An Analysis of Monopoly, or Why Monopoly is Worse than Poker

The game of Monopoly (I am considering the four player game played without house rules) is played over four phases that are roughly distinct.

• In the first phase, players are randomly given properties by the roll of the dice. It is unusual that you should not buy a property on which you land, so everyone generally buys everything they land on. (It's possible that, at some point, your opponents have too little money, in which case it may be worth auctioning the property off and buying it for less (just enough to outbid your opponents); I suspect that this is a rare occurrence.)
• In the second phase, players trade properties in order to accumulate monopolies. It is unusual that you receive a monopoly from the first phase through random dice rolling (in a four player game); if you do, you already have a huge advantage. Trading takes some skill, but not a whole lot of skill if you know the actual values and expected ROI of the monopolies. Still, the negotiation can give you a leg up in the next phases.
• In the third phase, players build houses and hotels on their monopolies. It is known that the the sweet spot is three houses, both because of the large rent leap from two to three houses and because of the limitation of houses available to build during the game. The skill in this phase is in managing your cash flow; if you have a row of opponent properties in front of you, you must keep your cash to avoid mortgaging properties. There is a bit of skill in the odds calculation here, but not much.
• In the last phase of the game, players roll the dice repeatedly until all players but one are eliminated from the game. There are - essentially - no interesting decisions in this phase.

With any set of players who are not total morons, who have a rudimentary understanding of probability, and who know the relative property values on the board, there is little chance that the players' holdings will vary much in value by the time the fourth phase is entered. One player's properties might be landed on 16.2% of the time, while another player's only 12.8% of the time. The first player is in a better position. And I suspect that both players had some fun during the negotiations and resource management up to this point. But here's where the problem starts.

In poker, you may have a hand that wins 16.2% of the time and your opponent a hand that wins 12.8% of the time. There is much more left to the game. You don't know what your opponent holds in his hand. You're not playing only against the system, for which the percentage is known, you're also playing against your opponent. You have to play not only the odds of your hand and what you might draw, but also the style of your opponent, a never-ending continuous assessment that continues to challenge right up until the cards are revealed. He might bluff. He might fold. He might call or raise. You only have clues as to the value in his hand, and therefore how to evaluate your own. The power of the cards plays only one part of the game.

Compare this to Monopoly. When the fourth phase is reached, players simply roll and roll and roll until one of them wins. There is nothing left to play; all information is open, there are no more properties or houses to buy, no more resource management, no hidden values to assess. As long as the percentages are close, any property on which you have three houses or more is going to kill or nearly kill you if you land on it. Additional damage is not that relevant. If you have only $50, you are just as dead landing on a property that costs $600 as one that costs $900 or $75.

In Monopoly, the percentages for win/loss in phase four are going to be a few points: 12% vs 16% or something like that. First one to roll badly loses.

Gamewise, there is no real favorite, no unexpected winner or loser, no underdog. On any particular roll, however, the odds will vary wildly. You might be entering at a long stretch of properties owned by an opponent. On this particular roll, your odds of surviving might be 60 to 12.5, in which case survival is a win for the underdog. This is the thrill of gambling; however it is the "low" sort of gambling that allows no choices, not even on whom or how much to bet. The game state is set, you're 100% in and you simply await the outcome. You can't fold and save your money for the next game, or bluff your opponent into not charging rent. You can't bet on another player.

That's why Monopoly ultimately fails as an interesting game, when compared to other luck heavy games such as poker.

Ignorance Sucks

Not knowing things irritates me. I may be in the minority on this.

Exhibit A: Snaps

Last sukkot I was introduced to the bar puzzle/game Snaps, one of those hilarious "in-the-know" games enjoyed by the people who know the rules and supposedly challenging and frustrating for those who don't. The game is allegedly about trying to guess a word given clues by one player, but it's actually about figuring out how the clue system works. Something to do with snapping fingers.

To some people, this is entertaining; if you're one of those people, don't clink on the above link. I was simply irritated. You would think that a game-player like me would be interested in trying to figure the game out, and I was for about four minutes. After that I got bored and wanted the answer.

The person leading the game was not tuned into this; he thought it was unsporting to give away the answer, so he just kept playing new words. After unsuccessfull trying to persuade him that I was no longer interested in guessing, I used my smart phone and looked up the answer. This might be construed as cheating, except that I never agreed to participate in the game in the first place.

