If you missed them, here are Part 1 and Part 2 of this series

Now that we've covered your pre-tournament preparation, I want to focus on their structure, on what goes on during the actual tournaments, and how to navigate it.

Tournament Structure

PTQs, and all large Magic events, use the Swiss system to decide their pairings. This means you will (generally) play players with the same record as you every round. You may get paired up or down if there are an uneven number of players in any points ranking. Match points in Magic are awarded as 3 per win, 1 per draw and 0 per loss. A bye is counted as win.

The swiss system is organized so that at the end of the rounds, there will be only one undefeated, and the rest of the top8 will be based on their total number of match points. This rarely happens because for that to happen perfectly there has to be an specific number of players (8, 16, 32, 64, 128, 256, etc) so that each round there is an even number of people with an undefeated record, and nobody chooses to intentionally draw. What almost always happens is that when the tournament gets down to 4 undefeateds, these players draw. The reason is that while they would only need a loss and a draw to top8, two losses would put them out, and there is no advantage to going into the top8 with a better record than anyone else (though if the play/draw rule being tested out at Pro Tour Amsterdam is popular, this could change.)

Generally speaking, you need less than two losses to make top8. Except in instances where an abnormally large number of players attend a PTQ (think 300+), X-0, X-0-1, X-1s, and X-0-2s are guaranteed into top8. Next up comes X-1-1, which is usually the cut-off score and usually based on tiebreakers. X-2s can make top8, but it usually requires either some drama with players being paired against a higher or lower ranked opponent due to their not being an even number of players with their number of points. This can easily mess up with math. Sometimes smaller PTQs (64 or under) will also allow for one or two X-2s to make top8. To make top8 with X-2 you will need very good tiebreakers.

A word on tiebreakers. There are three tiebreakers in Magic – Opponent match win percentage, the percentage of your games you won, and the percentage of games your opponents won (throughout all of their matches). This is similar to how the BCS and other sports ranking associations rate strength of schedule. It rewards you for winning early in the tournament and having your opponents do well also.

If you've ever noticed that a first round loss puts you at a lower tiebreaker level than other players with the same record, it's because every player you beat after round one will have at least two losses – some of them more. If the player you beat round one decides to stay in at 0-7, you will see that your tiebreakers will take a hit from it. If you start off 5-0, each of your opponents will generally have fewer losses going into later rounds. Therefore, it is a big advantage to win the early rounds as your odds of making top8 at x-1-1 are directly correlated with playing other players at the top tables.

The first tiebreaker is the only one that generally ever matters for a PTQ due to the number of rounds you play. The fewer rounds, the more likely that the first tiebreakers could be even. The more, the less likely. I'd say this becomes a deciding factor in something like one out of every hundred PTQs. I wouldn't be concerned with it.

Understanding the Math of the Final Round of Swiss

This is probably the question I get asked most at PTQs - Can I draw into top8, or do I need to play? The math for this seems very complicated, but it really isn't. Most of it comes down to logic.

Round 8 of an 8 round PTQ is about to get underway. The first thing the staff does it post the standings for everyone to review.

How will the above situation play out? Here's what we do know - Andy, Bob, Carl and Dennis are each 6-0-1, and because there is an even number of players at x-0-1, they will all play each other, and probably draw. They will end the swiss at 20 points. Four spots of the top8 are filled. Next we have five players at 18 points. If each of these players were to draw, at least would be knocked out. I say at least, because we still have two players with 16 points who can hit 19 points. In this situation, we have seven people playing for the remaining four spots. Someone will have to play.

Because of how DCI reporter pairs the final round of a swiss event, players will play the opponent with their closest competitor in terms of tiebreakers, unless they have already played. That means Elizabeth vs. Frank, George vs. Helena, and Isaac vs. Jack.

