real career highlights and I am so proud of each and every episode we’ve made SW: Me too, and we have made such a wide range of them SH: From Voting and Polling to Quantum Information Science and Symmetry Discovery to Blackjack and Lightspeed Bullet Time. It’s been a wild ride for sure SW: And do we know what this means next for Carry the Two? SH: The specifics haven’t been finalized yet, but the one thing I can promise is that Carry the Two is not going anywhere. Just stay subscribed to our podcast feed or YouTube channel and there will be more episodes before you know it SW: I mean, that’s a relief. It really has been a pleasure working with you, and best of luck with your next steps SH: Thank you so much, goodbye everyone! (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™ (1-800-MY-RESET) to help 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 instagram also at IMSI dot institute! That’s IMSI, spelled I M S I. 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. SH: Isn’t it strange to decussions SW: Decussions (laughing) SH: I’ve had concussions, leave me alone SW: (Laughing) I’m renting a 20 foot uhaul truck. I have a bed and a couch and 3… SH: I was literally putting in my request for movers and needed somewhere to paste that text because I had lost it once already SW: It was parallel parking and you were like, “nailed it” SH: Especially because like I didn’t really know how to finish that SH: Caree… blebleble (tongue noise) SW: (Laughing) I mean agreed but I don’t know if we can say that SH: Vocalizing (shave and a hair cut two bits)