tag:theconversation.com,2011:/au/topics/chance-23942/articlesChance – The Conversation2022-05-22T12:35:47Ztag:theconversation.com,2011:article/1827982022-05-22T12:35:47Z2022-05-22T12:35:47ZCOVID is no gamble: physics-inspired simulations predict waves in four countries<figure><img src="https://images.theconversation.com/files/462438/original/file-20220511-15-grrad.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Nejron Photo/Shutterstock</span></span></figcaption></figure><p>As a physicist, I am trained to look for patterns in data. For example, the motion of the tiniest particles may seem random, but it contains patterns and symmetries.</p>
<p>The same can be said of human movements and interactions. Most humans move to and between familiar places (home and work, for instance), and may encounter the same individuals, like colleagues, most days. But, naturally, there are also random interactions in our complex modern world. There’s a good chance that we will bump into random strangers as we go from one place to another. <a href="https://www.frontiersin.org/articles/10.3389/fnhum.2014.00168/full">Human motion</a> consists of both “regular patterns and random variations”.</p>
<p>Being able to track and predict human movements and interactions can be invaluable in studying the spread of infectious diseases. But how does one account for inherent randomness? Some scientists used <a href="https://www.pnas.org/doi/10.1073/pnas.2012326117">cellphone data in Germany</a> to track the effects of human mobility on the spread of COVID-19.</p>
<p>But could there be a simpler approach?</p>
<p>A <a href="https://www.washingtonpost.com/graphics/2020/world/corona-simulator/">March 2020 article</a> in the Washington Post gave my colleagues and I an idea. The article sought to explain to readers how social distancing could slow the spread of the new coronavirus. The writers generated a simulation using dots of different colours that moved in random directions and kept bumping into each other. The “infected” dots (representing people) bumped into “uninfected” ones and passed on the infection. </p>
<p>The Washington Post simulations studied the spread of disease as a contact process – an idea that has been studied in extensive detail <a href="https://projecteuclid.org/journals/annals-of-probability/volume-2/issue-6/Contact-Interactions-on-a-Lattice/10.1214/aop/1176996493.full">mathematically</a>. The dots also reminded us of the random (<a href="https://www.britannica.com/science/Brownian-motion">Brownian</a>) motion of gas atoms and of diffusion – a well studied problem in physics, chemistry and engineering. </p>
<p>Inspired by that article, we looked for a way to find useful patterns in the apparent randomness of human mobility, as a means to study the spread of a highly infectious disease like COVID-19. The exercise started out as an intellectual diversion during lockdown. It has since resulted in <a href="https://www.sciencedirect.com/science/article/pii/S0378437121002867">the publication</a> of three <a href="https://www.sciencedirect.com/science/article/pii/S1755436521000608">peer-reviewed</a> <a href="https://www.sciencedirect.com/science/article/pii/S0960077921011383?dgcid=author">articles</a>. Our models proved to be very accurate when compared with observations. </p>
<p>For the <a href="https://www.sciencedirect.com/science/article/pii/S0960077921011383?dgcid=author">third article</a>, Professor D.P. Mahapatra and I studied the more complicated aspect of predicting multiple infection waves using our Monte Carlo model. The results were compared with reported data from four countries with representative sizes: India (around 1.4 billion people), the US (330 million), South Africa (60 million), and Serbia (7 million). These showed reasonable agreement with the timing of the COVID-19 waves encountered in these different countries. </p>
<h2>A game of chance</h2>
<p>To build our model, we used what is known as a <a href="http://openbooks.library.umass.edu/p132-lab-manual/chapter/introduction-to-mc/">Monte Carlo Simulation</a>, commonly used in physics as well as fields as diverse as engineering and finance. The Monte Carlo method is named after the luxurious gambling destination in Monaco, where – as with any other casino – games of chance are common. </p>
<p>What makes Monte Carlo simulations so appealing is their ability to predict different potential outcomes because they make provision for the presence of random variables or elements. In gambling, for instance, variables could include the player, the dealer, the shuffling of cards and the number of players around a table.</p>
<p>In the case of the spread of disease through contact (or proximity-based) interactions, one random variable is human movement. To account for this in our simulations, we used what is known in probability theory and statistical physics as a “random walk”. This process aims to determine the probable location of any subject that is in a random motion. Each different outcome is a snapshot, a multitude of which is then combined to make up a whole.</p>
<p>Our <a href="https://www.sciencedirect.com/science/article/pii/S0378437121002867%22%22">first paper</a>, published in 2021, studied the impact of mobility restrictions and intervention strategies in curbing the spread of COVID-19. The simulations showed that the rise in the number of infections within a controlled and restricted population followed a <a href="https://www.statisticshowto.com/power-law/">power law</a> instead of the assumed <a href="https://royalsocietypublishing.org/doi/10.1098/rsos.200786">exponential growth</a> used in most <a href="https://idpjournal.biomedcentral.com/articles/10.1186/s40249-020-00718-y">epidemiological modelling.</a> </p>
<p>The power-law scaling showed that the number of infections (or fatalities) within a constrained population increased in a manner such that it was proportional to a (fractional) power of time. One of the interesting takeaways from this paper was that the power-law behaviour for epidemic growth emerged naturally from our simulations. Such power-law growth was observed in <a href="https://www.science.org/doi/10.1126/science.abb4557">early data from China</a> and explained using a modified epidemiological model that incorporated lockdown and other social-distancing scenarios. </p>
<p>This paper was followed by a <a href="https://www.sciencedirect.com/science/article/pii/S1755436521000608">second</a> publication in December 2021, which provided an empirical model to analyse and make accurate predictions for incomplete epidemic growth curves that followed power-law scaling.</p>
<h2>Assessing successive waves</h2>
<p>The extended simulations described in our <a href="https://www.sciencedirect.com/science/article/pii/S0960077921011383?dgcid=author">third paper</a> sought to take into account the impact of mitigation strategies like lockdowns, together with recovery and infection rates, to study multiple waves of infections. By applying our simulations to recorded and estimated infection numbers, we found that our models were very accurate. These simulations suggested a possible fifth wave for South Africa. The results also indicated that further work was required to include a reinfection rate, in the light of new variants such as omicron, which had clearly shown an ability to evade previous immunity. This work also showed that the number of successive waves of COVID-19 infections in any country depends on population density, the intermixing rate, and most importantly the timing and duration of control interventions such as quarantines and lockdowns. Interventions like mask mandates and vaccinations were included under this category.</p>
<h2>COVID is here to stay</h2>
<p>We have continued tweaking our simulation model, particularly with respect to reinfections from new variants. We have now <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4098382">incorporated</a> two essential lessons learned from our simulations: the increased mobility of the most vulnerable members of the population as restrictions are eased; and rising reinfections as recovered individuals are infected by new variants.</p>
