Probability and luck are a important part of any card game. Usually we ignore it while playing and not calculate exact probabilities, and go by “feeling” or “gut” to build our decks. However, today, I present a new tool that will assist any player in building a deck by calculating the probability of any given combos. This guide will give examples on how to use this tool.
An introduction to hypergeometric probability can be found here:
Go here for the calculator: YuGiOh Probability Calculator
Importing the Deck
 You can import ydk, ydke, omega code, or list. Since often many of the top decks are published on tcgplayer in a list format, we will import a list for this example. Go to TCGplayer Infinite
 Click on the icon that says “Export” → “Copy Deck to Clipboard”.
 Go to the probability calculator here: YuGiOh Probability Calculator
 Click on “Import decklist”.
 Paste the contents of the deck from the text file you downloaded from Step 3. Then click import.
 Click on decklist to expand and see the deck.
 You can add cards simply by typing the card name and clicking on the card using the search.
 You can also remove cards by clicking on the red trashcan on the corner of the card.
Calculating the Probability of Combos

Click “Add Combo”.

Let’s say the unique combos for this Dinosaur deck are as followed:
A. Combo 1: Babycerasaurus + Miscellaneousaurus Discard Miscellaneousaurus. Banish it from the GY> Special Summon Animadorned Archosaur.
 Archosaur’s effect activates> destroy Babycerasaurus from hand>search Double Evolution Pill.
 Babycerasaurus effect activates> Special Summon Souleating Oviraptor>search 2nd copy of Babycerasaurus.
 Normal Summon Babycerasaurus. Activate Oviraptor’s effect> destroy Babycerasaurus on field> Special Summon the other Babycerasaurus from GY.
 Babycerasaurus in GY activates its effect → Special Summon Miscellaneousaurus from Deck.
 Overlay Miscleannocerasaurus + Oviraptor → Evolzar Dolkka.
 Link Summon Linkuriboh using Archosaur. Link Summon Secure Gardna using Linkuriboh.
 Activate Double Evolution Pill → Banish Linkuriboh and Archosaur to Special Summon Ultimate Conductor Tyranno.
B. Combo 2: Lost World + Souleating Oviraptor + Babycerasaurus
 Activate Lost World. