The Mathematics of Winning Monopoly
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- čas přidán 7. 12. 2016
- I talk to Hannah Fry and compare our mathematical investigations into playing Monopoly. I’ve put all my probabilities below.
You can buy a signed copy of Hannah's book on Maths Gear:
mathsgear.co.uk/collections/b...
In the UK you can also get it from Waterstones:
www.waterstones.com/book/the-...
There is a Kindle edition on Amazon:
www.amazon.com/Indisputable-E...
You can download all of my monopoly code here:
www.dropbox.com/s/f5xndyafuj2...
Here are Hannah’s plots:
www.dropbox.com/s/sme0ezqsb69...
CORRECTIONS:
- I said the game has “finite money” but Chuck Monster has correctly pointed out that the official Monopoly rules state "It [the bank] never runs out of money; if it runs out of bills, players can use any convenient items as substitutes until the bank gets enough money."
Support my videos on Patreon:
/ standupmaths
Filming by Trunkman Productions
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/
BEHOLD MY NUMBERS!
From 100,000,000 rolls.
00 2.854% - GO
01 2.109% - Old Kent Road/Mediterranean Avenue
02 1.919% - COMMUNITY CHEST
03 2.261% - Whitechapel Road/Baltic Avenue
04 2.404% - Income Tax
05 2.757% - Kings Cross Station/Reading RR
06 2.317% - The Angel Islington/Oriental Avenue
07 1.017% - CHANCE
08 2.308% - Euston Road/Vermont Avenue
09 2.278% - Pentonville Road/Connecticut Avenue
10 6.325% - JAIL
11 2.719% - Pall Mall/St. Charles Place
12 2.61% - Electric Company
13 2.395% - Whitehall/States Avenue
14 2.477% - Northumberland Avenue/Virginia Avenue
15 2.804% - Marylebone Station/Pennsylvania RR
16 2.8% - Bow Street/St. James Place
17 2.62% - COMMUNITY CHEST
18 2.94% - Marlborough Street/Tennessee Avenue
19 3.096% - Vine Street/New York Avenue
20 2.868% - Free Parking
21 2.839% - The Strand/Kentucky Avenue
22 1.212% - CHANCE
23 2.731% - Fleet Street/Indiana Avenue
24 3.197% - Trafalgar Square/Illinois Avenue
25 2.897% - Fenchurch St Station/B&O RR
26 2.719% - Leicester Square/Atlantic Avenue
27 2.689% - Coventry Street/Ventnor Avenue
28 2.821% - Water Works
29 2.601% - Piccadilly/Marvin Gardens
30 0% - GO TO JAIL
31 2.675% - Regent Street/Pacific Avenue
32 2.616% - Oxford Street/North Carolina Avenue
33 1.116% - COMMUNITY CHEST
34 2.494% - Bond Street/Pennsylvania Avenue
35 2.553% - Liverpool Street Station/Short Line
36 2.239% - CHANCE
37 2.085% - Park Lane/Park Place
38 2.086% - Luxury Tax
39 2.552% - Mayfair/Boardwalk - Zábava
I think I just witnessed two mathematicians go on a date
Honestly not far off
technically you are right.
One of them being pregnant.
@@Rotceev They're mathematicians. Technically correct is the ONLY kind of correct! :D
It’s like a weird non touching foreplay being observed
Hannah: how a mathematician does math
Matt: How an Engineer does math
Lmao
Im glad im an engineer
@@grooveseeker6269 Haha same here
What is a math?
I try to do engineer math, but always end up deciding it's so much more work.
Nerd Flirting: "Stop critiquing my indenting."
Its python, its bugs...
Made dice rolling overly complicated
This whole video was the nerd version of get a room.. I enjoyed it.
LOL Thats hilarous
What a neg
Can we see Matt Parker, Hannah Fry, James Grime and Tom Scott play monopoly together?!
Holly Krieger too !!
This would be so amazing, oh my... And James Veitch would comment on the game! Hehehe
Or as I call them, Harry, Ron, Hermione and Neville
X Jungbluth I like how you think!
Hmm
Yes, that's all well and good, but what's the optimal angle to apply force when I've started to lose and wish to flip the table?
Vertically upwards at the very end of the long side of the table. Gives you optimal leverage. ;)
verdatum Just don't slide your chair backwards before standing up when someone lands on your street and you pretend to be extatic about it. It takes more energy on the short term, but it saves you from having to sit and wait until you lose.
Don't accuse someone of lying because they have come to a different result than you. The optimal angle to flip something is perpendicular to the line from the point of action to the center of mass. Depending on the table, that could be anywhere from a few centimeters under the middle of the table's top to a few cm off the ground.