Exhibit B: Books (and films, and other media)

I enjoy books, movies, etc a lot more when they've been "spoiled" for me. To me, the enjoyment from art isn't the anticipation and suspense of not knowing what is going to happen. It's from the artful way it is done. I've downloaded movies just to watch them at home before going to the cinema to see them. I read plot summaries online before reading a book, watching a movie, or even a television episode. If it's good art, I like to watch or read it more than once.

The term itself - "spoil" - implies that I'm out of touch with the common folk on this one. It's not spoiling to me; it's getting the plot out of the way so I can concentrate on the enjoyment of the media.

Exhibit C: Dice

For some, the anticipation of the unknown and uncontrollable is a thrill, for me it's a pain. I feel that the game is over right before the die is tossed: in the planning and the strategy that brought us to that point that matters. Once it's tossed, it doesn't even feel like playing to me anymore; it's like punishment. The win isn't exciting; the loss is irritating. It's a no win scenario for me.

Oddly, I don't mind at all when an opponent does something unexpected. In fact I love it; that's playing. I love talking to people who say unexpected things. In fact, I love the unexpected all over the place: random encounters in the real world, serendipitous discoveries in stores or on the radio.

In other words, I'm happy to continuously discover the interesting and good. Withholding knowledge just for the sake of withholding it is not my idea of fun.

Some Finer Points on Skill and Luck

Let's say that a game gives me two opportunities: I can try to pick a black card from 2 red cards and 1 black card, or I can try to pick a black card from 99 red cards and 1 black card.

I have a 100% chance of successfully choosing the opportunity that I want [1]. There is no waiting for the results, no possibility of error, and nothing my opponent can do to prevent or overturn my choice.

Nevertheless, the game doesn't end after that choice. Once I have chosen, I must still pick the card and await the result. Between the time that I chose my opportunity and the moment that the card is revealed to me, I contribute nothing to the game. There is no skill I can exercise, no feat I can accomplish. All I can do is await the outcome. [2]

In a game of Chess, when I choose to make a legal move on my turn, there is a 100% chance of my move occurring. Between that move and my next move, my opponent may respond in many different ways. There is no skill I can exercise, no feat I can accomplish [3]. All I can do is await the outcome.

The difference between these two games is that in the former case, I await pure chance to determine the results, while in the latter case, I await the skills of my opponent to determine the results. In either case, I can be lucky or unlucky. Luck in picking cards is obvious. In playing Chess, luck may have to do with my opponent's mental state, somehow having hit a blind spot in his evaluation or knowledge, his having a weakness to which I played [4], and so on.

Here's a third game: I'm shown the location of the black card in a set of three cards, and then I go read a book. Now I come back and have to remember where the black card is. I remember that it's not the right card, but I can't remember if it is the middle or the left card. I decide to pick one of those two cards.

My choice is partially skill and partially luck [5]. My skill has reduced the amount of luck. After my decision, I must again await the result of my choice.

If I play the game a dozen more times, I will win every time - no luck involved. The first time I played, I didn't realize how hard it would be to remember. Or, perhaps, I hadn't yet come up with a workable mnemonic system.

If the first game is luck, and the twelfth game is not luck, when does the game change from being one of luck to one of skill? After all, some people will win every game, even the first one; they have a natural skill. Some will always rely on luck.

I determine from these questions that a) my skill can reduce the amount of luck, or eliminate it entirely, and b) beyond the reach of my skill there is still luck. A wild guess. Or an educated guess. A wild swing. The hope that my opponent will under- or over-estimate my play.

If a game relies entirely on skill, it is a puzzle, or it is a foregone conclusion (e.g. tug-of-war with a baby).

Yehuda

[1] Assuming that I can evaluate the situation correctly, and assuming that my opponent can't cheat or otherwise manipulate the odds as I understood them.

[2] Roman's comment on my last post noted that, though my choice of a card is in fact irrelevant, human nature ascribes importance to the selection of the card; if the card is simply flipped at random, it doesn't feel the same as my "picking" a card. This is true, and a fact of human nature that good games exploit.

[3] Assuming that I cannot influence the decision through meta-game actions, such as trying to make him nervous. I could, however, use the opportunity to plan my next move.

[4] That can also be skill on my part, and not only luck; for instance, I may play moves quickly, thereby rattling him.

[5] Of course, it may actually be the right card, and I remembered incorrectly.