<p>These factors also apply to South Africa, where life is returning to <a href="https://www.gov.za/covid-19/about/coronavirus-covid-19-alert-level-1">“normal”</a> for many people. Our latest model predicts a significant fifth wave – which experts have now <a href="https://businesstech.co.za/news/government/583420/south-africa-records-highest-positivity-rate-yet-of-fifth-wave/">confirmed</a>. In our simulations, the numbers for <a href="https://www.worldometers.info/coronavirus/country/south-africa/">South Africa</a> are set to rise rapidly towards the end of May and beginning of June. If unabated, this would lead to a long crescendo, with this fifth wave peaking only towards the end of 2022. That climb and peak, and other possible subsequent waves, will depend on the procedures followed to mitigate it. </p>
<p>Our models and ongoing work bear out the growing consensus that COVID-19 is now globally endemic and here to stay.</p><img src="https://counter.theconversation.com/content/182798/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Smarajit Triambak receives funding from the National Research Foundation, South Africa. </span></em></p>Monte Carlo simulations can predict different potential outcomes because they provide for the presence of random variables or elements.Smarajit Triambak, Professor, University of the Western CapeLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1790822022-03-22T12:16:35Z2022-03-22T12:16:35ZThe ‘hot hand’ is a real basketball phenomenon – but only some players have the ability to go on these basket-making streaks<figure><img src="https://images.theconversation.com/files/453118/original/file-20220318-19-gfjkk4.jpg?ixlib=rb-1.1.0&rect=233%2C0%2C5748%2C3161&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Kevin Durant is one of the NBA players who shows the ability to go on hot streaks.</span> <span class="attribution"><a class="source" href="https://newsroom.ap.org/detail/KnicksNetsBasketball/e57ce0bc5e624b1ea17f1892fd47d63b/photo?Query=kevin%20durant&mediaType=photo&sortBy=&dateRange=now-14d&totalCount=59&currentItemNo=2">AP Photo/Seth Wenig</a></span></figcaption></figure><p>March Madness is here, and basketball fans are making predictions: Who will be the <a href="https://www.ncaa.com/news/basketball-men/article/2021-03-01/11-greatest-march-madness-cinderella-stories">Cinderella story of the college tournament</a>? Which teams will make a run to the Final Four? And of course, which player is going to get “hot” and carry their team to a championship?</p>
<p>To say a player is “hot” or has “hot hands” means the player is on a streak of making many consecutive shots. A question that has dogged researchers, coaches and fans for years is whether players on these streaks can defy random chance, or if hot hands are just an illusion and fit within statistical norms.</p>
<p>We are two researchers who study <a href="https://scholar.google.com/citations?user=mVj8o7gAAAAJ&hl=en">information sciences</a> and <a href="https://kelley.iu.edu/faculty-research/faculty-directory/profile.html?id=WINSTON">operations and decision technologies</a>. In <a href="https://doi.org/10.1371/journal.pone.0261890">our recent study</a>, we examined whether players can indeed get hot in actual live-game situations. Our analysis showed that some players do get consistently “hot” during games and make more shots than expected following two shots made consecutively. However, when we looked at all players together, we found that usually when a player makes more shots than normal after making consecutive shots, they are likely to revert toward the shooting average by missing the next one. Hot hands do exist, but they are rare.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/N3X8qQUXAI0?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">When players get hot, they are a force to be reckoned with on a basketball court.</span></figcaption>
</figure>
<h2>The science of going on a streak</h2>
<p>Fans have always believed in the ability of players to go on a hot streak – as reflected in video games like <a href="https://www.si.com/extra-mustard/2013/11/25/why-on-fire-lives-on-20-years-after-nba-jam">NBA Jam where the virtual ball would catch fire</a> if a player made multiple shots in a row. But academics have been skeptical of the idea ever since a 1985 study concluded that what people perceive as hot hands is nothing more than the <a href="https://doi.org/10.1016/0010-0285(85)90010-6">human brain’s tendency to misunderstand chance and averages.</a></p>
<p>This changed in 2017 when a seminal paper showed that the original study – and the later ones based on it – <a href="https://theconversation.com/momentum-isnt-magic-vindicating-the-hot-hand-with-the-mathematics-of-streaks-74786">suffered from small but significant selection bias</a> that threw off the statistical calculations. Basically, the way the team chose which shots to look at when searching for streaks or a hot hand threw the math itself off. When researchers accounted for this bias, the hot hand turned out to be real. </p>
<p>The vast majority of studies on hot streaks in basketball have focused on <a href="https://doi.org/10.1016/0010-0285(85)90010-6">either free throws</a>, <a href="https://doi.org/10.1016/j.euroecorev.2021.103771">three-point contests</a> or <a href="http://dx.doi.org/10.2139/ssrn.2450479">controlled field experiments</a>. We wanted to test the theory in actual competitive games and used data from the 2013-14 and 2014-15 NBA seasons. But in actual game situations, shots are not identical. To control for this, we <a href="https://doi.org/10.1371/journal.pone.0261890">developed a model that predicts how often a shot will go in</a> based on a number of different factors. These included who the shooter was, the distance from the basket, the type of shot, the distance from the closest defender, who the closest defender was, whether the shot was assisted and other considerations. It is only thanks to the modern, <a href="https://theconversation.com/the-nfl-joins-the-data-revolution-in-sports-64717">data-driven era of sports</a> that we could even do such an analysis.</p>
<p>Using this model, we were able to simulate any shot by flipping a figurative coin that represents the probability any particular shot will go in. We could then quantify the hot hand effect by comparing the real world field goal percentage of a player after they were on a streak with the expected percentage obtained through simulating the same shots in our model.</p>
<p>For example, imagine that in the real world a player made 55% of shots after making the two shots before. But our model only predicted he would hit 46% of shots after making the two shots before. If this difference between the model prediction and the real world is statistically significant over time, then it is <a href="https://doi.org/10.1371/journal.pone.0261890">good evidence that the player can get hot and go on streaks</a>.</p>
<p><iframe id="lgLuM" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/lgLuM/2/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<h2>Who has the hot hand?</h2>
<p>Our analysis looked at 153 players who took at least 1,000 shots during the 2013-14 and 2014-15 NBA seasons. We examined shots taken after two, three and four consecutively made shots.</p>
<p>When looking at the shots from all the qualified players, we found that if a person made the two shots prior, their chance of making the next shot was 1.9% percentage lower than the model predicted – their make rate would regress to the mean. </p>
<p>However, when we looked at players individually, the hot hand emerged for a sizable set of players. Specifically, there were 30 players who exhibited a statistically significant higher field goal percentage on a shot following two makes compared to their expected field goal percentage. Of the players who demonstrated the ability to go on hot streaks, the average hot hand effect led to a 2.71% increase in the chance of making a third shot in a row.</p>
<p>For streaks of three and four consecutively made shots, the hot hand effect was even higher – 4.42% on average and 5.81% on average, respectively.</p>
<h2>Why do some people get hot?</h2>