Elizabeth and Frank can safely draw in as well. Only George, Helena, and Isaac can possibly beat their match points, and two of them will have to play each other. The remaining player will get paired down. He will face one of the two players with 16 points, the other player with 16 points will be paired down. Because of how opponent match percentage is calculated, getting paired down will hurt your final tiebreakers if you win. Neither of the 16 point players poses a significant risk to Elizabeth and Frank's tiebreakers. It would probably require each of their opponents to still be in the tournament, and lose. This will almost never happen at an event this size - it is at the least considerably lower odds than winning a single match of Magic.

This means that we have five people playing for the remaining two spots in the top8.

George vs. Helena

Isaac vs. Jack

Ken vs. Laura.

The winner of George vs. Helena is guaranteed in. Isaac is guaranteed in if he wins. Assuming George and Helena play, then Jack is in with a win as well. Ken is so far behind on tiebreakers that he would require either a miracle, or Elizabeth and Frank to play it out in order to make top8.

This isn't the only way this can play out, though. George and Helena can choose to draw, but the results will probably be bad for Helena. While Isaac's tiebreakers are worse, that won't matter. He will either end up at 7-1 and 22 points, or he will be out of top8. Jack has a very strong 64% tiebreaker. If he wins the match, he will probably end up above both George and Helena in the standings to end up in 7^th place. Helena will have to hope that the math gods somehow bless her just enough to get above George in the standings.

Note that in the above example, there is a shot for an x-2 to make top8. It just requires everyone to play out the final round. If the tiebreakers were closer – much closer – then this could happen. If the difference between 5 and 9 was two or three points, then you get into a situation where a match can draw, but is taking a risk that nobody else draws.

In general, if you want to figure out if you can draw, try and figure out how many people can get into top8, and how many places are ‘open'. If there are more matches then spots, you can't draw. If there are less matches than spots, and you have the highest tiebreakers, you can draw.

Navigating a tournament

When you are playing in a large tournament, it's easy to get bogged down in numbers. Your 1-1, 3-1, 4-1, etc. Don't worry about anything until you are at last the last two rounds. Focusing on your score before that is useless. There is a reason that people generally refer to their score as X and blank. The X isn't important while you are still alive in the tournament. What's important is your number of losses and draws. They are what really determine if you top8, not your wins.

Up until the last two rounds, you should be taking each game as it comes, and focusing on the match at hand. Everything that came before and will come after is meaningless. Don't let previous failures, or false bravado from your undefeated record, change your decision making. Too many players will keep a incredibly risky hand because they're up a game anyway, or because they are still in the tournament with a loss.

During the last two rounds, try and examine the standings. If you are x-1, you almost certainly have to play anyway. If the tournament is smaller, you can sometimes make the strategic decision to draw in the next to last round instead of risking a pair down in the final round. I used to do this all of time about eight to ten years ago when PTQs averaged closer to eighty people. With the larger PTQs of today, this will almost always put you

Sometimes there are nine people playing for eight slots. If one match ends favorably for you, keep in mind you can choose to draw later on in the match than just the beginning. Don't slow play to try and force the situation, but if it comes up, take advantage of it.

Keep in mind in the final round that tiebreakers can go up or down a fairly significant amount. While you never want to draw yourself it, there are times it is best to take a risky draw as opposed to playing a horrible matchup. I wouldn't suggest it often, but if the numbers are close, and if you feel you have a better chance relying on your previous opponents to win as opposed to winning your current game, then go ahead and take the draw.

I've done it once at a PTQ going into the 3^rd game on the draw in a terrible matchup. I had about a 40% chance of making top8, and far less than that to win the game. My opponent took the draw, and I made top8. For about a minute, before they fixed one misreported match, and I was ended up 9^th on breakers (It was one of the opponents the other person vieing for 8^th had played, whose match was misreported in terms of who lost). I still believe it was the correct decision, even if it ended up poorly that time.

Next week, I'm going to finish up this series by talking about what you do when you make top 8, and going beyond just the facts, and talking about the entire experience of PTQing, and how to get the most out of it.