I have recently managed to convince my (now) wife to play Monopoly with me, which has caused her to realize she is much better than she thought. Even I was mildly surprised at her newfound skill. This has forced me to expand on my knowledge of the game with the hopes of improving my own skills and therefore chances of winning against my new and quite formidable opponent. Expanding my knowledge on this topic has been no easy task, given that previously in my lifetime I have read many books on Monopoly, own at least 10 official versions, created my own magnetic travel Monopoly, and even wrote a computer program (in Pascal of all languages) to simulate the game and keep track of the related statistics. This post tells of some of the things I have learned this time around.

The first hurdle of my learning process was to understand and come to terms with the changes that have been made to the game since the boards that I'm used to playing on were issued. This was somewhat difficult because the version I have recently purchased is entirely in Polish (as it was purchased here in Warsaw, Poland) and has some mistakes in the rules and cards. In fact the recent changes to the rules and those few mistakes created some intense confusion while playing with my wife and some of her family here in Poland. Luckily, I understood very little of what was said during this confusion, and therefore avoided the additional controversy present in many board game nights.

With the help of a great source (Monopoly-History.com) I was able to nail down that none of the recent rules changes are seriously game changing:
  • You can't pay 10% income tax, only $200,
  • You start the game with less small change, but more $100 bills (still $1500 total),
  • Three of the Community Chest cards are slightly different:
    • Pay school fee of $50 instead of $150,
    • From sale of stock receive $50 instead of $45,
    • Collect $10 from every player instead of $50,
  • Luxary tax is now $100 instead of $75, and
  • The dark purples are now brown.
After learning Polish well enough to read the rules and cards, I also realized that the remaining differences between my Polish version and my older versions are most likely mistakes or translation errors:
  • Some of the Chance and Community Chest cards are slightly different/messed up:
    • The "advance to nearest utility" card tells you to advance to "Elektrowni" (electric company), roll the dice, and pay owner the appropriate amount (instead of 10 times the amount thrown),
    • The "advance to the nearest railroad" cards simply tell you to go to the nearest railroad, creating confusion on whether or not to go forwards or backwards, then continues to tell you to roll the dice and pay owner the appropriate sum (which makes no sense at all, they must have just copied and pasted from the previously mentioned card, and
  • The rules say to collect "2 miliony dolarów Monopoly", which means 2 million Monopoly dollars (they must have gotten confused with the Here-and-Now edition),
Since sorting out the above, fewer arguments developed, but I was still having a hard time winning consistently. Next I thought I would attempt to better understand the statistics and data engrained within Monopoly. Inspired by the Information is Beautiful blog to attempt to create a few of my own visualizations, I thought an "all encompassing" Monopoly visualization would be the way to go:


While making this image I learned more about Monopoly than I was expecting, and now that I have it, I have found it to be a useful reference when confronted with difficult mid-game choices. All at once, it shows:
  • The chances of receiving money, paying money, or being relocated if you draw a chance or community chest card,
  • The monetary return on investment you will gain for each visitor that lands on one of your spaces, if that space is fully upgraded at the time (shown in terms of the cost of the local buildings: for example if someone lands on your fully upgraded Tennessee Avenue they will pay you $950, which is worth almost 10 houses on Tennessee at $100 per house, or almost 2 full hotels), and
  • The theoretical chances of landing on each space within the first 22 rolls of a game (normalized such that Reading Railroad is not faded at all and Mediterranean Avenue is minimally faded). Jail was not used for normalization even though it is by far the most landed on space because it would overpower all the other data, eliminating most of the distinction between the other spaces.
As a side note, while working towards this visualization, I came up with a cool video that shows what happens to the probabilities of landing on each space for each of the first 8 rolls of any Monopoly game. I like to think of this as a representation of the quantum probabilities of every monopoly game, or a weighted combination of all the possible Everett Universes encompassing the entire board with time:

Also, a huge thanks to Brad Frost Web for starting me off with a Monopoly photoshop template.

Please contact me (or comment below) for more information, how I did my calculations, the raw data that went into this visualization, or any number of (slightly uglier, excel based) graphs and charts that provide insight into additional interesting Monopoly data.


Wedding Speech: Love's Amplification of the Effect of Quantum Consciousness on Physical Systems

[transcript] I wanted to start out, well basically I wanted to tell a little bit of a story, just one out of so many, and I'm going to start it by reading something I gave to Amanda a while ago. It might not make that much sense, but I'm gonna do my best to explain it in two minutes or less, well let's say 8 minutes or less. So let me read it first. It says, 'Don't worry, with optimism, our wave function will create the luckiest universe. Seemingly unlucky moments like these', now I'm not talking about now, I gave this to her in a completely different situation, 'Seemingly unlucky moments like these will further entangle our quantum states and prove to be positive editions to our future's past.' So as you can probably tell --

This is the man I'm marrying. I've married, sorry, this is gonna be a little hard.

-- OK, so let's get into this a little bit, and Graeme sort of alluded [to this] a little bit. He said [he would], 'leave the explanation of quantum mechanics up to me.' So I'm not sure that can be done in 8 minutes or less but, first of all, has anyone heard of quantum mechanics, at least? Alright, that's a good start, a little sparse, but does anyone understand quantum mechanics? Two! Alright, where's the second one? I knew nick would put up his hand. Where's the second one? Fred, forgot about Fred. Ok, so you guys are gonna have to help me out a bit, because I don't understand, and I kind of doubt these guys (i'll talk to them later), but there's a couple things I've sort of figured out. One, it's pretty weird, it's pretty messed up, which is interesting because it happens to be the single most tested and proven theory of pretty much any scientific theory (I mean, it's just gone through all these [tests]). But okay sorry, I don't want to get too much into the science here today, I want to ...anyway. The other thing about it is just [that] there's a weird consequence of quantum mechanics when you look at how its effect combines with things like consciousness, the mind, and love, it does some weird things. It can actually have a huge effect on the world and the universe. And I'm not talking about if your conscious mind thinks of something and you actually do it. That's one very powerful thing, but the other thing is just an immediate direct mind-love effect on the universe. So I'm gonna tell you a story about Amanda and I that will hopefully make this a little [clearer]. I thought I'd tell a story instead of going into the scientific proof. But if you are interested in the proof, there's lots of books I can recommend, and I will get into that later [in the evening].