<p>It’s important to note that having a hot hand does not mean any player can suddenly make baskets from anywhere on the court. For example, Tim Duncan, Roy Hibbert and Marcin Gortat all showed the ability to go on hot streaks, but these are all centers who do not typically take shots far from the basket. Their hot hands increased their shooting percentages of close-range shots. This led us to the hypothesis that part of the hot hand effect may come from what is called the <a href="https://joshkaufman.net/explore-exploit/">explore and exploit approach</a>, which refers to a short period of exploring different approaches to solving a problem followed by a period of exploiting the best approach found. For basketball, this would look like a player finding a mismatch during a game – perhaps a shorter player defending them than normal – and exploiting it by taking more of a certain type of shot. Research has also suggested that the explore and exploit approach is connected to <a href="https://doi.org/10.1038/s41467-021-25477-8">streaks of success in artistic and scientific careers</a>. </p>
<p>While this hypothesis is plausible, it may not be the only factor accounting for hot streaks. Could short-term neuroplasticity – the ability of a player’s brain to quickly adapt to conditions in a game – be a cause? What about focus and mental preparation? Whatever the reason, our study provides strong evidence that supports the existence of hot hands. For coaches and players in the NBA or in this year’s NCAA March Madness, it might be a good strategy to follow the old cliche: “Go with the hot hand.”</p>
<p>[<em>The Conversation’s science, health and technology editors pick their favorite stories.</em> <a href="https://memberservices.theconversation.com/newsletters/?nl=science&source=inline-science-favorite">Weekly on Wednesdays</a>.]</p><img src="https://counter.theconversation.com/content/179082/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A study shows that a select group of NBA players really do go on hot streaks by making more shots in a row than statistics suggest they should.Konstantinos Pelechrinis, Associate Professor of Computing and Information, University of PittsburghWayne Winston, Professor of Decision and Information Systems, Indiana UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1468402020-09-29T19:59:05Z2020-09-29T19:59:05ZCurious Kids: could our entire reality be part of a simulation created by some other beings?<figure><img src="https://images.theconversation.com/files/359745/original/file-20200924-22-pvzq.jpg?ixlib=rb-1.1.0&rect=22%2C367%2C3811%2C5386&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Unsplash</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span></figcaption></figure><blockquote>
<p><strong>Is it possible the whole observable universe is just a thing kept in a container, in a room where there are some other extraterrestrial beings much bigger than us? Kanishk, Year 9</strong></p>
</blockquote>
<p><a href="https://theconversation.com/au/topics/curious-kids-36782"><img src="https://images.theconversation.com/files/291898/original/file-20190911-190031-enlxbk.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=90&fit=crop&dpr=1" width="100%"></a></p>
<p>Hi Kanishk!</p>
<p>I’m going to interpret your question in a slightly different way.</p>
<p>Let’s assume these extraterrestrial beings have a computer on which our universe is being “simulated”. Simulated worlds are pretend worlds – a bit like the worlds on Minecraft or Fortnite, which are both simulations created by us.</p>
<p>If we think about it like this, it also helps to suppose these “beings” are similar to us. They’d have to at least understand us to be able to simulate us.</p>
<p>By narrowing the question down, we’re now asking: is it possible we’re living in a <a href="https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/">computer simulation</a> run by beings like us? University of Oxford professor <a href="https://nickbostrom.com/">Nick Bostrom</a> has thought a lot about this exact question. And he <a href="https://www.youtube.com/watch?v=nnl6nY8YKHs">argues</a> the answer is “yes”.</p>
<p>Not only does Bostrom think it’s possible, he thinks there’s a decent probability it’s true. Bostrom’s theory is known as the Simulation Hypothesis.</p>
<h2>A simulated world that feels real</h2>
<p>I want you to imagine there are many civilisations like ours dotted all around the universe. Also imagine many of these civilisations have developed advanced technology that lets them create computer simulations of a time in their own past (a time before they developed the technology).</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=840&fit=crop&dpr=1 600w, https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=840&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=840&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1056&fit=crop&dpr=1 754w, https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1056&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/359742/original/file-20200924-16-eiyg96.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1056&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Do you think our whole world could be created by someone using more advanced technology than we have today?</span>
<span class="attribution"><span class="source">Yash Raut/Unsplash</span></span>
</figcaption>
</figure>
<p>The people in these simulations are just like us. They are conscious (aware) beings who can touch, taste, move, smell and feel happiness and sadness. However, they have no way of proving they’re in a simulation and no way to “break out”.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/curious-kids-is-time-travel-possible-for-humans-140703">Curious Kids: is time travel possible for humans?</a>
</strong>
</em>
</p>
<hr>
<h2>Hedge your bets</h2>
<p>According to Bostrom, if these simulated people (who are so much like us) don’t realise they’re in a simulation, then it’s possible you and I are too.</p>
<p>Suppose I guess we’re not in a simulation and you guess we are. Who guessed best? </p>
<p>Let’s say there is just one “real” past. But these futuristic beings are also running many simulations of the past — different versions they made up.</p>
<p>They could be running any number of simulations (it doesn’t change the point Bostrom is trying to make) — but let’s go with 200,000. Our guessing-game then is a bit like rolling a die with 200,000 sides. </p>
<p>When I guess we <em>are not</em> simulated, I’m betting the die will be a specific number (let’s make it 2), because there can only be one possible reality in which we’re not simulated. </p>
<p>This means in every other scenario <em>we are</em> simulated, which is what you guessed. That’s like betting the die will roll anything other than 2. So your bet is a far better one.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=401&fit=crop&dpr=1 600w, https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=401&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=401&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=504&fit=crop&dpr=1 754w, https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=504&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/359743/original/file-20200924-20-12zqekv.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=504&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Simulated or not simulated, would you bet on it?</span>
<span class="attribution"><span class="source">Ian Gonzalez/Unsplash</span></span>
</figcaption>
</figure>
<h2>Are we simulated?</h2>
<p>Does that mean we’re simulated? Not quite. </p>
<p>The odds are only against my guess if we are assuming these beings exist and are running simulations.</p>
<p>But, how likely is it there are beings so advanced they can run simulations with people who are “conscious” like us in the first place? Suppose this is very unlikely. Then it would also be unlikely our world is simulated. </p>
<p>Second, how likely is it such beings would run simulations even if they <em>could</em>? Maybe they have no interest in doing this. This, too, would mean it’s unlikely we are simulated. </p>
<h2>Laying out all our options</h2>
<p>Before us, then, are three possibilities:</p>
<ol>
<li><p>there are technologically advanced beings who can (and do) run many simulations of people like us (likely including us)</p></li>
<li><p>there are technologically advanced beings who can run simulations of people like us, but don’t do this for whatever reason</p></li>
<li><p>there are no beings technologically advanced enough to run simulations of people like us.</p></li>
</ol>
<p>But are these really the only options available? The answer seems to be “yes”.</p>
<p>You might disagree by bringing up one of several theories suggesting our universe is not a simulation. For example, what if we’re all here because of the Big Bang (as science suggests), rather than by a simulation? </p>
