# Tournament Simulator

A calculator for all of your tournament math needs, designed to support both players and scorekeepers with any possible event structure. This is still a work in progress; if you notice any flaws or have any suggestions, please get in touch.

See the usage notes at the bottom of the page for more information about any of these settings.

#### Tournament details:

#### Player details:

#### Multiplayer settings:

#### Usage notes:

- "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.
- If the tournament gives out byes in the early rounds, enter them in the byes field, separated by commas. For example if 30 players get round 1 bye and half of those players get another bye round 2, you'd enter "30, 15".
- If you don't know your average opponent match win (OMW) percentage you can leave it blank and the simulator will guess the most likely value based on your match points and round.
- The "number of rounds played" field includes byes and match losses; it's just asking what round of the tournament you're on. Be careful to only enter data once the round is fully over; if you check your opponent-match-win-percentage in the tournament software while a round is still ongoing, you may get an intermediate value since some of your previous opponents haven't finished their matches yet.
- Note that on complicated tournaments and/or when run on a mobile phone, this calculator can take a few seconds to simulate enough tournaments to get reliable results. Please be patient, it'll always return an answer in at most 30 seconds.
- For more accurate results, you can enter multiple player details in the "full standings" field. Enter the player's points and then OMW%, then repeat for all other players. Separate all numbers by a space or line break. 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.) - The "win percentages" field dictates the chance of winning based on who goes first. (Conditional on not being a draw.) For example, if in a 4-player game the first player in turn order has a 40% chance of winning and the other players each have a 20% chance of winning, enter "40, 20, 20, 20". (Integers only.)

#### Technical details:

- It calculates points such that a draw affects all players in a multiplayer match, even those that previously lost the game.
- It assumes that players 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.
- It assumes that all players are evenly matched, and have an equal chance of winning against any other player.
- If the intentional draw checkbox is checked, it assumes that all players 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 it 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 do affect the most likely 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 simulates only the Swiss portion of events, not single elimination.
- We assume 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 caused by both players agreeing to a bribe, a double match win used as a fix for judge error, etc.
- This doesn't account for mixed incentive structures, where e.g. 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 pairings algorithm this simulator uses omits a few things that would significantly slow it down to impliment and that are unlikely to impact the final result. These are: 1. Prioritizing players with the fewest byes to give another bye to, 2. Backtracking and redoing pairings if players in the attempted last match have already played each other, and 3. the OGW% and GW% tiebreakers. (It does respect power pairings, the 0.33 minimum on MWP, and not pairing a player against someone they've already played at all of the higher tables.)

#### 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.

This calculator is intended to combine their functionality into a single package that's more flexible and accurate than all of the others, along with adding other useful features like custom tiebreakers and multiplayer math. If you notice anything that it can't do but you wish it could, please let me know and I'll see about adding that functionality.