But generally, 90° is not optimal to just make the table flip: It is, however, a good way to flip the table if you factor in the risk of hurting your fellow players, because the axis of the optimal rotation will go through the two legs most distant to you. A bit more energy investment to give the table a negative x movement (towards you) should be worth it.
Sorry, the line shouldn't connect to the center of mass, but to the axis of rotation mentioned before. So the force applied should be perpendicular to the plane that is spanned by the axis of rotation and the point of attack?
Optimal means nothing more than 'best possible choice'. From a physics standpoint, 'best' is naturally interpreted to mean 'with the lowest energy expense' and that is the question you answered.
I took 'best' to mean 'with the least risk of injury', resulting in, ideally, a flip on the spot.
I can see that the question follows a pattern of physics-test-like questions (stating information, desired property, being concise) and so it's natural to assume the side-condition is minimizing the energy required.
That however is not proof. It's just recognizing a pattern you know from somewhere else.
Optimality on its own means nothing, you must state what side-condition to use if you want to be precise. Or what value any given solution has to you (a quality function).
quarantine day 6,421: youtube asked me to watch 2 mathletes go on a monopoly date. I obliged.
O youtube
Oof, I noticed first after liking that I was apparently number 666😂
made me laugh out loud. thank you
Talk math with a lady? Yuck!
Upvote for "Mathletes."
Isn't the optimum way to play Monopoly to own at least one of each set and then keep going around the board until your opponents get sick of the game?
Deathly dull
That's hilarious
That is what happens most times I play. I don't think I have made a complete set in years, it is either reach a stalemate or occasionally one person makes a set and the other(s) can't. It has been a very long time since I played and more than one player had a set.
"Monopoly: The Fast-Dealing Property TRADING Game". If you're not trading, you're not playing it right.
@@srangara109 the problem with that is no-one has any possible incentive to trade properties most of the time. If you get a situation where no-one has a set then there may be a time when that makes sense. But if you play with only 2-3 players, it is common for one player to make a set and also hold properties sufficient to block anyone else from making one. That us the way the vast majorities of games I have played have ended.
There's actually infinite money in Monopoly. From the rulebook:
"The Bank never “goes broke.” If the Bank runs out of money, the Banker may issue
as much more as may be needed by writing on any ordinary paper."
@@rastas_4221 underrated
When I was a kid I used a typewriter to print money.
@@rastas_4221 The only difference in real life is that printing more money leads to inflation. Just ask Venezuela.
@@jacobschiller4486 or the Weimar Republic
@@69_pigeons_in_a_trenchcoat or the USA in 3 years time
Waaaaaay to circuitous. Get to the point! It's my turn and the family is getting suspicious.
The first rule with monolopy:
Study time is _before_ game time.
*Rolls eyes annoyingly and starts tellings the one story you find most embarrassing about youself... again*
@Tyler Durden - Isn't locking down the houses kind of like cheating? It's not like you're winning the game in style...
@@jamesfilosa6277 no, it's capitalism.
@Tyler Durden the house and money myth, in monopoly the bank can create more houses and money in case of shortage. ie hide all of the other board games so pieces from those dont get used. its actually a home rule too lock maximum number of houses, but not hotels.
@Tyler Durden Maybe you have another rulebook than me, but the only thing you can do while it is another persons turn according to all rulebooks i have here does neither allow you buying houses on other peoples turns, nor does it state that houses go up for auction.
But locking up houses helps win nonetheless.
I actually controlled a few games trading upgrading one of my streets to hotels against money and/or streets.
when two persons lean over a laptop and giggling on a piece of python code then you know
NERDS!!!! ;)
Then what does watching two people lean over a laptop and giggling about a piece of Python code make us lot? 😂
@@ym10up nerds by association
@@duetopersonalreasonsaaaaaa Spectating nerds
I never thought I would watch the two smart kids in class comparing answers and agreeing so peacefully.
On my high school (business academy) we were doing this "live" in front of a teacher with my friend; just after finishing the test we met at first row and started comparing results (silently to not interrupt others) and trying to figure out "why do you have these numbers different?"; worked exceptionally well in Accounting and Math. Presented by a mistake after a week when teacher bring back corrected tests is on much lower level then finding your mistakes right after you did everything and has full head of it.
And no, this is not a common practice, we were just too "good boys" that we were allowed to take a pencil and underline our mistakes; once or twice a teacher even allowed us to correct ourselves if those were some stupid mistakes in numbers or so. Lovely days ;)
"This is more fun than actually playing Monopoly!"
There are few things that aren't...
