The Mathematics of Winning Monopoly

Рет қаралды 2,980,110

7 жыл бұрын

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

Пікірлер: 4 900

@zevbl8970 6 жыл бұрын

I think I just witnessed two mathematicians go on a date

@realitant 4 жыл бұрын

Honestly not far off

@Rotceev 4 жыл бұрын

technically you are right.

@Blobby3822 4 жыл бұрын

One of them being pregnant.

@thedosiusdreamtwister1546 4 жыл бұрын

@@Rotceev They're mathematicians. Technically correct is the ONLY kind of correct! :D

@olivershore4508 4 жыл бұрын

It’s like a weird non touching foreplay being observed

@billingsleypiano394 3 жыл бұрын

Hannah: how a mathematician does math Matt: How an Engineer does math

@authenticbaguette6673 3 жыл бұрын

Lmao

@grooveseeker6269 3 жыл бұрын

Im glad im an engineer

@billingsleypiano394 3 жыл бұрын

@@grooveseeker6269 Haha same here

@VespaT5 3 жыл бұрын

What is a math?

@ronarscorruption 3 жыл бұрын

I try to do engineer math, but always end up deciding it's so much more work.

@funguyscienceman 3 жыл бұрын

Can we see Matt Parker, Hannah Fry, James Grime and Tom Scott play monopoly together?!

@jackwilliams7193 3 жыл бұрын

Holly Krieger too !!

@DerivativeOfJungbluth 3 жыл бұрын

This would be so amazing, oh my... And James Veitch would comment on the game! Hehehe

@HedmanHedmanHedman 3 жыл бұрын

Or as I call them, Harry, Ron, Hermione and Neville

@Javerni 3 жыл бұрын

X Jungbluth I like how you think!

@mdashrafulahmed2820 3 жыл бұрын

Hmm

@senseimatt3097 4 жыл бұрын

Nerd Flirting: "Stop critiquing my indenting."

@GertvandenBerg 3 жыл бұрын

Its python, its bugs...

@isaiahsevere4192 3 жыл бұрын

Made dice rolling overly complicated

@robertohayes8386 3 жыл бұрын

This whole video was the nerd version of get a room.. I enjoyed it.

@Andy-si1pl 3 жыл бұрын

LOL Thats hilarous

@karepanman2770 3 жыл бұрын

What a neg

@iansullivan9738 5 жыл бұрын

Waaaaaay to circuitous. Get to the point! It's my turn and the family is getting suspicious.

@aknopf8173 5 жыл бұрын

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*

@jamesfilosa6277 5 жыл бұрын

@Tyler Durden - Isn't locking down the houses kind of like cheating? It's not like you're winning the game in style...

@Rabbit-the-One 4 жыл бұрын

@@jamesfilosa6277 no, it's capitalism.

@FableMythLore 4 жыл бұрын

@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.

@player-ye3hk 4 жыл бұрын

@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.

@verdatum 7 жыл бұрын

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?

@franzluggin398 7 жыл бұрын

Vertically upwards at the very end of the long side of the table. Gives you optimal leverage. ;)

@stylis666 7 жыл бұрын

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.

@franzluggin398 7 жыл бұрын

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.

@franzluggin398 7 жыл бұрын

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?

@franzluggin398 7 жыл бұрын

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).

@chicken2nite351 3 жыл бұрын

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."

@Noahtheorigianl 3 жыл бұрын

@@rastas_4221 underrated

@neilgerace355 3 жыл бұрын

When I was a kid I used a typewriter to print money.

@jacobschiller4486 3 жыл бұрын

@@rastas_4221 The only difference in real life is that printing more money leads to inflation. Just ask Venezuela.

@69_pigeons_in_a_trenchcoat 3 жыл бұрын

@@jacobschiller4486 or the Weimar Republic

@TheSummersilk 3 жыл бұрын

@@69_pigeons_in_a_trenchcoat or the USA in 3 years time

@RoderickEtheria 3 жыл бұрын

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?

@AnjaHuebel1 3 жыл бұрын

Deathly dull

@TheTonyExpress 3 жыл бұрын

That's hilarious

@lonedonkey101 3 жыл бұрын

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.

@srangara109 3 жыл бұрын

"Monopoly: The Fast-Dealing Property TRADING Game". If you're not trading, you're not playing it right.

@lonedonkey101 3 жыл бұрын

@@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.

@rickyspanish4951 3 жыл бұрын

quarantine day 6,421: youtube asked me to watch 2 mathletes go on a monopoly date. I obliged.

@crystalsheep1434 3 жыл бұрын

O youtube

@joelkronqvist6089 3 жыл бұрын

Oof, I noticed first after liking that I was apparently number 666😂

@neolulubeats 3 жыл бұрын

made me laugh out loud. thank you

@seanleith5312 3 жыл бұрын

Talk math with a lady? Yuck!

@matthewcox7985 3 жыл бұрын

Upvote for "Mathletes."

@GroovingPict 7 жыл бұрын

"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.

@HermanVonPetri 7 жыл бұрын

You win this round!

@Gabu_ 7 жыл бұрын

GroovingPict The perfect instance of the joke!

@SomeRandomFellow 7 жыл бұрын

GroovingPict and it seems like a good idea at first but when you look at it it sucks

@TheLadiesDream 7 жыл бұрын

The Parker Square... That was straight SAVAGE.

@acorn1014 7 жыл бұрын

I found the obligatory Parker Square comment.

@SgtRegg 3 жыл бұрын

when two persons lean over a laptop and giggling on a piece of python code then you know NERDS!!!! ;)

@ym10up 3 жыл бұрын

Then what does watching two people lean over a laptop and giggling about a piece of Python code make us lot? 😂

@duetopersonalreasonsaaaaaa 2 жыл бұрын

@@ym10up nerds by association

@ym10up 2 жыл бұрын

@@duetopersonalreasonsaaaaaa Spectating nerds

@hyphen8d725 3 жыл бұрын

I never thought I would watch the two smart kids in class comparing answers and agreeing so peacefully.

@siriusczech 3 жыл бұрын

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 ;)

@juggling8557 4 жыл бұрын

purring British accent: "It's just nice to get your hands dirty with a bit of matrix multiplication" Me: take me now.

@nrichj1556 4 жыл бұрын

Juggling sx#

@codinginthesaddle5641 3 жыл бұрын

Take me hoooooome country roaaaaads. To the place I beloooooong

@kennethsizer6217 3 жыл бұрын

100%

@tomerator 3 жыл бұрын

Why didn’t you time stamp this

@dominicthompson82 3 жыл бұрын

@@tomerator 9:01

@effyleven 3 жыл бұрын

What beautiful hair! Such a lovely colour. (Her's is nice, too.)

@davidf2244 3 жыл бұрын

There's no apostrophe in possessive pronouns, only possessive proper ones. Like names.

@livintolearn7053 3 жыл бұрын

lmao

@jimohare2665 3 жыл бұрын

@@davidf2244 no one cares

@thechuckster9025 3 жыл бұрын

Guys I’ve got some bad news...

@DuringDark 3 жыл бұрын

I'm relieved, I feel like every other comment on a Hannah Fry video is thirst^π^π^π

@jonskowitz 3 жыл бұрын

"This is more fun than actually playing Monopoly!" There are few things that aren't...

@christianrasmussen1 4 жыл бұрын

1:31 that eyebrow is visibly excited!

@amosw766 3 жыл бұрын

Very cute content

@BruCipHiF 3 жыл бұрын

came to the comments looking for anyone else that noticed it aswell. Thank you, good sir!

@christianrasmussen1 3 жыл бұрын

@@BruCipHiF :D

@vigilantcosmicpenguin8721 3 жыл бұрын

Who wouldn't be excited about all these calculations?

@adam6543 3 жыл бұрын

Very pretty aswell 😍

@wolfelkan8183 6 жыл бұрын

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.

@jboot111 6 жыл бұрын

Wolf Elkan in an interesting twist, Brady lucks his way into winning against all of them

@demonking86420 6 жыл бұрын

And there has to be a Parker Square

@smoothred9453 5 жыл бұрын

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

@LongfellowLP 5 жыл бұрын

I feel that Monopoly is a game that rewards being diabolical, so I'm predicting a finish of Hannah > Brady > Grimes > Matt

@PantheraLeo04 4 жыл бұрын

Brady and Grey should do an episode just of them playing monopoly together.

@BallerDan53 5 жыл бұрын

That eyebrow movement at 1:30 is insane. That's true talent right there!

@michaelprozonic 4 жыл бұрын

that’s nerd flirting and it is a secret code…..of course

@gerarddunne956 4 жыл бұрын

🤣🤣🤣🤣🤣

@carlbrovsky7500 4 жыл бұрын

Thank god someone else noticed

@pagansunite4005 4 жыл бұрын

I think it was a twitch more so, but if not that is pretty talented.

@arnaud78 4 жыл бұрын

That looked to me more like a nervous twitch... Haha

@gabelluc9573 3 жыл бұрын

The chemistry here is insane, this is the kind of friendship that I want in my life!

@sevenaries 3 жыл бұрын

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

@andyl.7713 3 жыл бұрын

Thank you!

@wonder_slime5031 3 жыл бұрын

So helpful. Thanks!

@SrMrRicardo 3 жыл бұрын

Comment I was looking for. Thank you!

@robertbach9376 2 жыл бұрын

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

@levi1929 2 жыл бұрын

@@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

@Reciomane 7 жыл бұрын

quantum monopoly: your boot is in every cell at every time until you put down your drink

@catnai2008 7 жыл бұрын

Best comment haha!

@ballsrgrossnugly 5 жыл бұрын

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?

@thomaswalsh4552 7 жыл бұрын

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 :)

@willerwin3201 4 жыл бұрын

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.

@commonsenseisnt779 4 жыл бұрын

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!

@devilmaster73 3 жыл бұрын

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.

@anthonygarcia5375 3 жыл бұрын

@@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

@olafbuddenberg4787 3 жыл бұрын

Funny. I just rage-quit and flip the table. :)

@ugahenne 3 жыл бұрын

@@devilmaster73 "You are assessed for street repairs" :-)

@B-MC 3 жыл бұрын

"You cant rig monopoly, its mostly luck" "Luck is mathematical and we are the gods"

@WaxxyOne 6 жыл бұрын

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.

@gregnixon1296 4 жыл бұрын

"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.

@notquiteordinary 4 жыл бұрын

@@popcultexpress what dude? No the actual rules state they have finite houses and hotels. Idk why ppl can't understand this game

@wolftreetruck4946 4 жыл бұрын

so monopoly banks money count is the same as that of real life

@trixn4285 4 жыл бұрын

@@PackinForSuperbowl Except that he did listen and you did not, too.

@mallusaih 4 жыл бұрын

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.

@freakingraze 4 жыл бұрын

That joke on millenials buying a house hits deep

@xcvsdxvsx 4 жыл бұрын

I'm a millennial that owns a house. Quite a nice one in fact. It can be done.

@dubbleyou248 4 жыл бұрын

TreeFiddy Silicon Valley? Gee whiz that’s expensive

@supremelordoftheuniverse5449 3 жыл бұрын

xcvsdxvsx me too. Mortgage conditions in Sweden are quite generous

@Schluker 3 жыл бұрын

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.

@cacamilis8477 3 жыл бұрын

@@xcvsdxvsx Of course it's possible. Doesn't mean it's likely on average.

@bmorr 3 жыл бұрын

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!