<p>That’s a good point, but it actually fits within the Simulation Hypothesis, under options 2 and 3 — in which we’re not simulated. It doesn’t go against it. This is why the theory leaves us with only three options, one of which then must be true. </p>
<p>So which is it? Sadly, we don’t have enough evidence to help us decide. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/curious-kids-what-started-the-big-bang-79845">Curious Kids: what started the Big Bang?</a>
</strong>
</em>
</p>
<hr>
<h2>The principle of indifference</h2>
<p>When we’re faced with a set of options and there is not enough evidence to believe one over the others, we should give an equal “credence” to each option. Generally speaking, credence is how likely you believe something to be true based on the evidence available.</p>
<p>Giving equal credence in cases such as the Simulation Hypothesis is an example of what philosophers call the “<a href="https://www.oxfordreference.com/view/10.1093/oi/authority.20110803100001616">principle of indifference</a>”. </p>
<p>Suppose you place a cookie on your desk and leave the room. When you come back, it’s gone. In the room with you were three people, all of which are strangers to you.</p>
<p>You have to start by piecing together what you know. You know someone in the room took the cookie. If you knew person A had been caught stealing cookies in the past, you could guess it was probably them. But on this occasion, you don’t know anything about these people.</p>
<p>Would it be fair to accuse anyone in particular? No. </p>
<h2>Our universe, expanding</h2>
<p>And so it is with the simulation argument. We don’t have enough information to help us select between the three options.</p>
<p>What we do know is if option 1 is true, then we’re very likely to be in a simulation. In options 2 and 3, we’re not. Thus, Bostrom’s argument seems to imply our credence of being simulated is roughly 1 in 3. </p>
<p>To put this into perspective, your credence in getting “heads” when you flip a coin should be 1 in 2. And your credence in winning the <a href="https://phys.org/news/2016-01-mathematician-real-chances-powerball-largest.html">largest lottery in the world</a> should be around 1 in 300,000,000 (if you believe it isn’t rigged). </p>
<p>If that makes you a little nervous, it’s worth remembering we might make discoveries in the future that could change our credences. What that information might be and how we might discover it, however, remains unknown.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/SYAG9dAfy8U?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Famous astrophysicist Neil deGrasse Tyson has said it’s “hard to argue against” Bostrum’s Simulation Hypothesis.</span></figcaption>
</figure><img src="https://counter.theconversation.com/content/146840/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sam Baron receives funding from the Australian Research Council</span></em></p>Philosopher Nick Bostrom’s theory suggests there’s a one-in-three probability we live in a simulation.Sam Baron, Associate professor, Australian Catholic UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1331342020-03-11T15:35:11Z2020-03-11T15:35:11ZRoll up the Rim: How COVID-19 has changed the contest — and maybe your odds of winning<figure><img src="https://images.theconversation.com/files/319162/original/file-20200306-57209-ed48y2.jpg?ixlib=rb-1.1.0&rect=0%2C232%2C5000%2C3061&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">By adding a 'digital roll' to its iconic game, Tim Hortons' Roll up the Rim contest now has some statistical similarities to slot machines.</span> <span class="attribution"><span class="source">(Photo Illustration/The Conversation)</span></span></figcaption></figure><p>Roll up the Rim, Tim Hortons’ iconic seasonal sweepstakes, is back … sort of. Just days before the launch of this year’s contest, the coffee chain took the unprecedented decision to eliminate the use of its regular promotional paper cups because of concerns about COVID-19. </p>
<p><a href="https://uwaterloo.ca/statistics-and-actuarial-science/people-profiles/michael-wallace">As a researcher of health statistics</a>, I agree with <a href="https://www.newswire.ca/news-releases/tim-hortons-r-announces-changes-to-roll-up-the-rim-to-win-r-in-light-of-current-public-health-environment-831161016.html">the company’s statement </a> that it’s not “the right time” for their staff to collect winning rolled-up rims “that have been in people’s mouths during this current public health environment.”</p>
<p>Changes had already been planned for this year’s game, including a digital element, fewer prizes and a more complex game structure. After removing the physical cups, Tim Hortons has scrambled to reconfigure the contest even further.</p>
<p>All these changes mean players this year face a probability puzzle, one that turns the traditional game into a casino-style slot machine.</p>
<p>So how can you be a high roller (or at least win a free coffee)? As a statistician, <a href="https://theconversation.com/mcdonalds-monopoly-a-statistician-explains-the-real-odds-of-winning-106051">I think about these things</a>.</p>
<h2>A familiar contest to Canadians</h2>
<p>For over three decades, Roll up the Rim followed a familiar format: buy a coffee in a promotional paper cup, roll up the cup’s rim and maybe (just maybe) win a prize.</p>
<figure class="align-left ">
<img alt="" src="https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=622&fit=crop&dpr=1 600w, https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=622&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=622&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=782&fit=crop&dpr=1 754w, https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=782&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/319165/original/file-20200306-118966-tu0z7w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=782&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">One of the major changes in Tim Hortons Roll up the Rim contest this year is the chance to have ‘digital rolls’ using the firm’s app.</span>
<span class="attribution"><span class="source">(Tim Hortons)</span></span>
</figcaption>
</figure>
<p>With millions of free coffees and doughnuts available each year — along with a comparatively tiny pool of major prizes, including TVs, cars and cash — players became accustomed to the heavily advertised 1-in-6 chance of winning.</p>
<p>These odds were easy to verify: Tim Hortons produced a pre-specified number of promotional cups, of which a pre-specified number were winners. If there were 60 million cups of which 10 million were winners, then picking a cup at random gave you a 1-in-6 shot at a prize.</p>
<p>Before the COVID-19 outbreak, Tim Hortons planned to use physical cups for only the first half of the four-week contest — part of the company’s plan <a href="https://www.cbc.ca/news/technology/tim-hortons-roll-up-the-rim-1.5468748">to cut down on waste</a>. The company <a href="https://timhortons.sfo2.digitaloceanspaces.com/rutr-rules/FINAL%20-%20RUTR%202020%20Official%20Rules%20and%20Regulations%20EN.pdf">had previously stated</a> that this year, paper cups would come with lower odds: just one out of every nine would be marked as a winner. </p>
<p>Tim Hortons has hastily replaced this element of the game with an at-the-register instant win component. Customers will, with those same 1-in-9 odds, be told at the point of sale if they’ve won a coffee coupon. But buyer beware: those odds are per-transaction, not per-beverage purchased on the same order. Available during the first two weeks of the contest (March 11-24), Tim Hortons estimates this will lead to some $1 million a day in complimentary hot beverages. That $14 million total approximately equals the value of all minor prizes (beverages and baked goods) originally assigned to the physical cup component of the promotion.</p>
<p>So what about the big ticket items? The TVs, cars and cash? For those, you’ll need to play another new element to the game.</p>
<h2>All about the app</h2>