"The one with Park in it" or as I like to call it now, the Parker Square... because, you know, it's almost but not quite all the way around.
You win this round!
GroovingPict The perfect instance of the joke!
GroovingPict and it seems like a good idea at first but when you look at it it sucks
The Parker Square... That was straight SAVAGE.
I found the obligatory Parker Square comment.
That eyebrow movement at 1:30 is insane. That's true talent right there!
that’s nerd flirting and it is a secret code…..of course
🤣🤣🤣🤣🤣
Thank god someone else noticed
I think it was a twitch more so, but if not that is pretty talented.
That looked to me more like a nervous twitch... Haha
What beautiful hair! Such a lovely colour. (Her's is nice, too.)
There's no apostrophe in possessive pronouns, only possessive proper ones. Like names.
lmao
@@davidf2244 no one cares
Guys I’ve got some bad news...
I'm relieved, I feel like every other comment on a Hannah Fry video is thirst^π^π^π
1:31 that eyebrow is visibly excited!
Very cute content
came to the comments looking for anyone else that noticed it aswell. Thank you, good sir!
@@BruCipHiF :D
Who wouldn't be excited about all these calculations?
Very pretty aswell 😍
purring British accent: "It's just nice to get your hands dirty with a bit of matrix multiplication"
Me: take me now.
Juggling sx#
Take me hoooooome country roaaaaads. To the place I beloooooong
100%
Why didn’t you time stamp this
@@tomerator 9:01
quantum monopoly: your boot is in every cell at every time until you put down your drink
Best comment haha!
I would have thought that you could know where your piece was, but not how many moves it was making, or know how many moves it was making, but not where it was?
The chemistry here is insane, this is the kind of friendship that I want in my life!
"This is more fun than playing Monopoly" is always true.
Unfortunately this is just true. After the novelty wears off you realize that the decisions matter very little and it's just gambling for no stakes.
What about risk?
@@_Baleful than tell me why every game with my best friend ends up me having a good start, him winning the mid game and me winning with a plottwist
@@bae509 you answered it yourself if it has the same outcome.
@@tomr6955 when?
This is all good for theoretical studies, but I think we need to see it play out in practice. Matt Parker vs. Hannah Fry, who wins in Monopoly. Maybe throw in Brady Haran and James Grimes if we want more players.
Wolf Elkan in an interesting twist, Brady lucks his way into winning against all of them
And there has to be a Parker Square
I think between them, hannah is the most diabolical, grimes is the most intelligent, brady is the most simple and lucky, and matt is smart but i feel like he just lives in thepry and simulation and would quite suck
I feel that Monopoly is a game that rewards being diabolical, so I'm predicting a finish of Hannah > Brady > Grimes > Matt
Brady and Grey should do an episode just of them playing monopoly together.
That joke on millenials buying a house hits deep
I'm a millennial that owns a house. Quite a nice one in fact. It can be done.
TreeFiddy Silicon Valley? Gee whiz that’s expensive
xcvsdxvsx me too. Mortgage conditions in Sweden are quite generous
Where I live the cost of a decent flat equals roughly 13 years of average income. So having a family and own a place of your own is a huge struggle for young people. Not to mention the mortgage criteria which are plain nasty.
@@xcvsdxvsx Of course it's possible. Doesn't mean it's likely on average.
Here's how I win in Monopoly:
1. Early game: Buy every property you land on and pay or use get out of jail free cards when you get in jail.
2. As soon as you can, trade with the poorest or least aggressive player in the game such that you both get a monopoly. Yeah, they'll get one too, but they won't improve it much.
3. Get as many houses/hotels as you can afford on that monopoly. If necessary, mortgage non-monopoly properties.
4. Late game: Once you have an improved monopoly, stay in jail as long as possible.
That's what works in the real world. It's not like you get a choice of what color properties you land on, and any talk of rates of return or the "best" monopolies to own is just silly. The analysis is cool, but you're playing a silly game, not running a mutual fund or retirement plan.
Buy what you can, swap what you can, build as fast as you can, and then get lucky!
Actually, never buy hotels. The proper rules of monopoly say there are only 32 houses and 12 hotels in the game, and can be only used at one time.
The trick is, if all the houses are being used, no one else can buy them.
So a simple scenario: say you've played out and you own monopolies on the three groups that include oriental, st. charles, and st. james... and you've made enough to buy 3 houses on each property. That means 27 houses (9 properties, 3 houses each) are being taken up by you that no one else can buy. There are only 5 houses left for others, and therefore no other person can even buy a hotel. If you have the chance to buy 4 houses, do it, but buying hotels frees up houses for other people, and thats why you don't buy hotels.
