Parents often ask us what their child is really getting out of Pokémon. The honest answer is a lot of maths, dressed up as a card game about dragons and lightning mice.
Underneath every match sits a deck of exactly 60 cards, 6 of them hidden as prizes, and a hand of 7 to start. From there the whole game is fractions, percentages and chance. The lovely part is that it is all school-level maths, the kind an 8 to 12 year old can follow, and your child does the sums without even noticing.
Below we break down the maths behind each part of a game. We show the working so you can check it, and so you can sit with your child and work it through together.
The 60 card deck, and why four is the magic number
A Standard deck is always exactly 60 cards. You are allowed up to 4 copies of any card, except for basic Energy, which has no limit. Those two rules shape every deck ever built.
Why do players run 4 copies of their best cards? Because more copies means a better chance of drawing one early. Here is the working for the most important moment, your opening hand of 7 cards.
Pretend you draw your seven cards one at a time. With 4 copies in a 60 card deck, the chance the first card is not one of your four is 56 out of 60. For the second card it is 55 out of 59, because one card has already gone. Keep going for all seven cards and multiply them together: 56/60 × 55/59 × 54/58 × 53/57 × 52/56 × 51/55 × 50/54. That comes to about 0.60, or 60%.
So 60% of the time you miss the card in your opening hand, which means 40% of the time you open with at least one. Four copies buys you a roughly 40% chance every single game.
Doing the same sum for fewer copies gives a neat ladder for the opening seven: one copy about 12%, two copies about 22%, three copies about 32%, four copies about 40%. Every extra copy lifts your chances, which is exactly why players run four of the cards they most want to see early.
There are two more numbers hiding here. You cannot run more than 4, so 40% is about the best a single card can do on its own. And the deck must be exactly 60, so every card you add waters down all the others. Choosing your 60 cards is the first real maths decision of the game.
Six cards you never see at the start: the prizes
At the start of a game each player puts 6 cards face down as prize cards. You take one each time you knock out an opponent's Pokémon, and taking all 6 wins the game. The catch is that those 6 cards are picked at random from your deck, so 6 of your 60 cards are locked away where you cannot use them yet.
That leads to a simple but important sum. The chance that one particular card is sitting in your prizes is 6 out of 60. And 6/60 is the same as 1/10. So any single card has a 1 in 10, or 10%, chance of being stuck in the prizes at the start.
This is another reason to run more than one copy of a card that matters. With two copies, the chance that both are prized is 6/60 × 5/59, which works out to about 0.0085, or under 1%. So two copies means that more than 99 times out of 100 you can reach at least one of them during the game.
It helps to picture the 60 cards split into three piles at the start: 7 in your hand, 6 in your prizes, and 47 left in your deck to draw. Six are hidden, and 54 are yours to work with. Good players plan around the idea that any one card might be in that hidden six.
The opening hand, and the dreaded mulligan
To start a game you must have at least one Basic Pokémon in your opening 7 cards. If you have none, you show your hand to your opponent, shuffle it back, and draw a fresh 7. That is called a mulligan, and your opponent gets to draw one extra card for it. So a mulligan quietly hands your opponent an advantage.
How often does that happen? It depends on how many Basic Pokémon are in your deck. Say your deck has 12 Basic Pokémon. The chance the first card you draw is not a Basic is 48 out of 60. Then 47 out of 59, and so on for seven cards: 48/60 × 47/59 × 46/58 × 45/57 × 44/56 × 43/55 × 42/54. That works out to about 0.19, or 19%. So roughly one opening hand in five would be a mulligan.
Here is how the mulligan chance falls as you pack in more Basic Pokémon: 6 Basics about 46%, 8 Basics about 35%, 10 Basics about 26%, 12 Basics about 19%, 15 Basics about 12%. The more Basics, the smoother your starts, and the fewer free cards you gift your opponent.
This is a genuine trade-off your child gets to weigh up. Too few Basic Pokémon and the hands stumble. Too many and there is no room for the cards that actually win the game. Finding the balance is the maths.
Supporters, Balls and digging: changing the odds on purpose
Here is the part that turns Pokémon from a game of luck into a game of skill. You do not have to accept the odds you are dealt. You can change them, on purpose, by choosing the right helper cards.
Many cards exist only to help you find other cards. Supporters like Professor's Research let you draw a fresh handful. Ball cards like Poké Ball and Nest Ball let you search your deck for a Pokémon. Each one effectively lets you see more of your deck, which lifts the chance of finding what you need.
Picture this. You have one special card you really want, a single copy. On its own it turns up in your opening seven only about 12% of the time, because that is 7 out of 60. Now add four Ball cards that can go and fetch it. You are no longer hunting one card. You are happy to draw the card itself or any of the four searchers, so five cards now help you.
The chance of seeing at least one of those five useful cards in your opening seven is 1 minus (55/60 × 54/59 × 53/58 × 52/57 × 51/56 × 50/55 × 49/54). That bracket comes to about 0.53, so the chance of success is about 47%. You have lifted your odds from 12% to nearly half, just by choosing four support cards. That is the whole idea behind deck consistency.
If you want to play with these numbers yourself, the draw calculator on this site does exactly this sum for any deck you like.
The cost of digging: discarding to find
Searching is powerful, so it usually comes at a price. Ultra Ball, for example, lets you search your whole deck for any card at all, but it asks you to discard two cards from your hand first. Giving up two cards can feel like a loss.
The maths says it is usually a good deal. Think of it as a swap. You are trading two cards you did not specially need for the one exact card that wins you the turn. Two ordinary cards are worth less than the single perfect card, right now, when you need it.
This is a real maths idea called expected value, just in child-sized form. You weigh what you give up against what you gain, and you make the swap when the gain is bigger. Players make this judgement dozens of times a game.
Putting it all together in one opening
Watch how the pieces fit. Your child shuffles 60 cards and draws 7. They check for a Basic Pokémon, knowing a deck with around 12 Basics will fail that check roughly one game in five. They set 6 cards aside as prizes, aware that any single key card has a 1 in 10 chance of hiding there.
Then they look at the 7 in hand. Did the card they wanted show up? With four copies that was about 40% likely. If it did not, they reach for a Ball or a Supporter to go and find it, turning a 12% card into a near coin-flip. Every decision is a small sum, made quickly, under a little pressure.
None of it is written down as homework. It is just the game. But it is real probability, real fractions, and real decision-making, played out turn after turn.
Why this is so good for your child
Pokémon quietly builds the exact maths skills schools care about. Fractions and percentages, because the whole game runs on them. Probability and chance, because every draw is a roll of the dice your child learns to feel. Expected value and trade-offs, because every turn asks what is worth giving up.
It also builds the habits that sit around the maths. Planning several turns ahead. Managing limited resources. Staying calm when the odds are against you, and pressing your advantage when they are with you. These are the same skills used by scientists, weather forecasters, doctors and engineers, who all make decisions when they cannot be certain.
On top of all that it is sociable, it is played face to face, and it gives a child a friendly reason to do mental arithmetic for fun. If you have ever wished your child would practise their fractions without a fight, a 60 card deck might be the gentlest way in.
Sit down for one game. Ask them why they run four of a card, or whether to use that Ball now or later. You will hear them reason through the maths out loud, and you will see exactly what they are learning.
Regards, Brett A, father of Bayzen A (1020 championship points, ranked 6th in Oceania for the 2025 to 2026 season).
Decks mentioned