Winning Monopoly With Math!

I’m always on the hunt for tips to make myself a better puzzler and gamer. Sometimes you stumble across those tips in unexpected places.

For instance, I was reading, of all things, a book about mathematics and Christmas — The Indisputable Existence of Santa Claus: The Mathematics of Christmas — and inside, I found a statistical analysis of the best strategy for winning a game of Monopoly.

Yes, we’ve discussed this topic before, but even that previous deep-dive into the mechanics of the game wasn’t as thorough or as revealing as the work by Dr. Hannah Fry and Dr. Thomas Oleron Evans in this Christmas-fueled tome of facts and figures.

They started with a breakdown of how your first turn could go, based on dice rolls. This is the same breakdown as in our previous post, but with some important differences. For instance, they also considered the chances of going to jail after multiple doubles rolls.

Also, they covered the statistical impact of how landing on card spaces can affect where you land on your first turn. The Community Chest is a curveball, because of the possible sixteen cards, three will send you somewhere on the board: Go, Mediterranean Ave, and Jail.

A simple statistical analysis is complicated even further by the Chance cards — nearly half of the sixteen cards send you elsewhere: Go, Income Tax, St. Charles Place, Pennsylvania Railroad, Illinois Ave., Jail, and Boardwalk.

If you extrapolate forward from this point, you uncover some interesting patterns:

The orange property set benefits from all the ex-cons leaving their cells, and after their next turn the reformed criminals will likely end up somewhere between the reds and yellows… Illinois Avenue, with its own dedicated Chance card directing people to it, gets an extra boost, making it the second most visited square on the board.

The property that is visited least frequently is Park Place, where players spend just 2.1% of their time.

Check out this graph. This shows potential earnings from each complete color set, with the dotted line marking the point where your purchase of the property is canceled out by how much the property has earned in rent thus far. Everything above that is profit.

As you can see, blue and brown properties start close to the dotted line, because they’re affordable to buy and build on. The standouts on this graph are New York Avenue (which earns $30 a roll up through thirty rolls statistically) and Boardwalk, which is an expensive investment, but pays off handsomely down the line, remaining the top earning spot past thirty rolls.

Of course, that’s only single properties, and you can’t build on single properties. Let’s look at a chart for full color set revenue:

Some of our previous findings change radically. Boardwalk’s rating drops significantly, because of Park Place’s relative infrequency of being landed on (as we mentioned above).

So which properties should you nab to give yourself the best chance of winning? Well, that depends on how long the game lasts.

The average game of Monopoly takes approximately thirty turns per player, so the larger the number of players, the longer the game will last.

So, for a two-player game, your best bet is to go after the light blue or orange sets, since they’re better in the short term, and the odds are in your favor if the game stays short.

In a three- or four-player game, the orange and red sets are better, because the game is likely to last a while.

And if five or more people are playing, you’re really playing the long game, so the green set becomes your best chance for success.

What about building on those properties? Well, Fry and Evans considered that as well. If you’re playing against multiple opponents and know you’ll be in for a long game, then you definitely want to buy and place houses. But don’t fear if the first house takes a long time to start paying for itself.

As it turns out, your best strategy is to put three houses on your properties as quickly as possible, because the third house is the fastest to recoup on investment. So once the three houses are in place on each property, you can rest for a bit and regenerate your bank before investing further.

And there you have it. Better gaming through mathematics! The only thing better would be, well, playing practically any other game.

Kidding! (But not really.)


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PuzzleNation Blog Looks Back on 2017!

2017 is quickly coming to a close, and as I look back on an eventful year in the world of puzzles and games, I’m incredibly proud of the contributions both PuzzleNation Blog and PuzzleNation made to the puzzle community as a whole.

Over the last year, we explored board games and card games, strategy games and trivia games, dice games and tile games, do-it-yourself puzzlers and pen-and-paper classics. We met game designers, constructors, artists, and creative types of all kinds.