From there, you will win by simply waiting for the other to roll through the 15 spaces from oriental to free parking... of which you own 9 of those spaces with 3 houses each.
Its also the best strategy to try and get the light blue(oriental), pink(st. charles), and tan (st. james) as they cost the least, houses cost less, and give a strong reward.
These are the strategies that the professional players and national and world champions (yes they do exist) say is the way to win.
@@devilmaster73 I imagine the meta could be different for casual non pro play on account of the second leading player not doing the same thing so it ends up spreading out the buildings anyway
Funny. I just rage-quit and flip the table. :)
@@devilmaster73 "You are assessed for street repairs" :-)
I thought this was supposed to be about math, not c h e m i s t r y
exactly what I was thinking. Matt when's the marriage?!
Matt's a married man you know
hahaha, was thinking that the whole time
Lol! Excellent!
hAha tHaTs fUnNy!
14:41 "There's finite houses, finite money..."
Incorrect. While the houses and hotels are finite in number, the rules specifically state that if the bank is ever short on cash, substitute using paper or some other marker. The bank cannot run out of money.
"The bank cannot run out of money." And there it is: the proof that money is in itself worthless, given that it can be produced solely on the desire to expand the economy, without reflecting the basis of its value.
@@popcultexpress what dude? No the actual rules state they have finite houses and hotels. Idk why ppl can't understand this game
so monopoly banks money count is the same as that of real life
@@PackinForSuperbowl Except that he did listen and you did not, too.
Short answer is bank running out of money is very rare, and if happens u cant use paper. If bank rund out of houses/ hotels and multiple people want the last house, it is on auction.
1:30 watch her eye brow. That's talent.
Finally! I have a talent
That just made my day hahaha
woooooooooooow
That's a twich.
later later parts of this episode can be found at bangb...
"You cant rig monopoly, its mostly luck"
"Luck is mathematical and we are the gods"
TLDR: The properties to buy depend on the number of players in the game
1 Opponent:
Light Blue and Orange
2-3 Opponents:
Orange and Red
4+ Opponents:
Green
Thank you!
So helpful. Thanks!
Comment I was looking for. Thank you!
Really? Light blue and the 100$ lane generally work best for me. Trade high value properties, give opponents monopolies they can't afford and scale up cheap property value quickly
@@robertbach9376 the cheap lane is fine for some early cash, but it’s nearly impossible to bankrupt them there. I feel it’s best to have the light blues or the purples to fund the houses on my more expensive properties
No surprise the "Parker" is the least visited square...
Whateverworks. Cold blooded
Touché
Ouch, burn. Haha
@@HelgaCavoli Coulé
Professor Bohr? Is that you?
"Ultimately Monopoly is about winning money and crushing your relatives" Hahahahah, best comment of the video
Conan would be proud."To crush your enemies, see them driven before you, and to hear the lamentations of their women!"
I have never watched such a nerdy, non-comedic video while having such a large smile on my face. The dynamic between them was hilarious!
Thumbnail should've said "Two people you DON'T want to play Monopoly with" 😂
Two people I would love to play Monopoly with.
They are not taking into consideration the most important part. Social skills and the power of persuasion.
"You win by winning money and crushing your relatives".
I like her style.
What is best in life? "To crush your relatives, to see them driven before you and hear the lamentation of their wallets."
I won... sigh... ^jumps in steamroller^
At least I have a lot of fake money now. ;_;
They just explained why I always lost monopoly. I always bought the railroads, utilities, and park place.
comichound same here but now I know the real point of interest.
Really?? Lol loser.
I always bought the 2nd set on each side, because I thought I get more value for the same-price houses.
Didn't go too well, either. :(
But now Math is here so save us! Time to get the sweet, sweet monopoly revenge! :)
Park place...
How about Park(er) Square
I always seem to land on the railroads early on so I grab 3 or 4 of them before a single monopoly is made, and then eventually lose because of some orange monopoly or something
As a kid, my sister taught me that the key to winning monopoly is ALWAYS BE THE BANKER
but the banker doesn't even play :/ there's no decisions to be made by the banker.
@@KristopherNoronha Precisely. Making all the money but doing none of the work, that is a true Charlie Sheen move.
@@KristopherNoronha huh. We just had one person be banker and abused them if they stole
@@KristopherNoronha Since when? The banker is also a player, they just have the added responsibility of dealing with the money
@@mollymauktealeaf yes - but I also learnt that either of my older sisters - always the one who was the banker - always won. The endless supply of pilfering 500 notes more than makes up for the onerous obligations of banking. OP refers to this.