So this story starts with an adventure. Amanda and I go on endless adventures, all of our time together is unbelievably adventurous and exciting. So I want to talk about one adventure specifically. And actually I think it was Graeme...someone mentioned it. It had to do with a trip we decided to take to Disneyland. So we decided, well, we'll drive down to Disneyland, that should be fine. I was in Seattle at the time, but the car was in Edmonton, so I flew from Salt Lake City to Edmonton, because I was visiting Amanda right before, aswell, and she flew to Edmonton, we met there, we grabbed the car and we hopped in. Now I'm sure some of you might have driven to Disneyland, but we decided to take only about eleven days, the actual number (I think it was two weeks that was said), but we had eleven days, that's it, to drive down to Disneyland, and we had planned about three full days at Disneyland, and even that plan was detailed. But in addition to Disneyland, we thought well, it's on the way, we might as well stop at Seattle, Corvalis, Oregon, and we had an unplanned stop in New Port, Oregon, for about a day, we camped in Redwood, we visited Stephen in San Francisco, we stopped in Los Angeles for a walk down the beach and a few other things, and then of course Disneyland was the next stop, and we were there for a full three days ([which] was an excellent time), we even hit up Las Vegas, which is kind of a bit of a down...there were some ups and downs in the trip, but we hit is up again later and it was more of a sinusoidal... Then we camped again at the Grand Canyon and [visited] Salt Lake City. So, trying to put this all into eleven days and you start to get an idea of what the trip was like, and we didn't just drive through each of these places, we had a meaningful visit at each. For example, San Francisco is the one I want to talk about specifically.

In San Francisco, we were there for about 15 hours, but we managed to fit in a visit, (...where did we visit...) well we fit actually a few hours at the Exploratorium (because you can't miss that, obviously), we rode trolley's, walked down the presidio, we explored downtown, we even made it out to Alcatraz, I think I flowboarded down Lumbard Street, and we even bought Amanda a perl down at that (you know) "you pick your own perl" kind of a thing. So we fit it all in, and I think this was one of our more packed areas which made it a bit of an emotional experience. The whole trip was great, greatly exciting, from that respect. So Amanda was definitely not having the best time in San Francisco, for a number of reasons, and I think mostly because we just tried to pack way to much in. I was doing everything I could think of to cheer her up, and I've got some experience in that area, and so usually I can manage. Would you agree?


Ok, phew, usually I at least have a few ideas that work, the jokes or there's so many ways. I tried them all this day, and none of them were working. So I sort of turned to quantum mechanics. We were standing in a park and I could just tell, Amanda was (again) almost at tears, and so I had to do something. So I said 'Ok, let's make a deal Amanda. If I can quantum mechanically conjure a four leaf clover right at my feet, would you please...if I can do that, I mean, come on...would you please just smile for me, one time?' And she was like, 'well, what are the chances of him,' (I hadn't planted anything earlier, this wasn't a previously selected spot), 'what are the chances of him coming up with a four leaf clover'. So she agreed, just because she knew there was no chance. So my heart started beating just because I was like 'Oh jees, here we go, it's up to me now, um...', and I bent down, and sure enough, right between my feet (I didn't even look), the first clover I picked, just happened to have four leaves on it. I handed it to Amanda with full confidence, and... she burst into tears. But she did smile, and so it was, I think, it was happy tears, but I guess we will never know for sure. So normally, when i'm using my quantum mechanics and my consciousness to try and control the universe, or have some effect on the universe, normally it's a very limited effect, things that are chaotic systems, like the weather today, for example, it's more of a chaotic system, [and] it's much [easier to control]. Conjuring a four leaf clover at my feet was something that was just unreal. The reason that this was possible on that day, I think, is because of the strength of love between Amanda and I. We were, and are, and will continue to be forever so much in love, that amazing, infinitely improbable things can happen, and they happened that day, and they've been happening ever since. The really cool thing about this is [that] this is just one miniscule example. Our relationship as a whole has been a huge, a larger version of this clover story. Just the mere fact that she would thing for a second of coming back to me after the first mess up was a greater example than the four leaf clover, believe me. Statistically speaking, that was much less probable than finding a four leaf clover at my feet.

(We're almost done here. Sorry, I've crossed out so many things here to try and cut it down that I don't know what's next. Ok, I think the next...)

So let me read this again to you in the [new] context. (Oh, jees, I didn't even [show you this].) This is actually the very clover, I don't know if everyone can see it there, it's in between these two pieces of glass, that's the very clover I found, proof that I created it. But again it wasn't me that created it, it was our love together, it was Amanda. Not only that, I couldn't have done anything that I've done in the last six years without Amanda. Even when we're apart, none of the things I could have done would have been possible without Amanda. So, I'm going to read it again and maybe it will make a little more sense:

'Don't worry, with optimism, our wave function will create the luckiest universe, seemingly unlucky moments will further entangle our quantum states and prove to be positive editions to our future's past. Love, Trevor Prentice.'

Now let me just translate this a little bit. So, in other words, no matter what comes our way, Amanda, our love will keep us together, forever. And I mean that in the most scientific sense: forever, infinite, I love you.

- Trevor Prentice, 2008-08-08