We unraveled math puzzles and tackled the Crossword from Hell. We accepted the challenge of diabolical brain teasers, optical illusions, Internet memes, and more, even pondering our place in the world of puzzles as electronic solvers like Dr. Fill and AlphaGo rise in capability.

We delved into puzzle history with posts about the legacy of female codebreakers in World War II, game dice from centuries ago, theories about Shakespeare’s secret codes, and the long history of cryptography and the NSA. We brought to light valuable examples of puzzles in art, popular culture, famous quotations, and even the natural world as we pondered whether bees are verifiable problem-solvers like crows and octopuses.

We spread the word about numerous worthwhile Kickstarters and Indiegogo campaigns, watching as the puzzle/game renaissance continued to amaze and surprise us with innovative new ways to play and solve. We shared worthy causes like Puzzles for Progress, as well as amazing projects like new escape rooms, dazzling corn mazes, and the ongoing Kubrick’s Game interactive experience.

We cheered the 75th anniversary of the New York Times Crossword, and chronicled the many celebrations that marked the occasion, from guest crossword constructors like Bill Clinton and Lisa Loeb to a puzzle-centric cruise across the Atlantic!

We also mourned as friends and fellow puzzlers passed on. We said goodbye to David Lindsey and Raymond Smullyan, two underappreciated giants of the field. The pun-fueled show @midnight this year, which inspired our monthly hashtag game, also closed up shop, sadly.

We celebrated International TableTop Day, made puzzly bouquets in honor of International Puzzle Day, marveled at the records broken at the Rubik’s Cube World Championship, attended the American Crossword Puzzle Tournament and New York Toy Fair, and dove deep into an ever-expanding litany of puzzle events like the Indie 500, BosWords, Lollapuzzoola 10, and Crosswords LA.

We found puzzly ways to celebrate everything from Pi Day, the Super Bowl, and Star Wars Day to Halloween, Thanksgiving, and Christmas, and we were happy to share so many remarkable puzzly landmark moments with you. We even discovered Puzzle Mountain!

It’s been both a pleasure and a privilege to explore the world of puzzles and games with you, my fellow puzzle lovers and PuzzleNationers. We marked five years of PuzzleNation Blog this year, I recently penned my 800th blog post, and I’m more excited to write for you now than I was when I started.

And honestly, that’s just the blog. PuzzleNation’s good fortune, hard work, and accomplishments in 2017 went well beyond that.

Every month, we delivered quality content for the Penny Dell Crosswords App. From monthly deluxe sets and bonus boxes to Dell Collection sets and holiday bundles, dozens upon dozens of topnotch puzzles wended their way to our loyal and enthusiastic solvers.

And just last month, we launched our newest puzzly endeavor — Daily POP Crosswords — bringing you fresh, up-to-date cluing and relatable themes in world-class puzzles created by some of the industry’s best constructors! (Many of whom you’ve gotten to know in our recent interview series, Meet the Daily POP Crosswords Constructors!)

But whether we’re talking about the Penny Dell Crosswords App or Daily POP Crosswords, I’m proud to say that every single puzzle represents our high standards of quality puzzle content crafted for solvers and PuzzleNationers.

And your response has been fantastic! Daily POP Crosswords is thriving, the blog has over 2200 followers, and with our audience on Facebook, Twitter, Instagram, and other platforms continuing to grow, the enthusiasm of the PuzzleNation readership is both humbling and very encouraging.

2017 was our most ambitious, most exciting, and most creatively fulfilling year to date, and the coming year promises to be even brighter.

Thank you for your support, your interest, and your feedback, PuzzleNationers. The new year looms large, and we look forward to seeing you in 2018!


Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

A Puzzly Holiday Quiz!

It’s Santa’s big day, fellow puzzlers and PuzzleNationers, and we thought we’d celebrate this joyous day of family, friends, giving, and delights with a little Christmas Quiz!