<p>This year’s contest was always about one thing: driving consumers to Tims Rewards, the company’s loyalty app. In addition to the at-the-register component, <a href="https://www.timhortons.ca/roll-up-the-rim-to-win">players with the company’s rewards app also earn “digital rolls.”</a> A standard purchase earns one digital roll, while bringing in a reusable cup earns three digital rolls. (The company <a href="https://www.newswire.ca/news-releases/tim-hortons-r-announces-temporary-approach-to-reusable-cups-858270353.html">has suspended the use of reusable cups</a> also over concerns about COVID-19. Customers will get three digital rolls if they bring in a reusable cup, but the drink will be served in a paper cup.)</p>
<p>These digital rolls will appear to work just like the real thing: tap the screen to “reveal” whether you’ve won. But the reality is subtly — but significantly — different.</p>
<p>First, let’s look at the odds. We already know that for the first two weeks of the contest there is a 1-in-9 chance of getting your hot beverage purchase for free. Your odds have therefore gone down from the 1-in-6 of previous years, but digital rolls offer another chance to win.</p>
<p>Exactly what that chance works out to, however, is harder to compute.</p>
<h2>More players means worse odds</h2>
<p>The digital element of the contest has 8,620,056 instant win prizes, including all the major prizes originally intended for the physical cups. Depending on how players engage with the app, each purchase could generate zero, one or even three digital rolls. The company has stated the digital odds of winning a beverage or food prize “will be better than the 1-in-9 odds at restaurants.” Based on those odds and assuming all digital prizes are eventually awarded, this suggests Tim Hortons expects around 77 million — or fewer — digital rolls to be played.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=360&fit=crop&dpr=1 600w, https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=360&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=360&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=452&fit=crop&dpr=1 754w, https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=452&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/319167/original/file-20200306-57209-lg3z2e.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=452&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">The prizes in the Roll up the Rim contest range from millions of free coffees and doughnuts to electric cars.</span>
<span class="attribution"><span class="source">THE CANADIAN PRESS/Paul Chiasson</span></span>
</figcaption>
</figure>
<p>But the company cannot know for certain how many coffees it will sell or how many players will use the app. In statistics we often make guesses, and when we do it’s essential we understand what might happen if our guesses are wrong.</p>
<p>Here, if sales are lower than expected — or fewer people use the app — there will be fewer digital rolls and better odds for those who do play. But we can use this 1-in-9 guess to estimate your chances of winning at the various stages of the contest.</p>
<p>For the first two weeks, every customer has a 1-in-9 chance of winning instantly at the register. Players with the app additionally receive a digital roll. If this also comes with 1-in-9 odds, then your chances of winning at least one prize are boosted to better than 1-in-5. The environmentally conscious get three digital rolls for bringing in their reusable cups. These four chances to win (three digital, one at the register) give odds of 1-in-2.7 of winning at least one prize.</p>
<p>If the company’s estimate for the digital game is accurate, then players with the app can expect to win more frequently than in previous years. But remember: your odds get worse the more other people play the digital game — and this dependency ties into another key difference with this new way to “roll.”</p>
<h2>A coffee slot machine</h2>
<p>When we think about probability, we usually think about random events like the toss of a coin or the throw of a die. Many random events affected which particular cup you ended up with when playing the contest in previous years: maybe you left the house late, or there was traffic, or the guy in front of you ordered the same thing. Your chance of being given a winning cup was always 1-in-6.</p>
<p>The moment that cup was in your hands, however, your outcome became fixed. The words hidden under the rim — regardless of whether it was the delightful WIN/GAGNEZ UN CAFÉ/COFFEE or the dreaded PLEASE PLAY AGAIN/RÉESSAYEZ S.V.P. — would not change. From your perspective, your chances of winning were still, in a sense, 1 in 6. But in reality your chances of winning were 100 per cent or zero per cent. The action of rolling up the rim did not change that probability, it just revealed which of the two outcomes had occurred. (<a href="https://www.iflscience.com/physics/schr%C3%B6dinger%E2%80%99s-cat-explained/">Schrödinger’s coffee</a>, if you will.)</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1217093763224436736"}"></div></p>
<p>This year, digital rolls are the opposite. These can be played at any time after purchase, and their outcome is not pre-determined. Instead, <a href="https://timhortons.sfo2.digitaloceanspaces.com/crm/rutr/RUTR_2020_Official_Rules_and_Regulations%20_ENG.pdf">under the new rules</a>, each of the 8.6 million digital roll prizes are allocated a “winning timeframe”: a short interval of time at some point during the contest period. If you are the first player to play a digital roll during one of these timeframes, you win the associated prize.</p>
<h2>Time of play now a factor</h2>
<p>This means that, unlike the physical cups of previous years, the outcome of your digital roll is not determined until the moment you choose to play it. Slot machines follow a similar mechanic: hitting the jackpot doesn’t depend on when you last won or if the machine is “due” to pay out. It’s simply about whether you pull the lever at just the right microsecond.</p>
<p>There’s no way to know when to pull a lever on a slot machine and there’s no way to know when to play a digital roll in the Timmies contest.</p>
<p>But with Roll up the Rim, there is one possible way to shift the odds slightly in your favour. We already know that fewer players gives better chances for those that do participate — and it is tempting to speculate about the impact of COVID-19 on this aspect of the game. To do so, however, would be entirely inappropriate and I don’t want to give the impression that something as serious as the coronavirus outbreak should be considered a factor in something as frivolous as a sweepstakes.</p>
<p>Instead, I will make one entirely separate observation.</p>
<p>To win, you have to be the very first person to play a digital roll during a winning time frame. This means that you’re fractionally more likely to win if fewer people are rolling at the same time as you. The contest rules don’t state whether these time frames are distributed evenly throughout the day, but if they are — and you don’t mind being awake at 4 a.m. — then playing when most of Canada is asleep may be your best bet. After all, you’ll probably need the caffeine.</p><img src="https://counter.theconversation.com/content/133134/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Michael Wallace does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>The Tim Hortons coffee chain has made some changes to its iconic Roll up the Rim contest, including the addition of “digital rolls.” A statistician explains how this changes the odds of winning.Michael Wallace, Assistant Professor, Department of Statistics and Actuarial Science, University of WaterlooLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1027632018-09-07T03:14:48Z2018-09-07T03:14:48ZWe’ve crunched the numbers in McDonald’s Monopoly challenge to find your chance of winning<figure><img src="https://images.theconversation.com/files/235181/original/file-20180906-190639-eyf4yk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The code that could see you a winner in McDonald's Monopoly competition.</span> <span class="attribution"><span class="source">Paul McMillan</span></span></figcaption></figure><p>McDonald’s <a href="https://maccasplay.com.au/">Monopoly competition</a> is back this month offering a chance to win expensive prizes, all for the price of a Big Mac. </p>
<p>Given you could become tens of thousands of dollars richer by simply going on a Macca’s run, McDonald’s Monopoly games have in the past been subject to cheating and a <a href="https://www.thedailybeast.com/how-an-ex-cop-rigged-mcdonalds-monopoly-game-and-stole-millions">multimillion-dollar scandal</a>. </p>