@noalear 3 жыл бұрын

I thought this was supposed to be about math, not c h e m i s t r y

@asherrockriver9757 3 жыл бұрын

exactly what I was thinking. Matt when's the marriage?!

@condor2279 3 жыл бұрын

Matt's a married man you know

@zanido9073 3 жыл бұрын

hahaha, was thinking that the whole time

@fredg.sanford634 3 жыл бұрын

Lol! Excellent!

@saimohnishmuralidharan5440 3 жыл бұрын

hAha tHaTs fUnNy!

@thumper8684 7 жыл бұрын

The only way to win at Monopoly is not to play monopoly.

@WyattCarrell 7 жыл бұрын

Thumper 👍

@dozog 7 жыл бұрын

Not true! Most played games have at least one winner. The easiest way "not to lose at Monopoly" is not playing.

@monoludico6166 7 жыл бұрын

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).

@dozog 7 жыл бұрын

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.

@Arancil 7 жыл бұрын

Puerto Rico is my jam.

@muizzsiddique 7 жыл бұрын

Park Place? Park Lane? Surely you would call it Park(er) Square!

@SuviTuuliAllan 7 жыл бұрын

sauce?

@Sopel997 7 жыл бұрын

thanks, now i need monopoly version with parker square

@Kram1032 7 жыл бұрын

a numberphile and co. stars version!

@jamesryan6307 7 жыл бұрын

It works too, because the Park(er) Square is not quite the best (Boardwalk/Mayfair on their version).

@Drosophilax 7 жыл бұрын

Don't forget Free Parker. :-) (I guess he wouldn't mind getting money put under him) *g*

@MasterHD 4 жыл бұрын

"This is more fun than playing Monopoly" is always true.

@_Baleful 3 жыл бұрын

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.

@epauletshark3793 3 жыл бұрын

What about risk?

@bae509 3 жыл бұрын

@@_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

@tomr6955 2 жыл бұрын

@@bae509 you answered it yourself if it has the same outcome.

@bae509 2 жыл бұрын

@@tomr6955 when?

@austinpatrick2682 4 жыл бұрын

Thumbnail should've said "Two people you DON'T want to play Monopoly with" 😂

@silentgrove7670 3 жыл бұрын

Two people I would love to play Monopoly with.

@arcarc7229 3 жыл бұрын

They are not taking into consideration the most important part. Social skills and the power of persuasion.

@Loredannon 7 жыл бұрын

"Ultimately Monopoly is about winning money and crushing your relatives" Hahahahah, best comment of the video

@OneEyedJack01 6 жыл бұрын

Conan would be proud."To crush your enemies, see them driven before you, and to hear the lamentations of their women!"

@BigDaddyWes 7 жыл бұрын

1:30 watch her eye brow. That's talent.

@benloosen5577 7 жыл бұрын

Finally! I have a talent

@Arrica101 6 жыл бұрын

That just made my day hahaha

@awesomefajitas 6 жыл бұрын

woooooooooooow

@HelgaCavoli 6 жыл бұрын

That's a twich.

@Hordil 6 жыл бұрын

later later parts of this episode can be found at bangb...

@loganfong2911 3 жыл бұрын

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!

@michaelfay3886 Жыл бұрын

House rules s trike again - most players of any game with card decks shuffle after a repeat card is drwan.

@xkd 3 жыл бұрын

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.

@condorboss3339 7 жыл бұрын

"You win by winning money and crushing your relatives". I like her style.

@oz_jones 7 жыл бұрын

What is best in life? "To crush your relatives, to see them driven before you and hear the lamentation of their wallets."

@streak1burntrubber 7 жыл бұрын

I won... sigh... ^jumps in steamroller^ At least I have a lot of fake money now. ;_;

@MrRayne911 7 жыл бұрын

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_Rising_Dragon 7 жыл бұрын

The Heretic +

@ian4683 7 жыл бұрын

The Heretic did you see that lip-biting? she made the look indeed

@MM-qy7si 7 жыл бұрын

pregnant woman are always horny

@queenofyeay 7 жыл бұрын

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.

