Exact calculation
Hypergeometric law applied in real time
An Ashtra monster alone does nothing: the tool computes the real condition, holding the monster and the card to Set in the same hand.
Free tool
Ashtra Calculator
Calculate your odds of opening both an Ashtra monster and a Spell or Trap to Set in order to Special Summon it.
Import your deck
Optional: import your Ashtra deck and its Ashtra monsters, Spells and Traps are counted for you.
Cards in the Deck
Ashtra monsters
Settable cards (Spells and Traps)
Opening hand
Chance of opening an Ashtra monster and a card to Set
70.4%
Ashtra monster + card to Set
70.4%
Ashtra monster, nothing to Set
3.8%
Card to Set, no Ashtra monster
25.6%
Neither
0.2%
At least 1 Ashtra monster
74.2%
At least 1 card to Set
96.0%
By number of Ashtra monsters
| Ashtra monsters | 1st | 2nd |
|---|---|---|
| 1 | 11.6% | 14.5% |
| 2 | 22.1% | 27.1% |
| 3 | 31.5% | 38.2% |
| 4 | 40.0% | 47.8% |
| 5 | 47.6% | 56.1% |
| 6 | 54.4% | 63.2% |
| 7 | 60.4% | 69.3% |
| 8 | 65.7% | 74.5% |
| 9 | 70.4% | 78.9% |
| 10 | 74.5% | 82.6% |
| 11 | 78.0% | 85.7% |
| 12 | 81.1% | 88.2% |
By number of settable cards
| Settable cards | 1st | 2nd |
|---|---|---|
| 13 | 63.2% | 73.6% |
| 14 | 65.1% | 75.1% |
| 15 | 66.8% | 76.4% |
| 16 | 68.2% | 77.4% |
| 17 | 69.4% | 78.3% |
| 18 | 70.4% | 78.9% |
| 19 | 71.2% | 79.4% |
| 20 | 71.9% | 79.8% |
| 21 | 72.4% | 80.1% |
| 22 | 72.9% | 80.3% |
| 23 | 73.2% | 80.5% |
Click a row to apply that value.
Get these odds on your real deck, automatically
Build or import your deck, tag your Starters, Hand Traps and Bricks: the deckbuilder computes every probability for you, with no manual input.
Why use this tool?
Your imported deck
Ashtra monsters, Spells and Traps counted automatically
Import your deck: the tool finds your Ashtra monsters and your settable cards, and you can leave out the ones you would not Set.
Ratios to tune
Two tables to find the right ratio
See what one more Ashtra monster or settable card changes, going first as well as second.
How does the Ashtra deck work in Yu-Gi-Oh!?
The Main Deck Ashtra monsters (Akasuna the Battle Ashtra, Kuzuha the Hex Ashtra, Mikumari the Banisher Ashtra and Yoa the Plague Ashtra) share the same condition: you can Special Summon them from your hand by revealing 1 face-down card you control, then returning it to the hand or Extra Deck.
In practice, you need two things in your opening hand: an Ashtra monster, and a card you can Set face-down — a Spell or a Trap. The Set card returns to your hand after the Summon and can be Set again for the next monster.
A hand with the monster but nothing to Set, or with Traps but no Ashtra monster, does not get the deck going. This calculator measures exactly that risk based on the makeup of your Yu-Gi-Oh! Deck.
The mathematical formula
Letting N the deck size, M the number of Ashtra monsters, P the number of settable cards and n the hand size, the two groups are disjoint and the draw is without replacement. The probability of having at least one of each is:
1 − C(N−M, n)/C(N, n) − C(N−P, n)/C(N, n) + C(N−M−P, n)/C(N, n)
We remove the hands with no Ashtra monster and the hands with no settable card, then add back those with neither, which were counted twice.
How to use the calculator
- 1. Import your deck : Paste a YDKE code or pick a saved deck: Ashtra monsters, Spells and Traps are counted for you. Otherwise, enter the three numbers by hand.
- 2. Leave out the cards that should not count : Click a Spell or Trap you would never Set to take it out of the calculation.
- 3. Choose the opening hand : 5 cards going first, 6 going second: the probability and both tables update.
FAQ
Frequently asked questions about the Ashtra deck
From your hand, by revealing 1 face-down card you control and returning it to the hand or Extra Deck. Each Ashtra monster can only be Summoned this way once per turn.
Any face-down card you control works. The calculator counts Spells and Traps, which can be Set at no cost from the first turn.
It depends on the probability you are aiming for: the calculator's two tables show what each extra Ashtra monster or settable card changes, going first as well as second.
No: it only measures the opening hand, without the cards added afterwards by an effect. A card that searches an Ashtra monster is therefore not counted as a monster.
Other available tools
In the same category: Draw odds and Pots
Build an Ashtra deck that gets going every game
Free, no sign-up — open the deckbuilder and adjust your copy counts accordingly.