<p>But for those who prefer to play fair, what are your chances of actually snaring a prize?</p>
<h2>Prizes, prizes, prizes</h2>
<p>To take part you need to buy certain McDonald’s food items that include peel-off Monopoly tickets. Each ticket has three different possible outcomes: an “Instant win”, a “Chance card” or a “Collect to win”.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/seven-reasons-we-play-lotto-even-though-we-know-we-probably-wont-win-the-jackpot-70044">Seven reasons we play lotto – even though we know we probably won't win the jackpot</a>
</strong>
</em>
</p>
<hr>
<p>Instant prizes are either a McDonald’s food item such as a burger, or a non-food prize such as a movie ticket or a cash gift card, redeemed by entering the 12-digit code on the ticket into a phone app.</p>
<p>A “Chance card” ticket also provides a 12-digit code which, when <a href="https://maccasplay.com.au/#content">entered into an app</a>, provides another opportunity to nab an instant prize or a digital “Collect to win” ticket.</p>
<p>The “Collect to win” tickets are the real meat of the game, and yield the major prizes: sometimes a car or large amounts of money. To win one of these prizes, you need to collect all “Collect to win” tickets of the same colour, as you would playing the traditional Monopoly game. </p>
<p>For obvious reasons, McDonald’s doesn’t tell us much about how these tickets are distributed across Australia. But what it does tell us is the maximum number of prizes that can be awarded for each prize type.</p>
<p>Using some fairly basic number-crunching, we can get a better picture of what our chances are of winning a shiny new car just by purchasing a Big Mac meal.</p>
<h2>What the numbers reveal</h2>
<p>This year, McDonald’s says 136,634,083 tickets will be distributed across the fastfood giant’s restaurants, and <a href="https://maccasplay.com.au/pdf/Terms_and_Conditions_Monopoly_AU_2018.pdf">lists</a> the maximum number of prizes available.</p>
<p>While we have no way of determining whether or not this maximum is reached, we can still get a general idea of our chances of winning a prize by using these values.</p>
<p>McDonald’s says there is a one-in-five chance of winning an instant prize, which could either be a food prize or a non-food prize.</p>
<ul>
<li><p>about 18 million tickets yield instant food prizes, which gives a roughly 13.2% chance of winning</p></li>
<li><p>about 11.8 million tickets yield instant non-food prizes, which gives a roughly 8.7% chance of winning</p></li>
</ul>
<p>Of course, 13.2% plus 8.7% gives a 21.9% chance of winning an instant prize, on average, which roughly agrees with the one-in-five that McDonald’s claims.</p>
<h2>The Gambler’s Fallacy</h2>
<p>It’s important not fall for the <a href="https://www.investopedia.com/terms/g/gamblersfallacy.asp">Gambler’s Fallacy</a> when trying to collect instant win tickets. Collecting five tickets does not mean that one of them will always be an instant win ticket.</p>
<p>McDonald’s simply promises an average rate of an instant win, owing to the fact that about 20% of physical tickets include a prize of some sort. </p>
<p>There are 3,415,852 “Chance” tickets available, so you have roughly a 2.5% chance of getting a “Chance” ticket with your purchase. </p>
<p>McDonald’s says one in five, or 20%, of Chance tickets will result in an instant win. Working the numbers means you have a 0.5% chance of obtaining a Chance ticket that will also get you a prize, so it’s not a strategy you should be banking on. </p>
<h2>The bigger prize tickets</h2>
<p>While we know how many “Instant win” and “Chance” tickets there are, the details around the “Collect to win” part of the McDonald’s Monopoly game are more closely guarded.</p>
<p>Going by previous observations, it seems that for each “Collect to win” ticket colour, all but one of each set will likely by very commonly distributed. The final one, not so common.</p>
<p>In this year’s game there are two prizes available of a year of free fuel by collecting the three red tickets: The Strand, Fleet Street and Trafalgar Square.</p>
<p>So it’s entirely possible that the probability of finding that final red ticket in the set could be as low as 2 in 136 million.</p>
<p>If you are planning on trying to win one of the major “Collect to win” prizes, these are the odds we think you should be expecting, even if you have collected all but one of the tickets needed, based on the number of prizes avaailable:</p>
<h3>1 in 136 million (one prize each)</h3>
<ul>
<li>one year car rental </li>
<li>A$10,000 room makeover voucher</li>
</ul>
<h3>1 in 68 million (two prizes each)</h3>
<ul>
<li>A$5,000 travel gift card </li>
<li>one year of free fuel</li>
<li>car</li>
</ul>
<h3>1 in 45 million (three prizes each)</h3>
<ul>
<li>ultimate gaming package</li>
<li>home theatre</li>
</ul>
<h3>1 in 34 million (four prizes)</h3>
<ul>
<li>BBQ set</li>
</ul>
<h3>1 in 17 million (eight prizes)</h3>
<ul>
<li>A$1,000 shopping voucher </li>
</ul>
<h2>Can you hack the app?</h2>
<p>Given each ticket has a 12-digit code you can enter into the app to see if you’ve won a prize, a cheeky idea might be to enter random codes to see if you can guess a winning number. </p>
<p>There are several reasons why this is a waste of time (not least the fact that you need to present a physical copy of a ticket to collect a prize), but let’s also get some mathematical perspective.</p>
<p>Every ticket code consists of a combination of letters and numbers. There are 9 possible numbers (1-9, ignoring 0 so as not to confuse with the letter O) and 26 possible letters (A-Z, capitals only) that can appear in a ticket code.</p>
<p>This means there are 35 possibilities for each of the 12 alphanumeric characters in a code. So how many possible 12-character codes are there? We can calculate that with:</p>
<blockquote>
<p>= 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35</p>
<p>= 35<sup>12</sup></p>
<p>= 3,379,220,508,056,640,625</p>
</blockquote>
<p>But there are only a maximum of 136,634,083 tickets in the game.</p>
<p>So the probability of entering a random 12-digit code into the app and having it recognised as a valid ticket code is given by:</p>
<blockquote>
<p>= 136,634,083/(35<sup>12</sup>)</p>
<p>= 0.00000000004</p>
</blockquote>
<p>In other words, a 0.000000004% chance that you would have randomly picked a valid ticket code.</p>
<h2>Cracking codes takes time</h2>
<p>A number this small is hard to imagine, so let’s think of it another way. If you wanted to increases your chance of randomly picking a valid ticket code to roughly 4% (still a very slim chance!), you should be prepared to pick about 10<sup>11</sup>, or 100 billion random 12-character codes first.</p>
<p>If we assume that picking, entering and checking a code into the app only took you one second, then entering a hundred billion codes would take you about 3,180 years. The competition ends next month.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/the-quick-brown-fox-can-help-secure-your-passwords-online-31954">The quick brown fox can help secure your passwords online</a>
</strong>
</em>
</p>
<hr>
<p>Incidentally, this is one of the reasons why websites and email services encourage you to choose passwords that are at least eight characters long, with a mixture of numbers, letters and special characters. It takes a long time for people with nefarious intentions to guess your password if it’s as long as a McDonald’s Monopoly ticket code, even if they get a computer to help them.</p>
<p>So what’s the best way to play?</p>
<p>If you remember that McDonald’s Monopoly is much like a regular lottery, you’ll be better off as you can relax and know that there’s next to no chance that you will win a major prize.</p>
<p>The instant win aspect is a nice bonus if you’re already planning on having a meal at McDonald’s, since it’s not all that unlikely that you could end up with some extra fries or a drink.</p><img src="https://counter.theconversation.com/content/102763/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sarah Belet receives funding from the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). </span></em></p><p class="fine-print"><em><span>Jennifer Flegg receives funding from the ARC. </span></em></p>With some big prizes are on offer in the latest competition from the fast food giant, best to see what the numbers say.Sarah Belet, Postgraduate Student, Monash UniversityJennifer Flegg, Senior Lecturer in Applied Mathematics, The University of MelbourneLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/888622017-12-31T14:18:58Z2017-12-31T14:18:58ZTrust Me, I’m an Expert: Risk<p>Ah, the new year. A time for throwing off your shackles, following your bliss, quitting your job and abandoning your family to finally start the artisinal yak-butter-sculpture studio of your dreams. </p>
