Starter
Ideal: ≥ 75%Probability of having ≥1 Starter. Aim for 75%+ going 1st for a consistent opening.
Hypergeometric distribution
Probabilities of your
deck Yu-Gi-Oh!
What are the odds of drawing your Starter in your opening hand? How often will you hit a Brick? Find out with the automatic hypergeometric calculation based on your card tags.
Calculate my probabilities →What is the hypergeometric distribution in Yu-Gi-Oh!?
The hypergeometric distribution calculates the probability of drawing exactly k cards from a given group in a hand of n cards drawn from a deck of N cards containing K copies of that group.
In practice: if your 40-card deck contains 9 Starters, what is the probability of having at least 1 in a 5-card hand? The answer is around 79% — and that is exactly what our tool calculates automatically.
Our calculator uses the tags you assign to your cards (Starter, Extender, Hand Trap, Brick…) to calculate relevant probabilities with no manual input.
Hypergeometric formula
P(X ≥ 1) = 1 − C(N−K, n) / C(N, n)
N = deck size
K = copies in deck
n = cards in hand
X = cards from group drawn
Automatically calculated probabilities
Extender
Ideal: ≥ 50%Probability of having ≥1 Extender to continue your combo if the Starter is negated.
Hand Trap
Ideal: ≥ 60%Probability of having ≥1 Hand Trap to disrupt the opponent going 2nd.
Brick
Ideal: ≥ 80%Probability of drawing 0 Bricks. The higher this value, the better for your consistency.
Win Con
Ideal: variableProbability of having ≥1 Win Con card in your first 5 or 6 cards.
Non-Engine
Ideal: ≥ 70%Probability of drawing 0 Non-Engine cards. Reduces dead hands.
How to use the calculator?
- 1. Build your deck in the deckbuilder by adding your cards.
- 2. Hover over each card and click the tag icon (top left of the card) to assign a role: Starter, Extender, Hand Trap, Brick…
- 3. Open the "Stats" tab in the right panel — probabilities are calculated automatically.
- 4. Adjust your list based on results: if your Starter probability is below 65%, add copies or search cards.
Recommended probability thresholds by tag
| Tag | Recommended threshold | Going 1st (5 cards) | Going 2nd (6 cards) |
|---|---|---|---|
| Starter | ≥ 75% | ≥ 75% | ≥ 80% |
| Extender | ≥ 50% | ≥ 50% | ≥ 55% |
| Hand Trap | ≥ 60% | ≥ 55% | ≥ 65% |
| Brick (0x) | ≥ 80% | ≥ 80% | ≥ 75% |
| Non-Engine | ≥ 70% | ≥ 70% | ≥ 65% |
Yu-Gi-Oh! Probability FAQ
What is the hypergeometric distribution in Yu-Gi-Oh!?
The hypergeometric distribution calculates the probability of drawing a certain number of cards from a given group in a hand drawn from a deck. For example, with 9 Starters in a 40-card deck, the probability of having at least 1 in a 5-card hand is around 79%.
What Starter probability should a consistent deck aim for?
It is recommended to aim for 75%+ going 1st with 5 cards, which generally corresponds to 9-12 accessible copies in a 40-card deck.
How to reduce Bricks in your deck?
Aim for a "zero Brick" probability of 80%+, limit garnets to 1 copy each, and balance the engine/non-engine ratio to maximize your opening hand consistency.
What is the difference between Starter and Extender probability?
The Starter initiates the main combo, the Extender continues it if the Starter is negated. Aim for 75%+ Starter and 50%+ Extender for a robust hand in all situations.
Does the calculator work for 60-card decks?
Yes, the hypergeometric distribution applies regardless of deck size. A 60-card deck requires proportionally more copies to reach the same probability thresholds.
Other available tools
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