One of the trickier parts of designing a board game is balancing the game. You don't want certain options that depend on luck to tip the game to the player who gets it; also, you want to make sure the costs and benefits are roughly even as to not make one strategy the overwhelming favorite. If one choice makes one player the front-runner for the remainder of the game regardless of all subsequent actions, it's a bad game.
One of the problems will "traditional" American board games such as Sorry!, Life, and Monopoly are the reliance on luck. Luck in and of itself isn't a bad thing, but for many people playing a game that more or less determines the winner via a series of die rolls is a pretty awful way to spend time unless there is cash on the table. As such, many modern board game designers place as much emphasis on strategy as they can--and part of that is making sure the game is reasonably balanced.
Take Monopoly: Statistically, the player who has the orange properties is going to most likely win, since they are the most often landed upon. Likewise, while Boardwalk isn't the most frequently landed on space, the player who owns it fully developed will cause such a large one-time hit as to often win the game.Someone who is familiar with the payout of each property would be in the best position to win the game, but if all they even land on is Baltic and the Electric Company, they are out of luck. Quite literally.
There was a version of Sid Meier's Civilization (by Eagle Games, no longer in print) that was released a few years ago (not to be confused with the current one) that had balancing problems as well. There was one random event--the plague--that more or less devastated the player who was unlucky enough to get it. And the buildings expired after every era which normally only took a few turns. The cost of building a new building was more than anyone would ever get out of it, so that action was rarely taken.
Unfortunately, misrepresenting costs in decision-making is easy to do in board games. Until all of the factors and player personalities come into a real-life game, it is usually very, very difficult to put a static cost on anything and have it equal its benefit. (This is why playtesting is so important.) You don't really know if pricing artillery at 10 gold is worth it when infantry is worth only 5 until the game gets going. Monuments might be worth one victory point or three. This is a particularly difficult concept to cover when designing asymmetrical games, where both sides are operating under different rules and options.
Thankfully, there are a few design components that will allow a game to "self-balance"--that is, you don't have to put a cost on it; it naturally comes from the game itself. Note that I keep saying "cost," since this is what a majority of board games actions represent, but it could be anything, such as turn order or victory conditions.
1. The Auction. By far the most common, the auction lets the players determine the price of something. You never have to say it costs 10 Gold for a Stable or Four Workers for the Winery; you just let it out in the open and let the players determine the cost. It also helps dynamically within the game, since a Winery might be worth more early in the game than later.
There are several types of auctions; the most common are the English bid (the one most are familiar with--a player must pass or increase the bid) and blind (everyone makes a bid at the same time, and the highest player wins). I prefer blind since you don't have to worry about turn order and it's much quicker, but a lot of people don't. You will occasionally see a Dutch Auction variant (the bid starts very, very high, and slowly goes down; the first player to take the bid gets it.) This is also quicker and has more or less the same effect, but since it is unfamiliar many don't like it.
This also covers the bids in traditional card games such as bridge and 500 bid.
2. Changing Attractiveness. In this self-balancing technique, an option gets more lucrative as fewer people take it. This was used famously in the game Puerto Rico; any roles not chosen in a turn had a gold piece added to it. Eventually, even the most unattractive role would eventually be worth taking. Likewise, the popular Small World has a similar mechanic. There are a series of race combination you can select on your turn, but they are ranked in the order they appear. If there is a very effective combination at the bottom of the rank, you have to put a victory point on each one you pass over. Not only does this make getting that awesome combo more expensive, all passed-over combination--including the lousy one at the top--will eventually amass a huge pile of points.
3. Compensating Cost. I'm not sure how to describe this one, except that by taking a weaker option, you gain a benefit that roughly compensates for it. One example is in 1960: The Making of the President, where using a card that has a weaker value allows you to put more cubes in the rest cube bag--which means more benefits later. Conversely, playing a powerful card often nets zero rest cubes.
This would also cover such mechanics as "I divide, you choose": a player receives a number of cards, and they get to divide them into two piles. The opponent gets to choose which pile they want. This allows the first player to frame the decision as he likes--but the worst decision is the one he'll have to take, so there is an incentive not to make it too lopsided.
I'm tempted to put card-driven games (like my recently reviewed Twilight Struggle) under this, but since there is a hard value placed on each card I'm not sure if it fits. It's not really "self-balancing" as much as it is simply forcing more decisions to be made in relation to your opponent.
4. Balance By Proxy. While there may be cards of static cost and/or benefit, there are other ways to make the choices more self-balancing. While not exactly fitting of what we're talking about here, in the card game Citadels, each player takes all of the roles less one, chooses one, and passes the rest on. In a game where you bid for turn order (unlike Citadels), the ability to choose this first is inherent in the turn order bid. Other games have similar mechanics, where the first player in initiative (or whatever) gets to choose the best of the lot. So while everyone gets a free card or action, those who specifically put effort into it get first crack.
Of course, not all designers want their games to be balanced. Especially in the field of wargaming, some players consider it a point of pride to win a game playing a side that normally has a one in ten chance of winning. However, for most people, investing the time and energy in a game required that the game make an effort to be balanced. Similarly, games such as Cosmic Encounter and Fluxx do away with the pretense of balance altogether--the fun is either in making the best out of a bad hand or blind luck. These games can still be fun--some people enjoy crisis management and chaos more than equal opportunity.
And some can simply be balanced from sheer brute force of design. One of the examples of this is the classic Dune, where the six factions each have a list of unique benefits. There are a few wonky faction choices with less than six players, but otherwise you'll be hard-pressed to find a game where the balance is inherent in the game.
However, for most players, the time invested in a game should be one that gives most players at least a reasonable change of having the same opportunities. This is generally a mark of a well-designed game.