The primary mark of a good game is, of course, longevity. If a game's players continue to play rather than growing bored, it has sufficiently captivated them. As time passes for a game's players, they will inevitably experience both excellent and terrible "luck". Therefore, Church argues, the game must be enjoyable for the losers as well as winners, since anyone who plays sufficiently often will eventually lose. Virtually all games are fun to win, and hold their players through their luckier periods, but only the better games retain their players even when their luck, inevitably, reaches a sour stretch.
In applying Church's criterion, examine Monopoly. The game is very gratifying for a player who is lucky: A threatening opponent rolls the wrong number, lands on his [the lucky player's] property with hotel, groans, counts out bills equalling two thousand dollars, and hands them to the luckier player. However, there's arguably much less fun involved in being the paying player. From his perspective, he got "screwed" by the roll of the dice, and potentially lost the game not because of his inferior play, but due to random circumstances.
Of course, all this is moderated by the fact that Monopoly is a relatively light-hearted game, and that this very chance factor is part of its appeal. While Monopoly could be argued, technically, to fail Church's Criterion, this does not necessarily mean that it is a bad game or not fun to play, even for the loser.
One of Church's most common examples of a game which fails his criterion is Magic: The Gathering, often referred-to as "Magic". Magic is a "development game". In such a game, each player improves and utilizes resources (in Magic, spells and land, which provide spell-casting potential, drawn from the deck) and which player triumphs depends, abstractly put, on whose development occurs in a quicker and more powerful way. The gaping flaw in Magic, as a development game, is that "mana-screw"-- a phenomenon whereby random chance hamstrings a player's development-- creates scenarios which are completely unenjoyable to play. A player only drawing one land (main source of mana) card in his/her first eight (a not uncommon occurence) will almost never be able to play an effective game, despite no failure of his/her own strategy.
Examples of games which succeed according to Church's Criterion are Puerto Rico, and Ambition.
Puerto Rico is a development game wherein the players' developments, technically, never interact. (Nonetheless, the game is still enjoyably cutthroat, as players compete for very limited resources.) Even the losing players are usually able to build respectable developments, and the winner of a game is often not known until its end, when the scores are totaled.
Ambition is trick-taking card game wherein, the objective of each round being to score points without taking the most, the losers and winners of a round are often not known until its end. Likewise, entire games of Ambition are often, until the end, "anybody's game".
"Fun to lose", of course, is a simplification of Church's criterion. What's "fun", after all? That question is still unaddressed. While much of that issue is outside the scope of the criterion. A good game, according to Church, affords a player, despite inferior luck or skill: Numerous different (and hopefully balanced) play options, interesting strategic problems, and opportunities for some measure of success.
Puerto Rico, for example, achieves these goals. No matter how aggressively and effectively one's opponents are developing, a losing player still has many play options, and many profitable strategic avenues may be pursued.
In Ambition, the importance of having a "good" or "bad" hand is much less than in other trick-taking games: The play of one's hand is much more important than the hand itself. Church has often said that there are no good or bad hands in Ambition. Rather, each hand is a problem, and there are easier, as well as more difficult, problems.