<p>But big choices come with big risks. In this episode of Trust Me, I’m an Expert, Hassan Vally, an expert in epidemiology from La Trobe University, talks about “<a href="http://www.bmj.com/content/345/bmj.e8223">microlives</a>”, which measure how much your life span is increased or decreased by particular activities.</p>
<p>We all make trade-offs between risk and reward, Vally explains on the podcast and in an <a href="https://theconversation.com/stay-on-the-couch-or-go-for-a-run-theres-an-app-that-can-calculate-the-bigger-risk-86846">article</a> on The Conversation today. Every hour of television on the couch, for example, knocks 15 minutes off your life expectancy, on average. On the other hand, a daily serve of vegetables will increase your life expectancy by a couple of hours, and three coffees will add half an hour to your tally.</p>
<p>Even medical procedures can cost us “microlives”, as detailed in a <a href="https://cdn.theconversation.com/assets_for_articles/2017-12-22-microlife-table.pdf">table</a> Vally put together for us. </p>
<p>“Having a mammogram costs you four hours off your life span, but if that diagnoses a cancer that’s going to save you maybe 20 years on your life. You’ve got to be really careful about understanding the costs and benefits,” Vally says. </p>
<p>Also in this episode, Michelle Lim, a lecturer in clinical psychology at Swinburne University of Technology, discusses one of the biggest risks we face as social animals: loneliness.</p>
<p>Loneliness and isolation seem to be on the rise, but Lim explores the ways we can understand – and overcome – loneliness, without being afraid of it. </p>
<p>And finally, we ask the big question: have you stuck with your cocktail, liquor or tipple of choice over the holiday season? Alex Russell, a wine expert at CQ University, asks why we’re so reluctant step outside our gastronomic comfort zones, and how we can expand our horizons.</p>
<p>As an encounter with “spit-bucket gin” proves, it’s not a totally risk-free endeavour, but Russell says that with awareness and intention we can open up a whole new world of flavour. </p>
<p>Lastly, we wanted to pay a quick tribute to Jesse Cox, a friend and audio producer who recently died from a brain tumour. He was a giant in the podcasting world. He worked on programs like Trace, This Is About and Long Story Short, and helped influence many of the podcasters working in Australia today, including some of us here at The Conversation. </p>
<p>We’ve included in this episode a montage of Jesse’s work that was first broadcast on RN Breakfast <a href="http://www.abc.net.au/radionational/programs/breakfast/remembering-jesse-cox/9281560">here</a>, and check out his incredible back catalogue <a href="http://www.abc.net.au/radionational/jesse-cox/4119240">here</a>. </p>
<hr>
<p><strong>Music in this episode of Trust Me, I’m an Expert</strong></p>
<p>Kindergarten by Unkle Ho, from <a href="https://www.elefanttraks.com/">Elefant Traks</a></p>
<p><a href="http://freemusicarchive.org/music/Podington_Bear/Textural/Gears_Spinning">Gears Spinning</a> by Podington Bear</p>
<p><a href="http://freemusicarchive.org/music/Cletus_Got_Shot/none_given_1243/Cletus_Got_Shot_-_Working_Songs_for_the_Drinking_Class_-_05_Pour_Me_Another">Pour Me Another</a> by Cletus Got Shot: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Stompin_Riffraffs/Live_On_WFMUs_Fools_Paradise_with_Rex_11-10-12/StompinRiffRaffs_-_08_-_Wine_Wine_Wine">Wine Wine Wine</a> by Stompin Riff Raffs: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Ergo_Phizmiz/Timperley_Rhapsodies_Music_for_Frank_Sidebottom/08_Smells_Like_Timperley_Spirit_For_Robin_1629">Smells like Timperley Spirit</a> by Ergo Phizmiz: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Guitar_Lightnin_Lee_and_His_Thunder_Band/Live_at_WFMU_on_Burn_It_Down_with_Nate_K_11152015/Crawfish_And_Beer">Crawfish and Beer</a> by Guitar Lightnin Lee and His Thunder Band: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Waylon_Thornton/Rat_Brew/10_Muscadine_Wine">Muscadine Wine</a> by Waylon Thornton: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/The_Blue_Onesies/Jim_Rogers_Party_Shack_EP/03_The_Blue_Onesies_-_Glass_of_Wine_1464">Glass of Wine</a> by The Blue Onesies: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Dazie_Mae/Velvet_Dress__Stockings/01_-_Drink_Beer_Till_The_Day_That_I_Die">Drink Beer (Till The Day That I Die)</a> by Dazie Mae: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Lee_Rosevere/The_Big_Loop_-_FML_original_podcast_score/Lee_Rosevere_-_The_Big_Loop_-_FML_original_podcast_score_-_02_Easy_Life">Easy Life</a> by Lee Rosevere: Free music archive</p>
<p><a href="http://freemusicarchive.org/music/Podington_Bear/Soul/Blue_Highway">Blue Highway</a> by Podington Bear: Free music archive</p>
<p><a href="https://www.bensound.com/royalty-free-music/track/ofelias-dream">Ofelia’s dream</a>: Bensound</p>
<p><strong>Additional sound</strong></p>
<p><a href="https://www.youtube.com/watch?v=3OG6itojBiI">WH.GOV</a></p>
<p><a href="https://www.youtube.com/watch?v=s7L2PVdrb_8">Game of Thrones</a> theme music</p>
<p><a href="https://www.youtube.com/watch?v=2I91DJZKRxs">Jaws</a> theme music</p>
<p><a href="https://freesound.org/people/albertofrog/sounds/328633/">Pouring Whiskey</a>, Albertofrog: freesound.org</p>
<p><a href="https://freesound.org/people/JohnsonBrandEditing/sounds/243373/">Small crowd pre-concert talking party bar walla talking</a>, JohnsonBrandEditing: freesound.org</p>
<p><a href="https://freesound.org/people/megashroom/sounds/390335/">Pouring beer into short glass</a>, megashroom: freesound.org</p>
<p><a href="https://freesound.org/people/ultradust/sounds/166923/">Champagne cork pop and pour</a>, ultradust: freesound.org</p>
<p><a href="https://www.youtube.com/watch?v=-Gq5JZNMgIs">New Years Eve Sydney</a>, MrRobAU: YouTube</p><img src="https://counter.theconversation.com/content/88862/count.gif" alt="The Conversation" width="1" height="1" />
This month, we're talking risk. Three experts give their perspective on how long you might live, how to deal with loneliness – and how to step outside your comfort zone.Madeleine De Gabriele, Deputy Editor: Energy + EnvironmentLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/531032016-01-13T18:35:42Z2016-01-13T18:35:42ZAre Powerball drawings and ‘Quick Pick’ numbers really random?<p>The math behind all the discussion of tonight’s Powerball drawing assumes true randomness – equal likelihood for each number to be chosen, both in the drawing itself and, crucially, in the process of assigning “Quick Picks” to ticket buyers who don’t wish to choose their own numbers.</p>
<p>Are those assumptions reasonable?</p>
<p>Imagine a bag filled with 10 red marbles and 20 blue marbles. Close your eyes, reach into the bag and pull out a marble. You might call your selection random, but more importantly, the choice of red or blue is not equally likely. </p>
<p>In the Powerball drawing, winning numbers are selected from two clear containers: one container has 69 white colored balls with each ball numbered in black ink with an integer from 1 to 69. The other container contains 26 red balls with each ball numbered in black ink with an integer from 1 to 26. </p>
<p>The balls are dropped into the respective containers and then mixed in the container by what appears to be air injected from the bottom of the container. The air is then turned off and a ball is raised from the bottom via a platform and then removed from the container. This procedure is repeated for the selection of each ball (five white and one red, the “Powerball”). Generally speaking, it seems reasonable that each ball is equally likely to be selected by this process.</p>
<p>It is possible – though it’s a stretch – that balls with printed numbers requiring more ink to delineate the number on the ball may weigh more due to the extra ink than balls requiring less ink. Coupled with gravity, this may be enough to keep those balls lower in the container and thus more likely to be picked by the platform. In short, the ball marked 68 may be more likely to be picked than the ball marked 1.</p>
