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Showing posts with label "what are the odds?". Show all posts
Showing posts with label "what are the odds?". Show all posts

Saturday, January 1, 2022

"What are the odds?" I See an "Imagine" John Lennon License Plate in Florida

The current zeitgeist surrounding the The Beatles: Get Back documentary on Disney+ has elicited a question for me - how likely is it for me to see the rare specialty Florida license plate of "Imagine", depicting John Lennon?

Back in 2003 when it was introduced, there were around 50 types of specialty license plates in the state of Florida, per the South Florida Sun-Sentinel. Now there are almost 150 - and the Florida Department of Highway Safety and Motor Vehicles has all of this data public and readily available, including via some nice interactive Tableau dashboards.

As of December 2021, there are 1.9m registered specialty plates out there in the state - and 14k of those are "Imagine", ranking 39th. That's 0.8% - or 1 in 132 specialty plates.


But most cars don't have a specialty plate - there are 16.3m registered autos and pickups in Florida. "Imagine" plates make up 0.086% of this total - or 1 in 1,158.

At $25 in donation per plate, the "Imagine" plate is currently raising $352k per year for Florida Food Banks, and $4.8m all-time through August 2021. All specialty plates combined are raising $46.5m in donations per year! This doesn't include specialty plates currently in pre-sale, including the new plate benefiting Florida State Parks.

The current top 10 are below, with "Helping Sea Turtles Survive" overtaking the #2 spot over University of Florida's plate compared to 2020:


"Endless Summer", supporting Surfing's Evolution & Preservation, is #1, representing 6% of all specialty plates, and 0.7% of all registered Florida autos/pickups.


Disclosure: my household currently has the "Tampa Bay Rays" plate and has pre-ordered the "Florida State Parks" plate, and in the past has had the "Helping Sea Turtles Survive" and "Save the Manatee" plates. The full lists can be found here and here.

Wednesday, November 24, 2021

"What are the odds?" Bar Games Edition

Received two bar games-related questions in the past few days - both fitting "what are the odds?" style probability inquiries.

Yahtzee $5 Dice Roll

First: the game is a dice roll, with the aim to roll 5 dice to get a Yahtzee (all 5 dice match). You get 5 attempts, but unlike Yahtzee, you don't get to keep any matching dice - you have to reset your roll each time. Entry fee is $5, and the winner gets the pot of all entry fees (minimum pot size is $50). What does the pot size have to be for you to want to enter?

What we're looking for is at what point the expected value (E[V]) is positive. The odds of rolling a Yahtzee on one roll is if any one number matches on 5 dice, with 6 possible number matches. Thus (1/6) ^ 5 = 1 / 7776, times 6 = 6 / 7776 = 1 / 1296, or 0.08%. Verified here. Thus the odds of NOT winning on one roll is 1 - 0.08% = 99.92%.

Since there is no rollover, the math is pretty straight forward. The odds you LOSE 5 times is 99.92% ^ 5 = 99.6%. So the odds you WIN is 1 - 99.6% = 0.4%.

Your expected loss is 99.6% * -$5 = -$4.98, so we want to calculate at what point your expected winnings would be more than $4.98, and thus create a breakeven point. This can be calculated by your expected loss / odds you win, so $4.98 / 0.4% = $1,293. This is how large the pot needs to be before you'd be indifferent between lighting $5 on fire and playing the dice game; way higher than the $50 minimum pot size.

Odds You Miss Every Single Trivia Question

Second: the game is bar trivia, with 20 questions with 4 multiple choice answers each. Say you're trying to tank the game and miss every single question (for draft position next round maybe??) and you christmas-tree each question at random. What are the odds you get at least one question correct by accident?

If each guess is truly random, you have a 75% chance of getting a single question wrong. So the odds you get EVERY question wrong are 75% ^ 20 = 0.3%, meaning that it is extremely likely you will get at least one question right, at 1 - 0.3% = 99.7%.

There is actually a better chance you win the dice game than miss every trivia question!

