Match Play Procedures

Which team corks first -- the home team or the visitors?
Neither. The rules state that a coin is to be flipped before every game. The winner of the coin toss has the option of going first or second. In a two-out-of-three game set, the person who threw first in the first cork throws second in the second cork. A coin is tossed again for a third game.

Of course, it is seldom actually done this way in league play (though many argue that it should). The old, "See one or show one?" question is how it is done most often. As long as neither side objects, then it is fine to do it this way. If either side wants to do it right, however, then a coin must be flipped.
Does the first player listed on the line-up always throw the cork?
No. Any player on the team who is playing in that game may cork.
If my team doesn't have four people there, can we still play the match?
YES! In fact, you MUST play the match! If you don't, it is called a "Match Forfiet", and the penalties for Match Forfiets are severe! (Two of them in a season or just one in the last three weeks and everyone on the team is suspended from all league play for one year!)

If you have three players:

One of your players (it doesn't have to be the same one) may play each doubles by themselves, skipping the turn for the absent player, or you may optionally forfiet those games. In team games, one of the turns must be skipped for the absent player. In singles, one of the games is a forfiet (the home team decides which one).

If you have two players:

One of each of the doubles games is a forfiet, or both players may play each doubles by themselves, skipping the turn for the absent player. Both team games are forfiets. In singles, two of the games are forfiets (the home team decides which ones).

If you have only one player:

One of each of the doubles games is a forfiet, the other is played short-handed as above, or forfieted. Both team games are forfiets. In singles, three of the games are forfiets (the home team decides which ones).

So, by playing only a single game, one player can keep their entire team from being suspended for a year!
If some of my players are late, can we play games out of order to give them time to arrive?
Yes, if the other captain agrees. Rule 2(d) says that this is "at the discretion of the Captains". So if the other captain agrees, you can play games out of order except for Team 1001. Team 1001 MUST be played last (except in Doubles Leagues).
In Doubles, especially in a two-out-of-three game set, do the players always have to throw in the order they are written down on the line-up?
Yes, unless both Team Captains agree to do otherwise. (In a team game, there is no option.)
In Singles Chicago, who picks which games are played?
Rule 4(f) is clear enough:

"The winner of the first cork declares which game is to be played first. The loser of the first game declares which game is to be played next after cork is thrown for the second game. The remaining game is then played if necessary."

Note: In the Mixed Doubles League, the members in the original season voted to make it part of their format to play Chicago games in a set order (501, Cricket, 301).
What do you do if someone throws out of turn?
Rule 4(h) gives part of the story:

"If a player shoots out of turn and it is realized prior to the next player's turn, erase the erring player's score and return to the correct line-up. If it is realized after the next player's turn, all scores stand as written; but the next player on the erring player's team forfeits his/her turn. This will allow the opposing team to shoot twice and return the play to the correct line-up."

In addition to this, though, the Board of Directors has ruled in the past that under no circumstances can a player throwing out of turn be the last player to throw, winning the game.
What do you do about scoring mistakes? What if they have pulled their darts?
From Rule 3(c):

"Players may not remove their darts from the board until their score is recorded and acknowledged by the opponent."

The word "acknowledged" is rarely strictly enforced, but if you suspect a player of cheating, this rule is on your side. Notify the other captain that you intend to strictly enforce this (naturally it would apply to your team, too). The word "recorded" usually IS strictly enforced; if you pull your darts before you mark your score, you're out of luck.

On "pulled darts", again from Rule 3(c):

"In all games, the score of the three darts thrown will remain as written if one or more darts have been removed from the board."

So once the darts are removed, you can't change the thrown count. You CAN fix mistakes in addition or subtraction though. Again from Rule 3(c):

"In "01" games, errors in arithmetic not detected by the beginning of the same team's next turn, shall stand as written."

"In Spanish, Cricket, and Minnesota games, errors must be corrected before the opponent's next turn or will stand as written."