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The board of life

By Daniel M. Ryan
web posted March 31, 2008

MonopolyIt's almost impossible to find a North American that hasn't played the game of Monopoly. The game has been a phenomenal success for Parker Brothers, and still is for Hasbro. Intended to be a family game, it's aimed primarily at children and intended to be a good influence. It largely is, and I'm sure that it's been used as a life-planner primer by many parents.

Recently, I got the electronic version and sat down to play some rounds in order to figure out what is the roughly optimal strategy for winning. The list below isn't quantificative; I'm sure that quantification will reveal some additional rules (as well as wrinkles) that my own guesstimation hasn't. What I found is, the way to win most times is to use a "minimax" strategy that aims to split the property blocks and give control over most of the board. Since the game is determined by random tosses of the dice, this set of rules won't lead to victory all of the time. It will, however, work most of the time – at the price of the occasional defeats being either humiliating or (if one is unphilosophical) maddening.

The Life of Game

When I started playing, I was content to trust in luck, which led to a few defeats. By the time I ended the series, I had figured out a rule that, although counterintuitive, uses the minimax principle of game theory to tilt the game in my favour. This rule says that the moves you should make are the ones that maximize your chances when you're flat on your back, when your opponent has got you where (s)he wants you. This principle, when translated into Monopoly play, means splitting the property blocks and buying all the properties you can even if mortgaging has to be used. If luck doesn't do it, then buying properties off the opponent has to be used.

I had a game where I had both Boardwalk and Park Place, as well as a lesser-placed block of three other properties, and I still lost because the much-more-flush playbot had only one block: Mediterranean and Park Place - the lowest-valued one. I actually had every other property except for one of each of the other blocks, excluding the two that I owned as a piece. Thanks to the playbot having that low-valued block, and building on those two properties to the maximal, I got nickled-and-dimed right to bankruptcy. Of course, this in large part occurred because I had overextended myself financially in order to be a property hog.

Financial overextension as a strategy is based upon the randomness of the game. The more properties you control, the more chance of a small rent payment coming your way. More importantly, during the buy-with-both-hands phase, the more properties you control, the less rent you have to pay out. I have found that buying everything you can from the bank, right up to mortgaging almost everything you have, doesn't lead to bankruptcy…provided that your opponent controls no property blocks. (More exactly, the probability of buying your way into bankruptcy in this way is quite low.)

This leads to the next wrinkle: payoffs in order to split the blocks. In other words, if your opponent has two of a three-property block and you have none, or one of a two-property block with you without, then it is (over the course of the entire game) cheap insurance to buy a (or that) property in the block at a huge markup. By doing so, I actually stopped the playbot opponent from snagging two complete blocks from the bank during one game. One time I failed to do so was that game I mentioned in the above paragraph. Despite having control over most of the board, I still lost that one.

Also, I found that buying railroads at similarly inflated prices adds significantly to the trickle in, and helps minimize the trickle out.

Of course, this overall strategy means that the opponent can reach a cash holding in the upper four figures while I'm still paying mortgages off. In addition, I have found that (without at least one block that's improved up to the hotel level) the average drain from my opponent's wallet, even if all my mortgages have been paid off, tends to be made up for by passing "Go" and collecting salary - even if I have managed to snag or bargain for every property except for one of each block. I also found that, unlike confining the buying spree to properties from the bank, there are times when buying those unowned property is impossible without going bankrupt.

What I found further, though, is that doing so allows me to accumulate cash quickly once all the mortgages are paid off. Once my own wad is sufficiently high, a trade of properties which gives both my opponent and me one or more property blocks makes the game a horse race. The rules of the horse race are determined overall by gambler's ruin, although a rough quantification of probabilities is a real help in determining which block-filling properties should be traded for which. Being ignorant of this point took me from a game that was an almost sure win to one that was a slow ruination for me.

Nevertheless, against the toughest of the three gamebots in the Monopoly 3 software game, I managed to win most of the games. This record includes tyro's mistakes as well as any bad luck I had.