<p>Luckily, this is a testable assumption. Studying the results from previous drawings would allow an assessment of whether each number is occurring with similar frequency. Without doing the statistical calculation and data collection, given the nature of this device for generating balls/numbers, it’s safe to assume that this process generates each number with equal probability.</p>
<p>Evaluating the “Quick Pick” numbers is more challenging. Without a machine to generate numbers with plastic balls, lottery machines nationwide have been generating numbers for ticket buyers in ways that may not give each number exactly equal chances of being chosen.</p>
<p>The potential problems come from the fact that computers are devices programmed by humans and so, almost paradoxically, they must be given a systematic method to choose random numbers. In computer programming terminology, this is often called generating a “pseudo random” number. </p>
<p>In this process, the computer may use some information, such as the computer’s real time clock with precision to a millisecond, at the time that a request for a lottery ticket was made, to trigger a process that draws five numbers and one powerball number. This beginning number is often called the “seed.” Other seeds may be created from different phenomena that presumably occur without reason or predictability. From those seeds, additional calculations generate numbers at rates that approximate randomness.</p>
<p>The randomness of these machines’ results can also be tested, but with more difficulty: it involves either buying large numbers of “Quick Pick” tickets or collecting ticket information from a large number of people. Analyzing the frequencies of the numbers that were generated would reveal the degree of randomness of the Quick Pick process.</p>
<p>Without these data, it can be illuminating to look at the number of Powerball tickets sold and the percentage of the 292,201,338 possible combinations that are covered by those tickets. These data strongly suggest that the Powerball computers are generating combinations with equal probability and thus at random.</p>
<p>In conclusion, it appears we have both mechanisms operating randomly and are free to compute the odds of winning, probability that there’s at least one winner, and, most importantly, our expected profits.</p><img src="https://counter.theconversation.com/content/53103/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jeffrey Miecznikowski does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>The math behind all the probabilities being discussed for tonight’s Powerball drawing assumes each number is equally likely to be chosen. Is that what really happens?Jeffrey Miecznikowski, Associate Professor, Department of Biostatistics, University at BuffaloLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/530892016-01-13T15:42:54Z2016-01-13T15:42:54ZHas winning the lottery jackpot become too difficult?<p>The UK’s National Lottery recently <a href="https://theconversation.com/jackpot-why-longer-odds-will-never-put-us-off-the-national-lottery-49032">added more balls</a> to its Lotto machines, meaning that the chances of winning the jackpot are smaller. Has this ruined the fun? Do the lower odds mean that the vast majority of weeks are likely to go by without a big winner, just as we recently saw with <a href="http://www.bbc.co.uk/news/magazine-35250885">14 consecutive rollovers</a>?</p>
<p>Working out your chance of winning the Lotto jackpot is not difficult. Let’s start with the old rules. You need to match all of the first six balls drawn out of the machine. There are 49 numbers to choose from, and you have six of these on your ticket. Therefore, when the first ball is drawn, you have a six in 49 chance that it matches one of yours. Cross that one off.</p>
<p>There are now 48 balls left in the machine, and five numbers on your ticket. So when the second ball rattles to the bottom of the chute, there is a five in 48 chance that it matches one of yours. If you match the first two then, for the third ball, you have a four in 47 chance; for the fourth, three in 46; for the fifth, two in 45; and if you match all of the first five, then the final ball has a one in 44 chance of matching the last number left on your ticket.</p>
<h2>Crunching the numbers</h2>
<p>Multiply 6/49 by 5/48 by 4/47 by 3/46 by 2/45 by 1/44 and we have our answer: the chance of winning the jackpot with a single ticket under the old rules was 0.000000071511, or almost exactly one in 14m.</p>
<p>Under the new rules not much has changed, there are just 59 balls instead of 49. We can do the same calculation but replace 49 with 59, 48 with 58, and so on. This tells us that the probability of winning the jackpot under the new rules is 0.000000022194, or about one in 45m.</p>
<p>Clearly one in 45m is much less likely than one in 14m. But these probabilities are so small that it’s hard to get a feel for what they mean. Perhaps it’s easier to imagine how long it would take before you can reasonably expect to win, if you enter one ticket each draw: with two draws a week, under the old system you’d have to wait 134,000 years. Under the new system it’s 432,000 years. Quite a while, either way.</p>
<p>Alternatively, we can ask which is bigger: the probability of winning the Lotto jackpot on a single ticket, or the chance of dying this year by being struck by lightning? It turns out that, under the old rules, the two are pretty similar. Under the new rules, you’re about as likely to win the Lotto as you are to die by lightning strike just in July this year.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/108032/original/image-20160113-10419-4d61yx.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">It could be you, but almost certainly not.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<p>So will we see multiple rollovers on a regular basis? We are told that 32m people regularly play the National Lottery. What we don’t know is how many tickets for the main Lotto draw are sold each week, but let’s assume it’s somewhere around 15m.</p>
<p>If everyone used the “lucky dip” function to choose their numbers randomly, that would mean the chances of a rollover on any given draw are about seven in ten. So we can expect to see a jackpot winner about once in every three draws. The chance of seven rollovers in a row is then about 10%, and the chance of 14 rollovers in a row –- which is what caused the <a href="http://www.theguardian.com/uk-news/2016/jan/08/lotto-players-buy-tickets-record-jackpot-early">massive jackpot</a> on January 9 –- is about 1%, a once-a-year event.</p>
<p>What we can say, then, is that 14-time rollovers will not become the norm under the new system, though they will happen once a year or so. Under the old system we would have been waiting a thousand years for a similar event. And that is the point of the changes. More rollovers mean bigger prizes, and bigger prizes mean more publicity and more sales.</p>
<h2>Still worth it?</h2>
<p>So should you stop playing the Lotto in protest that winning the jackpot has become much harder? From a mathematics point of view, if you are only in it to win it, the best advice has always been not to play at all, even before the rule changes.</p>
<p>If you do play, you’re best off trying to pick numbers that are less likely to be chosen by someone else because this increases your chances of winning the whole jackpot, rather than sharing it. This means you should choose high numbers (above 31 because lots of people use birthdays) and avoid patterns like picking one number from each row. And play only when there are rollovers to maximise your expected returns.</p>
<p>On the other hand, if you find it fun to have a flutter, or if you are happy that a chunk of your money will go to good causes, then don’t let the maths stop you. Just bear in mind that you won’t win the jackpot. I can guarantee it. Well, almost.</p><img src="https://counter.theconversation.com/content/53089/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Matt Roberts does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A mathematician looks at the odds.Matt Roberts, Prize fellow and EPSRC research fellow in probability, University of BathLicensed as Creative Commons – attribution, no derivatives.