I'm here a bit late but for anyone else who was wondering, here are the property names in the US version:
Purple/Brown:
Old Kent Road -- Mediterranean Avenue
Whitechapel Road -- Baltic Avenue
Light Blue:
The Angel Islington -- Oriental Avenue
Euston Road -- Vermont Avenue
Pentonville Road -- Connecticut Avenue
Magenta:
Pall Mall -- St Charles Place
Whitehall -- States Avenue
Northumberland Avenue -- Virginia Avenue
Orange:
Bow Street -- St James Place
Marlborough Street -- Tennessee Avenue
Vine Street -- New York Avenue
Red:
The Strand -- Kentucky Avenue The Strand
Fleet Street -- Indiana Avenue
Trafalgar Square -- Illinois Avenue
Yellow:
Leicester Square -- Atlantic Avenue
Coventry Street -- Ventnor Avenue
Piccadilly -- Marvin Gardens
Green:
Regent Street -- Pacific Avenue
Oxford Street -- North Carolina Avenue
Bond Street -- Pennsylvania Avenue
Blue:
Park Lane -- Park Place
Mayfair -- Boardwalk
Railroads:
Kings Cross Station -- Reading Railroad
Marylebone Station -- Pennsylvania Railroad
Fenchurch Street Station -- B & O Railroad
Liverpool Street Station -- Short Line Railroad
Utilities are the same in both versions.
you couldn't give Hannah her own microphone
opsimathics your bad at monopoly
Jacob Gourlay You're bad at grammar.
Not just that. He also edited the whole video and left his own voice crackling max decibels at more than twice the volume than hers. That's rude, even if it wasn't on purpose.
Exactly!
Damian Reloaded Well he got the footage with the microphone only on him, so the only way to make her voice audible is raising the voice volume, and that affected both of their voices
Park Place? Park Lane? Surely you would call it Park(er) Square!
sauce?
thanks, now i need monopoly version with parker square
a numberphile and co. stars version!
It works too, because the Park(er) Square is not quite the best (Boardwalk/Mayfair on their version).
Don't forget Free Parker. :-) (I guess he wouldn't mind getting money put under him) *g*
I was just enjoying christmas eve and here I am training a genetic algoritm
Auxence Fromont capitalism wants to know your location
Best algorithm ever
@@luigisgl2639 mario
When I read this comment I was expecting it to be like 10 hours old, not a year. It's 7am on Christmas morning here now.
@@StuartFerguson55 merry christmas
The best part of this video is how excited you both are about doing these experiments.
The only way to win at Monopoly is not to play monopoly.
Thumper 👍
Not true! Most played games have at least one winner.
The easiest way "not to lose at Monopoly" is not playing.
Dozo G: No, you're wrong. Speaking about Monopoly, the only way to WIN is not playing it at all (e.g. You'll have won around 6 hours, which you'll may use to play real board games as Puerto Rico or Ticket to Ride).
MONO LÚDICO. Imagine two identical Mayflies, call them "Anthony" and "Betty", with a life expectancy of a full day. Now A decides to enjoy his life flying around sniffing fresh summer air while B decides to go indoor and play a game of monopoly. At the end of their 24 your lives they discuss.
A did not win anything by not playing monopoly. The only way for B to have "not lost" her time was not to play games.
Puerto Rico is my jam.
A good Monopoly game ends in bloodshed, divorce, arson,the cops being called and awkward family christmas dinners and maybe uncle Barry being involved in a hit and run
Yea, that's the spirit :D
7Ghos did you mean Uncle Ben?
3:50 Actually, the rules say: “CHANCE” AND “COMMUNITY CHEST”… When you land on either of these spaces, take the top card from the deck indicated, follow the instructions and return the card face down to the bottom of the deck.
So basically you never shuffle the chance and community chest cards mid-game. Other than that, nice video!
House rules s trike again - most players of any game with card decks shuffle after a repeat card is drwan.
Aww, I love how Hannah pays attention to how neat the code is. It's been a long time since I've met some coder who cared about that.
I'm upvoting this before even watching it, because Matt Parker + Hannah Fry is a guaranteed winner in my book.
They're like giggly little kids who learned a cool magic trick. I absolutely love that; math is arguably the greatest mystery of our time, or even all time, and they are having fun deciphering this great secret we have written in front of ourselves. Keep doing what you're doing :)
Fun fact, matt was spot on. The original purpose of monopoly was to highlight the aleged falsehoods and pitfalls of Capitalism
Aye, though I’m quite sure that was an intentional reference as his phrasing was a tad on the nose
So true... Or to see what happens to capitalism when taken to the extreme and left to its own devices. Money rules the world, or the people who own the most think it does. Or to show how the more you have, the more you want, and the more you have to lose! It's a dreadful game despite it being sort of 'fun' - so unfair. I'd rather play Scrabble or the Green game (environmental trivial pursuit).