@Funkestech 7 жыл бұрын

+MISTERComaToes Ok, for humans, what this MISTER guy said is that she's not horny for him, she's just horny for the math.

@ronarscorruption 3 жыл бұрын

The best part of this video is how excited you both are about doing these experiments.

@davidc1961utube 3 жыл бұрын

I’ve seen neater code written. Said everyone who ever looked at someone else’s code, ever. LOL

@nilen 3 жыл бұрын

@rogerwilco99 yes

@AiAiTheMonkey 3 жыл бұрын

There's literally no way to write code to please everyone sadly...

@vilkku792 3 жыл бұрын

Everyone that has written code has also said that about their own code

@luiswiederhold752 3 жыл бұрын

But this code is different, my eyes are literally bleeding

@Svenu2 2 жыл бұрын

And especially when mathematicians. And even more so if they write it in python. Spaghetti and abbreviations. Lovely

@BlobVanDam 7 жыл бұрын

I'm upvoting this before even watching it, because Matt Parker + Hannah Fry is a guaranteed winner in my book.

@Whateverworksism 6 жыл бұрын

No surprise the "Parker" is the least visited square...

@ShabbaDabb 6 жыл бұрын

Whateverworks. Cold blooded

@HelgaCavoli 6 жыл бұрын

Touché

@andrewdias2690 5 жыл бұрын

Ouch, burn. Haha

@anneaunyme 4 жыл бұрын

@@HelgaCavoli Coulé

@shambosaha9727 4 жыл бұрын

Professor Bohr? Is that you?

@notthere83 3 жыл бұрын

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.

@daminox 4 жыл бұрын

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.

@comichound 5 жыл бұрын

They just explained why I always lost monopoly. I always bought the railroads, utilities, and park place.

@Rg-fp2vg 5 жыл бұрын

comichound same here but now I know the real point of interest.

@maxonmendel5757 5 жыл бұрын

Really?? Lol loser.

@aknopf8173 5 жыл бұрын

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! :)

@emmahendrick147 5 жыл бұрын

Park place... How about Park(er) Square

@SuperSpruce 5 жыл бұрын

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

@opsimathics 7 жыл бұрын

you couldn't give Hannah her own microphone

@jacobgourlay9241 7 жыл бұрын

opsimathics your bad at monopoly

@ShuffleboardJerk 7 жыл бұрын

Jacob Gourlay You're bad at grammar.

@DamianReloaded 6 жыл бұрын

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.

@WickedGamerStyle 6 жыл бұрын

Exactly!

@IktaSol 6 жыл бұрын

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

@richdeering9580 3 жыл бұрын

As a kid, my sister taught me that the key to winning monopoly is ALWAYS BE THE BANKER

@KristopherNoronha 3 жыл бұрын

but the banker doesn't even play :/ there's no decisions to be made by the banker.

@buca117 3 жыл бұрын

@@KristopherNoronha Precisely. Making all the money but doing none of the work, that is a true Charlie Sheen move.

@nedben1602 2 жыл бұрын

@@KristopherNoronha huh. We just had one person be banker and abused them if they stole

@mollymauktealeaf 2 жыл бұрын

@@KristopherNoronha Since when? The banker is also a player, they just have the added responsibility of dealing with the money

@michaelfay3886 Жыл бұрын

@@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.

@tobiasgorgen7592 3 жыл бұрын

Fun fact, matt was spot on. The original purpose of monopoly was to highlight the aleged falsehoods and pitfalls of Capitalism

@bestcreations4703 2 жыл бұрын

Aye, though I’m quite sure that was an intentional reference as his phrasing was a tad on the nose

@yahccs1 2 жыл бұрын

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.

@aguyontheinternet8436 Жыл бұрын

More specifically, the benefits of Georgism

@peddersoldchap Жыл бұрын

Yeah central planning economy is much better than capitalism as we can see by looking at history...