To summarize, here's the set of rules I discovered, once that are so basic that any quick-witted kid could zero in on them:

  1. At the beginning, buy properties with both hands. Don't worry about mortgaging to do so.
  2. Don't trust in luck if your opponent is one property away from completing a block. Overpay to split the block, even if it means going a'sorrowing later.
  3. First priority is to split the property blocks by these means. Second priority is to get control of the railroads, or at least split them. Utilities are next, followed by buying every property that's in a split block except one for each. (Unless your opponent isn't very swift, there's no point in bargaining to complete a block.)  
  4. Courting gambler's ruin early on is a useful way to get properties from your opponent at that above-list price. The opponent will be more amenable to sell if he/she/it thinks you're feckless by nature. Offering more than you have in cash, impelling you to mortgage more to follow through on the offer, makes you look that way. (As I indicated above, the property-hog strategy does occasionally lead to bankruptcy. It's embarrassing when it happens, but the chances seem to be slight. Losing that way can be chalked up to bad luck, even if it seems foolish.)
  5. Be phlegmatic as your opponent accumulates cash while you're using mortgaging like payday loans. As long as your opponent cannot put a house or hotel on the board, the odds favour you keeping afloat and eventually unmortgaging everything.
  6. (This one may be a matter of style on my part:) I believe that it's best to not put any houses or hotels down until you've bought all the properties you can and have unmortgaged them, and also have enough cash to build free and clear. Doing so prolongs the game, which means that you can extract more rent from the properties you've paid for – including any from your opponent that you've overpaid for.
  7. Remember gambler's ruin when it comes time to make it a horse race. Also, have a good estimate of the probability of your and your opponents' resultant blocks when it comes time to make the Big Trade that starts the game smoking. Acquiring this skill may take a long spell of hard knocks.
  8. Unless that Big Trade is made, the game may very well be an interminable one unless you've snagged at least one choice block. Owning all the railroads won't do it.

As I mentioned above, any quick-witted and experienced player can win most of the time against a tough opponent through using those rules or a variant. (Note: These rules came from playing a bot opponent provided with the game. A human being can not only guess at what I'm up to sooner, but also can get miffed if I dabble in cardsharping or cat-and-mouse'ing. Of course, snatching defeat from victory's mouth, because the sure thing is boring, is quite possible with a bot opponent.)

The Game of Life

If the above decision rules are translated into life rules, as children might very well do, the results seem wholesome by modern standards. Monopoly primarily encourages investment. The cost of borrowing makes it plain that borrowing sets you back, so the habit of borrowing for productive purposes is encouraged. Also encouraged is spending with an eye towards receiving a future return. Entering into the debt-treadmill for any reason to do with an expected future return, ties in well with higher education and home ownership. It also ties in well with borrow-to-save financial tools such as retirement savings plan contribution loans. More to the point, it doesn't tie in very well with credit-card shopping flings for consumer goods. This financial reticence may very well provide an added career benefit: the less prone someone is to be entranced by plain consumer goods, the more prone (s)he is to avoid spending on and enjoying them through becoming a workaholic. All in all, the game seems to encourage a future-oriented attitude rather than present-centred fecklessness. A kid imbued with its rules would be inclined towards the typical middle-class professional or executive wealth pattern: living poor when young and not expecting real wealth until old age – and then rolling in it.

And yet…someone imbued with these virtues nowadays might as well be one of these people, or someone like them that's been caught in the subprime-mortgage net. Without shelter.

Perhaps unfortunately, a game like Monopoly is a sheltered game. Since its variables are few, and all are self-contained, it's easy to control then. Even the random character of the game can be controlled through relying upon regression to the mean. (This principle is what a property hog, like the one I was, is counting upon. More sophisticated variants are what statistical arbitrageurs – the derivative heavyweights – are themselves counting upon.)

What we're seeing now, though, is a sobering reminder that outside-world financial variables are not only unpredictable, they're not even random. Random events are independent of each other. One dice roll, or coin flip, has absolutely no influence upon the next. In a world of randomness, there are no such things as momentum bubbles and crashes that feed off themselves. In the game of life, the cautionary variant of the gamer's fallacy - as implemented through plain saving - is often good sense. ESR

Daniel M. Ryan is a regular columnist for LewRockwell.com, and has an undamaged mail address here.

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