Scrabble can be really unfair too. Someone gets 3 or 4 '50's and the other gets stuck with almost all vowels for half the game and almost all consonants the other half. 2-bag games (with the blanks and Y's in the consonant bag) solve that problem but after hundreds of games I found 2-bag games only total on average 30 or 40 more points than 1-bag games, and are not as varied.
OK I admit it, all 'chance' games are unfair, but statistics of many games should even out to roughly an equal number of wins per player unless skill plays a role as significant as chance.
More specifically, the benefits of Georgism
Yeah central planning economy is much better than capitalism as we can see by looking at history...
@@yahccs1 You are making a wrong assumption here.
Monopoly is unfair because the amount of skill to rng is very small.
While something like Scrabble, it requires skill, knowledge and language understanding.
All RNG games can lead to an unwinnable game for you, but average out like 3 games, and you'll see the better person winning all 3 or maybe 2 of the games.
Playing optimally in Monopoly is essentially just buy everything you land on, and... buy everything that gets put on auction... and then wait until you win.
There is very little tactics or play there. Even Ludo has more tactics and strategy than Monopoly. You have very little input on how to win.
That is how you count how "unfair" a game is. Will a skilled person win over an unskilled person the vast majority of the time... and will a very skilled person beat a skilled person the majority of the time?
I’ve seen neater code written. Said everyone who ever looked at someone else’s code, ever. LOL
@rogerwilco99 yes
There's literally no way to write code to please everyone sadly...
Everyone that has written code has also said that about their own code
But this code is different, my eyes are literally bleeding
And especially when mathematicians. And even more so if they write it in python. Spaghetti and abbreviations. Lovely
Miss Fry is awesome.
Miss Fri is soon a mother :D
Oh that lucky man
She looks similar to Gianna Michaels. Her voice and laugh too :)
That's Dr Fry to you...
zaphod2342 YEAHHHHHH, I had the same epiphany.
That reference to Settlers of Catan right at the end. Brilliant!
I was hoping a few people would enjoy that.
I'd totally watch a catan let's play of you :D
Me and my brother like to call it the Cettlers of Satan :)
+RedsBoneStuff Unfortunately me and my brother used to call Settlers of Catan "one of several games I would just leave halfway through for no reason at all". I could be doing well or just having lots of fun, it doesn't matter. For some reason this is one of two games I just never bother completing, the other being Axis and Allies.
This is like after the physics exam results come out and everyone is comparing numbers with their friends to find out who's the bigger nerd on which questions.
I remember those days. My friends and I would compare our scores and brag about them if we did better than each other... Good times!
I agree with Hannah, it is always nice to have an excuse to do some matrix multiplication.
How did she do that at 1:31 with her eyebrow!?
probably a twitch
That, or she's an alien/robot in human skin.
clickhead it's totally unexpected and hilarious
She's 3/8 pixie.
Lol. I noticed that too! I wondered if anyone else caught it. Haha. I think she likes him. Haha. Jk.
lmao the look on Hannah’s face when Matt says “I deliberately skipped your Monopoly chapter because I didn’t want to pollute my research”.
This is such a great video. Two very smart people talking about a subject they're passionate about (mathematics) and its applications to a common board game. Great stuff.
funny how i stopped following their mind process after 2 minutes but I keep watching because their nerd-chemistry is beautifully palpable
2:02 "I'll show you what I got"...
OMG that face I am dying... I wish all women did that face when I wanted to show them math.
The Heretic +
The Heretic did you see that lip-biting? she made the look indeed
pregnant woman are always horny
As a connoisseur of the sultry female lip bite... I can tell you that lip bites are not all created equal. That was not THAT type of lip bite. I can instantly recognize, without hesitation, the right sort (something of a fetish) and have for decades. This was more of perhaps anticipation. Having said this, Hannah is beyond doubt a woman who has in fact bitten her lip the right sort of way in her life. ...she is a very attractive, expressive and alluring woman with an exquisite mind. Lucky are the men who have witnessed a lip bite (of that right sort) from Ms Fry.
+MISTERComaToes Ok, for humans, what this MISTER guy said is that she's not horny for him, she's just horny for the math.
2:09 - "But I have my spreadsheet of results…"
Of course Matt would have a spreadsheet of Monopoly results. XD
I mean... We all have spreadsheets of something. After all, everything is a spreadsheet.