@SioxerNikita Жыл бұрын

@@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?

@robert4445 7 жыл бұрын

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.

@7Ghos 7 жыл бұрын

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

@ciano5475 7 жыл бұрын

Yea, that's the spirit :D

@gonzalotapia1250 7 жыл бұрын

7Ghos did you mean Uncle Ben?

@KramerPacer2 3 жыл бұрын

funny how i stopped following their mind process after 2 minutes but I keep watching because their nerd-chemistry is beautifully palpable

@auxencefromont1989 4 жыл бұрын

I was just enjoying christmas eve and here I am training a genetic algoritm

@dubbleyou248 4 жыл бұрын

Auxence Fromont capitalism wants to know your location

@luigisgl2639 3 жыл бұрын

Best algorithm ever

@nilen 3 жыл бұрын

@@luigisgl2639 mario

@StuartFerguson55 3 жыл бұрын

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.

@auxencefromont1989 3 жыл бұрын

@@StuartFerguson55 merry christmas

@willis936 5 жыл бұрын

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”.

@enfo14 7 жыл бұрын

That reference to Settlers of Catan right at the end. Brilliant!

@standupmaths 7 жыл бұрын

I was hoping a few people would enjoy that.

@Commandelicious 7 жыл бұрын

I'd totally watch a catan let's play of you :D

@RedsBoneStuff 7 жыл бұрын

Me and my brother like to call it the Cettlers of Satan :)

@benevolentworldexploder5395 7 жыл бұрын

+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.

@SomniaStellarum 7 ай бұрын

I’d love to see an updated video of this looking at communopoly!

@syedhussain4564 3 жыл бұрын

I came here to learn how to win at Monopoly but I’m leaving with a degree in Python and Mathematics

@cloudybrains 7 жыл бұрын

How did she do that at 1:31 with her eyebrow!?

@noahlowrie6742 7 жыл бұрын

probably a twitch

@cloudybrains 7 жыл бұрын

That, or she's an alien/robot in human skin.

@tianlechen 7 жыл бұрын

clickhead it's totally unexpected and hilarious

@Jimpozcan 7 жыл бұрын

She's 3/8 pixie.

@hawkeyestiguy 7 жыл бұрын

Lol. I noticed that too! I wondered if anyone else caught it. Haha. I think she likes him. Haha. Jk.

@NoriMori1992 7 жыл бұрын

2:09 - "But I have my spreadsheet of results…" Of course Matt would have a spreadsheet of Monopoly results. XD

@garr_inc 5 жыл бұрын

I mean... We all have spreadsheets of something. After all, everything is a spreadsheet.

@MrSonny6155 3 жыл бұрын

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.

@jamess.8279 3 жыл бұрын

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!

@drumguy1384 3 жыл бұрын

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.

@ashurroth6585 3 жыл бұрын

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.

@michaelfay3886 Жыл бұрын

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.

@drumguy1384 Жыл бұрын

@@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.

@cortster12 7 жыл бұрын

So... when's the next date?

@theminecraftwikiman 7 жыл бұрын

right? so cute

@IronWarrior4Ever 7 жыл бұрын

I know right, she gives him the eyebrow nod at 1:32

@baconology 7 жыл бұрын

totally adorable

@TurboSixxSpeed 7 жыл бұрын

wow, that's some serious eyebrowing! I think she gets a bit hot and bothered by a guy who can talk maths.

@Mikeontube 7 жыл бұрын

how about 2:04 :P

@dielfonelletab8711 7 жыл бұрын

Seems Hannah's audio is slightly too soft relatively.

@maxronaldo00 7 жыл бұрын

Dielfon Elettab she is pregnant

@Sikosm 7 жыл бұрын

maxronaldo00 is it a "thing" that pregnant women talk softly?

@FostersLab 7 жыл бұрын

I believe Matt's audio is a bit loud, sometimes even clipping :)

@BurakBagdatli 7 жыл бұрын

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.

