# Magic Math – Should You ID in the Final Round?

At big events, the last round’s pairings cause the players on top of the standings to go into a frenzy. “Can I take an intentional draw or not?” “Am I already locked for Top 8?” “Would my opponent accept an intentional draw?”

In this article, I’ll go over a few examples to explain when it is best to ID and when it is best to play out the match. I won’t go into the desirability of allowing IDs in tournament settings—that’s an interesting topic too, but I won’t focus on it today. I am focusing on maximizing prize winnings or Top 8 chances, given that IDs are allowed.

# Example #1

Suppose that at the start of Round 15 at a Grand Prix, the top of the standings looks like this:

Click to enlarge.

The pairings are as follows:

Table 1: Antoine vs. Ben
Table 2: Claire vs. Dave
Table 3: Eric vs. Frank
Table 4: Gabriel vs. Heather
Table 5: Ida vs. Jon
Table 6: Kai vs. Luis
Table 7: Masashi vs. Nicolai

In the last round, pairings always follow this pattern (where the rank 1 player plays against the rank 2 player, rank 3 plays against rank 4, and so on) if possible. Sometimes, you get small deviations—if the rank 1 player had played the rank 2 player earlier in the tournament, then they can’t play again—but generally speaking, it will always be close to this pattern. This only applies to the final round, though. In earlier rounds, pairings are random and don’t take tiebreakers into account.

### Q: Suppose that you are Dave. Should you offer an ID? What if you were Frank?

Yes and no, respectively.

In this scenario, the 4 players with 39 points are already locked for the Top 8. I think it’s best for them to ID and lock up places 1 through 4, therefore guaranteeing that they get to play first in the quarterfinals. The ID provides some time to grab food and to have a break before the Top 8. If Dave plays, then he gets a 50/50 shot between a 1st-place rank (if he wins the match) and an 8th-place rank (if he loses the match). I would prefer a guaranteed 4th-place rank because being able to play first in the quarterfinals is the most valuable of all the seeding benefits. Hence, Dave should offer an ID, and Claire will likely accept.

Below them, there are 8 players with 36 points, all of whom (under the assumption that Antoine, Ben, Claire, and Dave all reach 40 points) face win-and-ins. If Table 3 IDs, then Frank will very likely draw himself out of the Top 8 and finish in 9th place behind Eric instead. There’s a possibility of a tiebreaker upset so that Eric finishes 9th instead, but that only has a roughly one in ten chance of happening. Hence, Frank should not offer or accept an ID.

The end result would likely be a clean cut to the Top 8 at 39 points. For the two 34-pointers on Table 7, there is still an outside shot of sneaking into the Top 8 if one bottom 36-point match times out into an unintentional draw, but that is unlikely.

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# Example #2

Suppose that at the start of Round 15 at a Grand Prix, the top of the standings looks like this:

The pairings are as follows:

Table 1: Antoine vs. Ben
Table 2: Claire vs. Dave
Table 3: Eric vs. Frank
Table 4: Gabriel vs. Heather
Table 5: Ida vs. Kai
Table 6: Jon vs. Luis
Table 7: Masashi vs. Nicolai

Since Ida and Jon had already been paired in a previous round, tables 5 and 6 yield 36-34 point matchups.

### Q:Suppose that you are Frank. Your opponent Eric offers an ID. Should you accept?

Yes.

Let’s go over the tables one by one. It’s fair to assume that tables 1 and 2 will ID, so you can’t surpass those players. If you choose to accept the ID, then Eric will finish with more points than you as well, in which case there would already be 5 players locked for the Top 8. If you choose to decline the ID, then you will make Top 8 if you win, and miss if you lose.

Let’s suppose that tables 4, 5, and 6 all play. This makes sense because those players would likely finish 9th or 10th with an ID, while all have a shot at Top 8 with a win. This yields one player (Gabriel or Heather) with 39 points, who would be the 6th player locked for Top 8, and then the rest depends on tables 5 and 6. Assuming that all of those players have a 50% chance of winning their match, tables 5 and 6 yield the following possibilities:

• Two 39-point players with 25% probability. In this case, you would finish 9th with an ID.
• One 39-point player and one 37-point player with 50% probability. In this case, you would finish 8th unless the 37-pointer passes you with a tiebreaker swing.
• Two 37-point players with 25% probability. In this case, you would make Top 8 unless both Kai and Luis pass you with a tiebreaker swing.

