The University of Waterloo put out a press release to tout an extracurricular activity of a statistics professor. He devised a way to game a free prizes giveaway by the Canadian coffee chain Tim Hortons. (More coverage: here, here)
It's a bit weird because statistics is mostly absent from the strategy.
Here's the game. You buy a coffee and you get a chance to play a lucky draw for prizes. The advertised chance of winning a prize is supposedly 10 percent. Since the pandemic, all this happens online. There is a prize given out every 0.1 second.
The article described two methods of gaming this. The first method exploits the following operational detail: if there are no players in any interval, the prize is re-allocated to a future interval picked at random. Thus, as the day wears on, there are more and more intervals in which more than one prizes would be given away. So, the professor chose a time in the wee hours to play, and said he achieved an almost perfect win rate. He played 96 times, winning 94 prizes.
For this method, there were no data collected, so there could't be any statistical analysis. The article cited a one-time result and it's unclear how repeatable this strategy is. The win rate of 98% is based on a single sample. Perhaps the only analytical question is the best time to play. I'm not sure it's possible to game this precisely.
Also, to play 96 times, the professor had to have purchased 96 coffees. So he got 94 coffees paid for. Another amusing tidbit is that as a British guy, he usually drinks tea, not coffee. So he actually purchased 96 coffees that he wouldn't have otherwise... money spent to create an example for his intro stats class. (Actually, he won 67 coffees and 27 donuts. Assuming donuts are more expensive than coffees, the situation was a bit better than I portrayed. That said, in the crazy inflationary world we live in, a cappuccino in NYC now costs over $6 while a donut typically costs less.)
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Then apparently, Tim Hortons changed the game a bit, or other people started to play the game the same way, so the professor had to change his strategy.
The second method has marginally a little bit of statistics in it. The coffee chain started to put up real-time statistics of win rates so at least now he could collect data. He didn't want to break the no scraping rule so he had students manually collect the data. As a result, the dataset has "holes". Nevertheless, the general strategy remains the same as the first one - finding a time interval that has the highest win rate.
It sounded like this was just a simple curve fitting exercise, interpolating between the observed time points. What surprised me was the precision with which he stated his results:
He found that the statistically best time to play Roll Up To Win was 3:16 a.m. ET. When he played his rolls at 3:16 a.m, he had an 80 per cent win rate... The worst time of day? 11:46 a.m. ET
Is this supposed to mean that 3:15 a.m. is not good enough? Does the statistical lesson also include prediction error bars?
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It's also mildly amusing for them to admit that these methods can only win people free coffees - apparently there are bigger prizes, including a free car, but since those prizes are rare, they didn't have enough data to provide any strategy.
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While this is a fun nerdy thing to do, the people involved in the press release seem to have a warped understanding of businesses. They seemed to think Tim Hortons's marketing team would be alarmed by such gaming, and would actively want to thwart them. In reality, the budget for the game had been set, and the number of prizes given out was fixed.
The strategy of playing late in the game late at night meant that the professor would have been winning surplus prizes that no one else claimed during waking hours. Plus, he was winning only free coffees, not the free car. So, I suspect Tim Hortons's staff weren't losing sleep over this.
P.S.[4/10/23] Corrected spelling of the coffee chain's name in a few places.
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