Saturday, May 29, 2021

"What are the odds?" The Chances of a Canadian Team Winning the Stanley Cup Are Helped By 2021's Unique Playoff Structure

This season, due to the ongoing pandemic, the 2021 NHL division alignment's were changed, such that the 7 Canada teams only played eachother, including over the first 2 rounds of the Stanley Cup playoffs. Notably, no Canadian team has won the Cup since 1993 - a 26 season drought. 

This year's playoffs guarantee a team from Canada will make the semifinals - which of course increases the chance of that team making the Finals (something that's only happened 5 times since 1993), and subsequently winning it all. So how does this help (or hurt) the chances of a Canadian team finally winning the Cup again?

I'm looking to isolate the impact of the postseason format, so it's not as simple as proportionally taking the number of Canadian teams over the number of teams in the league each year (for example, when the league added 2 American teams in 1993-93, 8 Canada teams / 26 total teams = 31% Cup pre-playoffs). Since Canada teams have not been evenly spread across divisions (such as none in the Metropolitan), I want to start the analysis with the initial playoff field each year.

Just accounting for the number of Canadian playoff teams, the best chances since '93 have been 1996, 2004, 2015, and 2017, when 5 teams made the playoffs. Proportionally that would be a 31% chance - 5 / 16. Using this methodology, there is only a 0.23% chance that no Canadian team has won in the past 26 playoffs.

This divisional discrepancy affects the playoff matchups too - so I also broke down each round by seeding. The team with home ice and the higher seed is expected to win about 64% of the time, and calculating this across the entire playoffs identifies 2017 as the single best chance for a Canadian victor - 34%  that year. Using this methodology, there is only a 0.47% chance of no Canadian team winning it all since 1993.

As mentioned before, the impact this year comes from the guarantee of a team in the semifinals. So I took this a step further and looked at the odds of having no Canadian teams in the semifinals.

This ranges from 2016, when no Canadian teams made the playoffs, to 2017, when there was an 80% chance of having >= 1 Canadian team in the semis. More than one team can make it that far too, but this doesn't outweigh the fact that in no year is there a 100% chance of 1 team. If every semifinalist has a 25% of winning from there, this only shrinks the odds further (full table below). Using this methodology, there is a 2.06% chance of no Canadian team finishing their run as champions in the past 26 seasons.

SeasonCount CADOdds 0 in SemisOdds >= 1 in SemisOdds Win
1994431%69%17%
1995431%69%17%
1996534%66%17%
1997361%39%10%
1998361%39%10%
1999336%64%16%
2000347%53%13%
2001440%60%15%
2002440%60%15%
2003431%69%17%
2004526%74%19%
2006431%69%17%
2007336%64%16%
2008347%53%13%
2009347%53%13%
2010347%53%13%
2011255%45%11%
2012255%45%11%
2013431%69%17%
2014185%15%4%
2015526%74%19%
20160100%0%0%
2017520%80%20%
2018255%45%11%
2019336%64%16%
2020361%39%10%

Across all three methodologies, there are not many occurrences of Canada having a better than 1 in 4 chance to win it all. Even when considering the outcomes where more than 1 Canada teams reach the semifinals, the downside chance of no Canada team making it that far greatly reduced their odds in any given year. In this context, having at least a 1 in 4 shot at winning the Cup this year represents one of the best opportunities in almost 3 decades.

SeasonCount CADProportion OddsHome/Away OddsHome/Away, Semis-On Odds
1994425%25%17%
1995425%25%17%
1996531%24%17%
1997319%11%10%
1998319%11%10%
1999319%21%16%
2000319%16%13%
2001425%20%15%
2002425%20%15%
2003425%25%17%
2004531%29%19%
2006425%25%17%
2007319%21%16%
2008319%16%13%
2009319%16%13%
2010319%16%13%
2011213%13%11%
2012213%13%11%
2013425%25%17%
201416%4%4%
2015531%29%19%
201600%0%0%
2017531%34%20%
2018213%13%11%
2019319%21%16%
2020319%11%10%