@Alex24757 7 жыл бұрын

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.

@albert6157 4 жыл бұрын

This video is so wholesome, I'm seeing mathematicians having a good time being themselves. It's like a date which is cute.

@sundaycomicssection Жыл бұрын

I agree with Hannah, it is always nice to have an excuse to do some matrix multiplication.

@HK-cq6yf 6 жыл бұрын

9:22 Instead of calling it the Park Position, how about calling it the Park(er) Square?

@annapejskova1976 6 жыл бұрын

That's cruel. Also I'm disappointed that not many people got that.

@ShabbaDabb 5 жыл бұрын

Parker Position

@jonavuka 5 жыл бұрын

park property?

@emmahendrick147 5 жыл бұрын

Haha, I am breaking my brain trying to solve it right now

@adub303 3 жыл бұрын

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!

@xpucm0ca 7 жыл бұрын

Miss Fry is awesome.

@JonSebastianF 7 жыл бұрын

Miss Fri is soon a mother :D

@iafozzac 7 жыл бұрын

Oh that lucky man

@zaphod2342 7 жыл бұрын

She looks similar to Gianna Michaels. Her voice and laugh too :)

@alecclews 7 жыл бұрын

That's Dr Fry to you...

@jgigas9834 7 жыл бұрын

zaphod2342 YEAHHHHHH, I had the same epiphany.

@matteocanducci5822 3 жыл бұрын

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!!

@davidedwards267 2 жыл бұрын

As we approach Christmas it’s time to check in with this video and do some revision.

@jcortese3300 7 жыл бұрын

I just love Hannah's cheerful yet matter-of-fact blackheartedness about financially ruining her relatives. :-)

@jzero4813 4 жыл бұрын

Anyone else feel like a third wheel watching this?

@TheBrickagon 3 жыл бұрын

Somehow 😂😂

@MonzennCarloMallari Жыл бұрын

"Should I be listening to this? I feel like I'm learning a lot but not just about monopoly"

@JustinShaedo 3 жыл бұрын

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.

@victorlowe 2 ай бұрын

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)

@MartinDeHill 7 жыл бұрын

2:52 "For some stange reason I listed all 36 results you get when you roll two dice" FREAKIN MATHEMATICIANS

@jackhaehl2033 6 жыл бұрын

I need me a woman who reacts to code like that

@RogerBarraud 5 жыл бұрын

Dunno - I'm pretty sensitive about my indentation... ;-)

@ScribbleDribble 4 жыл бұрын

Yes omg

@tesseract2144 4 жыл бұрын

@M H Where there is 1 woman for 200 mens ?

@LukeSykpeMan 4 жыл бұрын

@@tesseract2144 Not that dramatic, but I can confirm. I did my computer science degree 2014-2018 and we were about 80% dudes.

@zaphodbeeblebrox7524 4 жыл бұрын

@@LukeSykpeMan I did mine 2010 and it was 2%

@gregnixon1296 4 жыл бұрын

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.

@KrazyKyle-ij9vb 3 жыл бұрын

Even before watching this video, I knew there was something about them light blues. A tier set right there. Cheap, yet mad rewards.

@mikeandyholloway 7 жыл бұрын

"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.

@kressckerl 5 жыл бұрын

Same😅

@YogiTehBear 5 жыл бұрын

The key to winning at monopoly is being the banker. I could have saved you a lot of time and math.

@kathrynpotts3318 4 жыл бұрын

stealing is still illegal

@ebonyrose8713 4 жыл бұрын

@@kathrynpotts3318 only if you get caught.

@snowrulz88888888 4 жыл бұрын

@@kathrynpotts3318 Ha tell that to the bankers that caused the last financial collapse and got a bail out.

@codeaddicts 4 жыл бұрын

😂😂😂

@pieterprinsloo8767 4 жыл бұрын

Just like real life

@dedsm 4 жыл бұрын

get the monopoly on the houses, that's the most important strategy, always works, and as an extra you stop having friends

@Gorvinhagen 7 ай бұрын

5:23 this video is just brilliant. you two make a great duo.