Simply answer the holiday-themed clues below! And, if you come up with the correct answers, you’ll reveal a message reading down, formed by the first letter of every answer!

Here we go!

  • Plant with pleasant results for those under its influence?
  • Santa’s helper OR Will Ferrell film
  • Vixen, for one
  • A treasured BB-gun brand
  • He famously sought a peppermint mine
  • One who wassails OR member of a loud festive mob?
  • Nationally observed day off
  • Donner’s son OR reindeer game outcast
  • There was no room here
  • The Grinch’s creator
  • One of the misfit toys
  • Scrooge’s ghostly partner
  • Four Sunday-period OR type of calendar
  • Hang this with care

Did you crack the clues and figure out the message? We hope so! Have a marvelous day!


Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

PuzzleNation’s 2017 Holiday Puzzly Gift Guide!

Happy Holidays and welcome to the PuzzleNation Blog 2017 Holiday Puzzly Gift Guide!

Each year, we scour the world of puzzles and games for the best, the most engaging, the most creative, and the most enjoyable products we can find, and we think this year’s collection is the best we’ve ever had!

We’ve got three different versions of the Gift Guide for your perusal, each of them absolutely loaded with all sorts of puzzly goodness and designed to make your puzzle and game shopping as easy as possible!

You can view the products in the Gift Guide organized by category, by age group, or randomly in a grab bag format!

So, if you’d like to view products sorted by category (puzzle games, board games, puzzle books, etc.), click the wreath!

If you’d like to view products sorted by age group, click the penguin!

And if you’ve got a puzzle lover on your list and you’re not sure what to get them, you can scroll through a wonderful mixed bag of products by clicking the crossword tree!

A lot of terrific companies and puzzle constructors are taking part in our gift guide this year, and we’re sure you’ll find something for every puzzle lover on your list! Happy browsing and happy puzzling to you and yours!

A Monopoly Game Unlike Any Other

I’m always on the lookout for great puzzly stories, and a friend of mine passed along this link to a puzzly holiday proposal from last year that totally fits the bill.

This story comes from a reddit user named Justinlebon26, who was looking for a meaningful and unique way to propose to his girlfriend Michal.

Check out what he came up with:

That’s right, he designed a Monopoly board all about their relationship. After all, the two of them enjoyed playing Monopoly so much that their handmade board fell apart. And with that, a plan slowly came together.

He designed new property cards to go along with the new spaces on the board. Some were places they’d gone on vacation, others were the streets where they’d grown up. How they met, their first date — all were immortalized on the board.

New Chance and Community Chest cards would follow, with one special addition to the deck.

With a friend’s help constructing the board, our young romantic’s gift was done. (Complete with the secret lurking beneath the Luxury Tax space)

He waited until Christmas day to unveil his gift, and they celebrated with an inaugural game.

So… how did it all turn out?

This is easily the happiest ending to a Monopoly game in history. Kudos to Michal and Justinlebon26, and here’s hoping they have many happy years of gaming ahead of them.


And thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

PuzzleNation 2016 Holiday Puzzly Gift Guide!

Happy Holidays and welcome to the PuzzleNation Blog 2016 Holiday Puzzly Gift Guide!

We’ve got three different versions of the Gift Guide for your perusal, each of them absolutely loaded with all sorts of puzzly goodness and designed to make your puzzle and game shopping as easy as possible!

You can view the products in the Gift Guide organized by category, by age group, or randomly in a grab bag format!

So, if you’d like to view products sorted by category (puzzle games, board games, puzzle books, etc.), click the wreath!

wreath1

If you’d like to view products sorted by age group, click the penguin!

holidaypenguin

And if you’ve got a puzzle lover on your list and you’re not sure what to get them, you can scroll through a wonderful mixed bag of products by clicking the crossword tree!

christmas-crosswords

A lot of terrific companies and puzzle constructors are taking part in our gift guide this year, and we’re sure you’ll find something for every puzzle lover on your list! Happy browsing and happy puzzling to you and yours!