Tournament Simulator

A calculator for all of your tournament math needs. The defaults are set to match the typical rules for Magic: The Gathering events, but you can change the settings to use this for pretty much any Swiss-style tournament structure.

See the footnotes for more information about each setting, and the technical details at the bottom for implementation details. On complicated tournaments and/or when run on a mobile phone, it can take a little while to simulate enough tournaments to get reliable results, but it will always return an answer in at most 30 seconds. If you have any questions or suggestions for improvement, please get in touch.

Tournament details:

Number of players:
Number of rounds:
Awarded byes:If the tournament gives some players byes, enter them here, separated by commas. For example if 30 players get a round 1 bye and half of those players get another bye round 2, you'd enter "30, 15".
UDUnintentional draw. In multiplayer events, this probability should include both draws due to running out of time and draws that occur as a compromise to a kingmaking situation. chance: %
Target standing:"Target standing" is whatever place on the standings players are trying to maximize their chance of reaching in the Swiss. In a tournament with a cut to top 8, this would be "8". For a day 2 cut you can change this to care about a specific number of match points, or being tied with a certain standings position.
Target type:
Allow intentional draws:

Player details:If you want to know a specific player's chances of making the cut, enter their info as of the last round to have ended.

Round:Enter the number of the last round to have finished
Match points:
OMW percentage:If you don't know your average opponent match win percentage you can leave this blank and the simulator will guess the most likely value based on your match points and round. %
Full standings:For more accurate results, you can use this field to enter multiple player details. Simply enter the player's points and then OMW%, then repeat for all other players. e.g. you could enter "6 50 3 66.5 3 66.5 0 50" as the full standings of a 4 player event. (Any whitespace character works as a separator.) Alternatively if you have access to the event standings on MTG Melee, you can copy the entire standings page text into this box and the calculator will parse out the individual players and point values.

For best results, include all players that could potentially get to your number of points within the number of rounds remaining, assuming you draw every future round. e.g. if you have 15 points and there are 2 rounds left, you'll want to enter everyone that has at least 11 points in the current round. (Note that this still cannot perfectly predict your results, because it doesn't know which players have already played which other players.)

Note that if you enter standings while a round is ongoing, you may be entering invalid data, since some players have finished their match and others have not. This will lead to incorrect results.

Multiplayer settings:

Players per match:
Min players per match:If the number of players in the event isn't divisible by the desired number of players per match, smaller games will be made to avoid byes if possible.
Points per win:
Points per draw:

Technical details:

Points are calculated such that a draw includes all players in a multiplayer match, even those that previously lost the game.
Players are assumed to have a mix of strategies for dropping; some drop once they're slightly behind, some drop only when it looks hopeless, and some never drop at all.
Players are assumed to be evenly matched, each having an equal chance of winning against any other player.
If the intentional draw checkbox is checked, all players will try to ID whenever doing so would increase their chance of making the cut. (Calculating this exactly is challenging due to the infinite regress inherent in most game theory problems, so this calculator uses an approximation. If you notice any situations in which players seem to be making irrational drawing decisions, please let me know so I can fix it.)
For determining the most likely match point distributions, tiebreakers and all players below the target standing * 1.5 are ignored for the calculation of whether two standings pages are "the same". e.g. if you're targeting top 8, then two potential standings pages that only differ in 13th place will be considered the same, as will two pages where first place differs in their OMW percentage but not their match points.
Note that the player details you enter do affect the most likely global match point distributions. e.g. if you enter player details of round 1 and 1 match point, then you're only simulating tournaments in which at least one player drew round 1, which will change the most likely final standings.
This calculator simulates only the Swiss portion of events, not any single elimination rounds after a cut.
The calculator assumes there are no weird edge cases like extra players losing round 1 due to joining the tournament late, an otherwise-invalid pairing being used because a player misreported a result that was later corrected, a double match loss penalty being issued by a judge, a double match win issued as a fix for judge error, etc.
The top cut field doesn't account for mixed incentive structures, such as where a player both wants to top 8 but also assigns nonzero value to being in a higher place than 8th when the cut is made.
The pairing algorithm for this simulation attempts to match the publicly-known details of popular Magic tournament software such as Eventlink and Command Tower.These programs are all closed-source, so their exact algorithms are a secret. This means that it, for example, correctly handles power pairings and the 0.33 minimum on MW%.This minimum is generalized to multiplayer as floor((1 / (number of players in a match + 1)) * 100) / 100. However in order to speed up calculation, this simulator makes a few simplifications that are unlikely to significantly impact the final results. These are: 1) If players need to get byes due to a non-divisible number of players in the event, it grants these byes to random players in the lowest point bracket rather than prioritizing players with the fewest previous byes. 2) It does not track the OGW% and GW% tiebreakers. 3) It allows players to be paired against a player they've already played before if they're among the lowest ranked players. 4) It does not fully minimize the number of pairdowns.For example, if the only players in a certain point bracket are players A, B, C, and D, and player B has already played both A and D, there is a legal pairing among themselves: A plays D and B plays C. But this simulator isn't guaranteed to find that pairing, and it may instead pair A vs. C and give pairdownsOr byes if this is the lowest bracket. to both B and D. 5) In 4-player-per-match tournaments, it does not follow the pairings guidelines from the Topdeck.gg MTR addendum and is willing to create multiple 3-player matches if needed to avoid byes. 6) If the tournament awards byes in multiple rounds, the simulation gives those byes to random players within the top bracket, not necessarily players who had a bye in the previous round. 7) In multiplayer it ignores the Topdeck directive to add fake opponents to the tiebreakers of a player who has a bye.

Comparison to other calculators:

There are several other calculators to help with tournament math, but are all rather limited in what they can do. I list them here for comparison and verification purposes.

Cards Realm: Can do a custom cut and rounds, but no draws.
Sixprizes: Same as Cards Realm, can do a custom cut and rounds, but no draws.
Galactic Treasures: Slight improvement, taking into account unintentional draws, but not intentional ones.
Limited Information: Does factor in IDs, but relies on unrealistic assumptions like "any pair downs always wins" and "nobody ever draws unintentionally".
LimitlessTCG: By far the best out of these calculators, but still can't account for byes, and has a somewhat confusing interface.
Swiss Triangle: Aims to show you the raw numbers so you can do the calculation yourself. Helpful but requires the human to still do most of the heavy lifting.
Brian Durkin's formula: Handy but can't account for events with extra rounds like GPs and RCs.