This video is so wholesome, I'm seeing mathematicians having a good time being themselves.
It's like a date which is cute.
Even before watching this video, I knew there was something about them light blues.
A tier set right there. Cheap, yet mad rewards.
9:22 Instead of calling it the Park Position, how about calling it the Park(er) Square?
That's cruel. Also I'm disappointed that not many people got that.
Parker Position
park property?
Haha, I am breaking my brain trying to solve it right now
I know I'm years late to the party, but when I hit that bit in the video I legit started scanning the comments for exactly this! I knew the Stand-up Maths fans would not disappoint!
I need me a woman who reacts to code like that
Dunno - I'm pretty sensitive about my indentation...
;-)
Yes omg
@M H Where there is 1 woman for 200 mens ?
@@tesseract2144 Not that dramatic, but I can confirm. I did my computer science degree 2014-2018 and we were about 80% dudes.
@@LukeSykpeMan I did mine 2010 and it was 2%
get the monopoly on the houses, that's the most important strategy, always works, and as an extra you stop having friends
I came here to learn how to win at Monopoly but I’m leaving with a degree in Python and Mathematics
"You haven't got very many comments on your code"
Before the utterance of that line I thought I had reached peak Fry-Mania.
I was so very, very wrong.
Same😅
Anyone else feel like a third wheel watching this?
Somehow 😂😂
"Should I be listening to this? I feel like I'm learning a lot but not just about monopoly"
They seem like two kids in math sharing their answers.
I'm curious whether or not they took into account the rule that, when you land on an un-owned property, you must buy it or it is auctioned off to the highest bidder. That is a rule that I did not know existed until I was an adult, though I spent much of my childhood playing the game. I'm curious if that would skew the results since it serves to dramatically shorten the game, and thus the number of expected turns per player.
It would change the profit graphs based on purchase price as well. If you got park place for 100 bc everyone thinks it's rubbish then you don't build anything on it you've still generated another income stream at discount.
I suspect that even at the highest level of maths, this will be impossible to simulate - far to many factors to include such as level of wealth, need to block another player, inter player personal rivalries..... the list goes on for ever......... In which case, as it is not feasible to simulate nad of course as per previous reply will affect the numbers in BOTH ways - best to assign it zero value.
@@michaelfay3886 Yeah, its easy enough to say if the property is available and the player has the money then buy, but what happens if they can't afford it and it goes to auction? That is entirely subjective and would likely be very difficult, if not impossible, to program in a realistic way.
I mean, you could just simulate a dice roll for what each player is willing to pay as a starting bid and pad it based on what they already own and if it completes or furthers a set, etc. That could be a rough approximation of how an auction would go, but for a simple example like this it may be too much work to be worth it.
Seems Hannah's audio is slightly too soft relatively.
Dielfon Elettab she is pregnant
maxronaldo00 is it a "thing" that pregnant women talk softly?
I believe Matt's audio is a bit loud, sometimes even clipping :)
I think Matt's wearing a mic but Hannah isn't. I'm actually finding it very difficult to hear her unless I make Matt too loud.
Hannah is wearing a mic. You can see it for example at 16:17 . The cable runs next to a button. I guess he didn't use her audio because most of the time you could only hear her hair dangling around. So he only used his mic's audio.
So... when's the next date?
right? so cute
I know right, she gives him the eyebrow nod at 1:32
totally adorable
wow, that's some serious eyebrowing! I think she gets a bit hot and bothered by a guy who can talk maths.
how about 2:04 :P
“This is more fun than playing Monopoly!”
True dat
You know what, their discussion really reminds me of when students share their answers after exams.
2:52 "For some stange reason I listed all 36 results you get when you roll two dice"
FREAKIN MATHEMATICIANS
Park Lane, Park Place, "Park Position", Park Square... wait on a minute.
PARKER SQUARE!
"Matt, I suggest a new strategy: let the redhead win..."
OMG THIS IS SO COOL! I already wrote that code with Matlab a lot of years ago but I am DEFINITELY gonna buy that book!!
This was hilarious to watch. Two people comparing their findings like children comparing candy after trick-or-treating XD I kept hearing "What'd you get for..?" As one peers over to look at the other's results, and then both go "excellent!" or "nice, nice" with giant smiles on their faces. Great video, I'm glad you didn't cut any of those parts out.
The key to winning at monopoly is being the banker. I could have saved you a lot of time and math.
stealing is still illegal
@@kathrynpotts3318 only if you get caught.
@@kathrynpotts3318 Ha tell that to the bankers that caused the last financial collapse and got a bail out.