Looking at the tiebreakers, you started the round at 70%, while Kai and Luis (the two 34-point players) had 68%. These numbers represent the average match win rate of their opponents in the tournament, where opponents who won fewer than 33% of their matches are instead counted as 33%. Byes don’t count as opponents.

So how much can tiebreakers change in one round? This depends on a number of factors such as the number of rounds, but let’s suppose that all of you had 3 byes, that tiebreakers were not reset at the start of Day 2, that half of your Day 1 opponents made Day 2, and that the ones that didn’t had a 50% match win rate (as you can see, many assumptions are needed to perform calculations, which is why last round tiebreaker math in reality is never perfect). In this case, your tiebreakers could fall to 68% if all of your previous opponents lose their last round and could rise to 72% if all of them win. Likewise, Kai’s and Luis’s tiebreakers end up somewhere between 66% and 70%. This implies that, as a rule of thumb, you’re safe if you have a 4% tiebreaker lead on your rival in a 15-round tournament.

Nevertheless, you only had a 2% tiebreaker lead in the example. Fortunately, this remains fairly safe. The probability that Frank would be surpassed by Luis is approximately 2% (I determined this number by enumerating all the win-loss scenarios, determining the probability for each, and convoluting on the set of scenarios in which one tiebreaker surpassed the other). As a result, an ID would yield close to a 75% probability of making Top 8, which is more than if you play, and thus it is in your interest to accept the draw.

You might consider shenanigans like declining the ID at first so you can try to win the match, and then offering an ID to Eric in case you lose a game. Eric would have an incentive to accept the ID even if he’s up a game because it still locks him for Top 8. Regardless, this is a risky proposition because Eric may also decline such an offer, for instance, because he desires the play-first benefits that come with a higher Top 8 seeding. I wouldn’t go for such a scheme in this case and just accept the ID when it is offered.

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# Example #3

Consider the standings here at the start of Round 16 at Pro Tour Born of the Gods, where the players in ranks 25 through 57 have 30 match points. The relevant part of the payout is as follows:

• 17th-25th place: \$2500 and 10 Pro Points
• 26th-50th place: \$1500 and 6 Pro Points
• 51st-75th place: \$1000 and 5 Pro Points
• 76th-100th place: 4 Pro Points

### Q:Suppose that you’re Reid Duke in 48th place with mediocre tiebreakers. Your opponent offers an ID. Should you accept?

Yes.

In these kinds of situations, the most beneficial course of action is usually to play if your tiebreakers are high and to ID if your tiebreakers are low.

With high tiebreakers, you can surpass many 33-point players if you win the round, therefore placing in the Top 25. This is, for instance, what happened in the match between Thomas Hendriks and David Fulk, who both started the round with 30 match points and high tiebreakers. David won and finished 24th, whereas Thomas fell to 55th place. With an ID, both players would have finished in the Top 50, but that would not have maximized their expected value.

With low tiebreakers, you can surpass no 33-point players if you win the round. Indeed, with a win, Reid would have finished 31st. With a draw, however, you are guaranteed to place above all 30-point players. Since you’re not passing 33-point players with your poor tiebreaks anyway, 31 points is almost the same as 33 points. In other words, a draw is almost as useful as a win in this situation! Reid accepted the ID and finished in 42nd place, giving him the same payout as if he had played and won.

Nowadays, Pro Points are based on record, and you can typically win more Pro Points by playing rather than drawing. This is a good change. But if you want to maximize your monetary prize (which is certainly relevant in the final round of a GP), then drawing with low tiebreakers and playing with high tiebreakers is still a good guideline. But, of course, check the standings first to verify that it will work out favorably with the payout cutoffs.

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