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Deck analysis

How your deck's
odds work

Every deck page carries a panel called Opening-hand odds: how often you mulligan, how likely a card is to show up early, what your opening seven tends to look like. This page explains where those numbers come from and how to read each one.

The figures below are for an example deck. Open the odds panel on one of your decks and follow its “How these numbers work” link to see every one of them worked out for that deck.

The idea underneath

Counting hands

A shuffled deck can hand you any seven of its cards, and every seven is as likely as any other. From 60 cards there are 386,206,920 different opening hands. That is a lot, but it is a number we can count exactly — and so is the number of hands that have any property you care about.

So every figure in the panel is a fraction: the hands where something is true, out of all the hands there are. Take a card you run 4 copies of. The hands with none of them are the sevens chosen from the other 56 cards, and there are 231,917,400 of those. Everything else has at least one copy, which works out to 39.9% of all openings. Mathematicians call this the hypergeometric distribution; the panel does this count for every figure it shows.

Exact, not simulated. Nothing is estimated by shuffling a few thousand practice decks, so there is no margin of error: the same list always gives the same numbers, to the last decimal, for every reader. They are worked out in your browser from the list on the page, change the moment the list does, and computing them sends nothing anywhere. The one random thing in the panel is the sample hand, and that is a picture, not a statistic.
The toggle

Given you kept your hand

A hand with no Basic Pokémon cannot be played. You show it, shuffle it back, and draw a new seven — a mulligan — until you have one. So the hands you actually play always hold a Basic, and a figure that counts the hands you would have thrown back is answering a question you never face.

With Given you kept your hand on (the default), figures about what your hand holds count only the hands you would keep. Take the example deck used on this page — 12 Basic Pokémon, 4 Evolution Pokémon, 10 Supporters that draw cards, 8 Items that search the deck, 16 other Trainers and 10 Energy. A Basic and a draw Supporter together turn up in 58.3% of all shuffles, but in 72.1% of the hands you keep, because the 19.1% of shuffles that were mulligans are no longer in the count. Turn it off to see every shuffle, mulligans included.

The toggle moves draw supporter and a basic together, dead hand and the dealt hand's curve. The rest — the mulligan rate itself, two or more Basics and the Supporter figure — always count every shuffle.

When you look past the opening seven — what you have seen by turn 3, say — the condition is still about the first seven. A Basic drawn on turn 2 did not save the opening hand.

Block one

Opening hand

Five numbers about the seven cards you start with. In the example deck:

Mulligan
The share of shuffles with no Basic Pokémon in the seven: 19.1%. The sentence beside it puts a cost on that. Each time you mulligan your opponent may draw an extra card, and since every redraw is a fresh shuffle with the same chance, the average number of mulligans per game is the mulligan rate divided by the rate of keeping — 0.24 extra cards for your opponent here.
Two or more Basics
A second Basic means a Pokémon on the Bench from the first turn, so a knocked-out Active is not the end of the game: 42.8%, over every shuffle.
Supporter in your first eight
Going second you draw a card before your first turn, so you have seen eight cards when you can first play a Supporter. Going first you draw too, but you may not play a Supporter on that turn at all, which is why this figure is for going second: 79.0%.
Draw Supporter and a Basic together
A Basic to start with and a Supporter that draws cards to keep going — the hand most decks hope for: 72.1% of the hands you keep, or 58.3% of all shuffles.
Dead hand
The opposite: a Basic, so you have to keep it, but no draw Supporter and no Item that searches the deck, so nothing in it finds you more cards: 8.0% of kept hands.

A “draw Supporter” is a Supporter our card data says draws cards, and a “search Item” an Item it says searches your deck.

The picture

Mulligan rate by Basic countWhat one more Basic buys you. The filled point is this deck.
0%25%50%67891011121314151617181920Basic Pokémon in the deck6 Basics · 45.9%7 Basics · 39.9%8 Basics · 34.6%9 Basics · 30.0%10 Basics · 25.9%11 Basics · 22.2%12 Basics · 19.1%13 Basics · 16.3%14 Basics · 13.9%15 Basics · 11.8%16 Basics · 9.9%17 Basics · 8.3%18 Basics · 7.0%19 Basics · 5.8%20 Basics · 4.8%12 Basics · 19.1%12 Basics · 19.1%

Each point is the mulligan rate a 60-card deck would have with that many Basic Pokémon; the filled point is the example deck's, labelled with its figure. Read it left to right to see what one more Basic buys. The curve flattens: going from 8 to 10 Basics cuts the rate from 34.6% to 25.9%, while going from 14 to 16 only takes it from 13.9% to 9.9%. The point moves as you add or cut Basics in the editor.

Block two

Deal a hand

The only part of the panel that is random, and the only part that is not a statistic. It shuffles your list and deals you seven cards — press Deal a hand for another. If they hold no Basic it shuffles again, as the rules say, and tells you how many mulligans that took. The next six cards are your prizes, shown face up but dimmed, so you can see what was set aside without mistaking it for your hand; turn off Show prizes to see only the seven.

Every particular seven is rare — there are 386,206,920 of them — so its own chance cannot say whether a hand is ordinary. How rare is this hand? can. Cards count by name, so two printings of the same card are the same card in hand, and the hand's chance is the number of ways to pick each card's copies from the copies you run, multiplied together. The curve counts every possible seven the same way and draws how often a deal lands on a hand that likely, with this hand marked. Most deals land in the middle of the hump, and a hand there is typical. Far to the left it is concentrated — several copies of the cards you run most of — and far to the right scattered, made of your one-ofs. Either edge is unusual, and under 5% it is rare. It says how ordinary the draw is, not how good it is.

One hand tells you what a game might feel like; it says nothing about how often. That is what the other blocks are for.

The fine print

What the numbers leave out

  • What your cards do once played. The figures are about which cards you hold, not what happens next. A Supporter that draws three cards, or an Item that finds a Basic, changes your game; the counts above stop at the hand.
  • Your opponent, and your choices. Nothing here knows what you are playing against or how you would play the hand.
  • Cards we do not recognise. A line in a list that our card data cannot match has no card to shuffle. When that happens the panel says how many cards its figures are over.
  • Advice. A figure says how often; it does not say whether to play a card. The panel never edits your deck, and nothing in it suggests what to cut.