😂😂😂
Just like real life
I still think I'll just buy everything I land on 😂
thats the best way to win
Previous turns, by other players, would influence your probability of landing on a particular square. If a previous player got a chance or community chest card that relocated them, then you can't get that card. The more players before you, the more chances they get that card, the lower your chance. So you'd need a new Markov chain for each number of players.
Hannah: "My research suggests that..."
Matt: "THIS IS WHAT I THINK"
He's a terrible listener
He is absolutely awful
Matt is a great guy, he gave me his autograph
Omggg
I just love Hannah's cheerful yet matter-of-fact blackheartedness about financially ruining her relatives. :-)
I am fascinated by the math that drives the contest. Knowing the probabilities of the dice over time mitigates the effect of their momentary unpredictability.
I’d love to see an updated video of this looking at communopoly!
"This is more fun than playing Monopoly!"
That's honestly a pretty low bar.
Nixitur This video was more fun to watch than playing monopoly!!
Nixitur being kicked in the balls is more fun than playing monopoly. indeed, practically anything is more fun than playing monopoly.
smoog anything *except monopoly
Monopoly is fun
But your watching a video on them explaining everything, that's even lower.
9:21 he had to stop himself from almost saying the parker square
Yes, I was hoping for the Parker Square to be mentioned!
The Markov Chains idea to find the steady state distributions of each spot on the board was literally genius...
Here is a presentation on that carlabernard.ch/beni/downloads/bernard_monopoly.pdf
Is such a joy watching 2 people geeking out hardcore!
My math teacher took away my rubber band shooter today...
He said it was a weapon of math disruption.
You're stretching it a bit with that joke
Just.. No. Shame on you.
Come on I’m sure we can band together.
If you want your initialised list: squares = [0] * 40
+Ruud Althuizen That is far more efficient! Thank you.
And for the dice rolls, you can just generate two random numbers between 1 and 6, instead of sampling from a fixed distribution.
Yes but generating 2 random numbers each time is more time consuming and not optimal. It is basically using just a tiny bit more space to define the distribution to reduce time needed for generation by half.
I don't think it is more expensive. It might actually be cheaper in to do a few bit-shifts and multiplications than to look up from a list.
stackoverflow.com/questions/7291911/javas-random-number-generator-complexity-of-generating-a-number
Since the cost for this is probably about 0.01% of the overall run-time of the program, optimising that would be useless.
What you should really be considering is readability and extensibility.
Readability: Currently, it is not immediately obvious what you are simulating. You could argue that everyone is familiar with rolling a fair dice, but not everyone is familiar with the distribution of results from rolling two dice. Thus you are hiding your true intention, when it is just as easy to show what you mean.
Extensibility: What if you wanted to modify the rules so that now you roll n dice, instead. With this method you would need to spend time predetermining the distribution whereas you could just generate n random numbers and add them together.
Additionally, I would argue that it also easier to write:
result = math.random(6) + math.random(6)
vs.
list = {2, 3, ...}
idx = math.random(length(list))
result = list[idx]
This is great I never thought someone would use a markov chain for this but it seems clear now. Wonderful
As we approach Christmas it’s time to check in with this video and do some revision.
The square that has a 'park' in its name but isn't even consistently named is truly a Parker Square of a square.
1:32 that was a feisty eyebrow fiesta!
Another important tip to winning is making the other players follow the rules such as the limited # of houses and hotels, or that you have to build properties within a set evenly(you can still do it 1 by 1, but you can't have 1 house on one and a hotel on another within the same set)
I've loved Monopoly my whole life, and I've also known that these properties are the best, and have always been the ones I chose. Awesome to see it confirmed here
I jumped up three snoots when I saw the video popping on my feed.
GFmanaic If that isn't hyperbole, what do you do for a living?
Professional high jumper and youtube commentator, why ?
GFmanaic slip of the N I assume mr Smoot jumper? = P
you could say it was a parker smoot
Risk is even worse than Monopoly.
You can start a game, instantly knowing you have lost after you got your cards while still having to sit through 4 hours of agony.
@JGfrm BrooKLynnn Reading this gave me so much anxiety. In hindsight, Risk was a pretty bad game. You have to deal with a predetermined outcome or chance, which both make strategy games less fun.
There is a reason chess survived for all these centuries: It's fair and doesn't rely on chance.
@dee dee That is considered rude here in Germany. Fighting to the bitter end is part of our culture.
5:23
this video is just brilliant. you two make a great duo.
Orange is one of the best groups to own regardless of how many players there are. They established that jail (or just visiting) is the most landed on square on the board. The odds of rolling on to the orange group is very high coming from the jail square, therefore you always want to own the oranges.