@thechickennuggetoffate9139 4 жыл бұрын

9:21 he had to stop himself from almost saying the parker square

@briansammond7801 3 жыл бұрын

Yes, I was hoping for the Parker Square to be mentioned!

@lachlanstewart9314 6 жыл бұрын

Park Lane, Park Place, "Park Position", Park Square... wait on a minute. PARKER SQUARE!

@jimweights8908 4 жыл бұрын

This is great I never thought someone would use a markov chain for this but it seems clear now. Wonderful

@stuartdoig3418 2 жыл бұрын

I have always enjoyed having the orange/red squares, in a few games I have gotten them with hotels and that corner is now known as "the corner of death" in my household. Normally there are 3-5 opponents, so slightly outside of their optimal range, but they're still deadly.

@RuudAlthuizen 7 жыл бұрын

If you want your initialised list: squares = [0] * 40

@standupmaths 7 жыл бұрын

+Ruud Althuizen That is far more efficient! Thank you.

@Multihuntr0 7 жыл бұрын

And for the dice rolls, you can just generate two random numbers between 1 and 6, instead of sampling from a fixed distribution.

@gametips8339 7 жыл бұрын

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.

@Multihuntr0 7 жыл бұрын

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]

@DanTheStripe 7 жыл бұрын

More Hannah Fry on this channel please! 😄

@PapiJack 4 жыл бұрын

Is such a joy watching 2 people geeking out hardcore!

@Mike.L. 4 жыл бұрын

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.

@apadgettski 4 жыл бұрын

Hannah: "My research suggests that..." Matt: "THIS IS WHAT I THINK"

@greenwoodorganics4681 3 жыл бұрын

He's a terrible listener

@jameshayward3842 3 жыл бұрын

He is absolutely awful

@nilen 3 жыл бұрын

Matt is a great guy, he gave me his autograph

@benben-sx4xb 3 жыл бұрын

Omggg

@patientestant 5 жыл бұрын

1:32 that was a feisty eyebrow fiesta!

@Marnige 4 жыл бұрын

You know what, their discussion really reminds me of when students share their answers after exams.

@u1richh 2 жыл бұрын

I have a few things my friends and I do to have short games: All taxes go into a pool to be collected when someone lands on free parking. Play aggressively, trade when it make sense to, no auctions, and place houses or hotels whenever you can. Also the first side of the board is really strong if you own it all. Especially if you own the first half of the board.

@SKyrim190 7 жыл бұрын

How is Hanna so adorable all the time?

@kaazmodan 6 жыл бұрын

Imagine Hannah paraphrasing Jeff Winger: "It's called chemistry, I have it with everyone!"

@KaliTakumi 7 жыл бұрын

Got excited when I saw Hannah Fry in the thumbnail

@Baconator1368 4 жыл бұрын

The Markov Chains idea to find the steady state distributions of each spot on the board was literally genius...

@lobovutare 4 жыл бұрын

Here is a presentation on that carlabernard.ch/beni/downloads/bernard_monopoly.pdf

@thebeardyyc 4 жыл бұрын

@5:30 is the best clip! “This is more fun than playing Monopoly” 😂 so true 🤣 Love this video, so cool to see two different approaches being compared.

@ProGangstaShit 7 жыл бұрын

Two of the best numberphile/mathematics people:)

@MrUncleTings 7 жыл бұрын

Hannah Fry is SO AWEOSOME. she should be put up there with famous intellects

@skybeard3113 4 жыл бұрын

They seem like two kids in math sharing their answers.

@jimsmith9853 3 жыл бұрын

They gave away my strategy. I have been using it since I was a kid. I always get the oranges and greens. Grab one of the yellows and reds so they cant develop heavily. I differ about the RRs they always worked well for me.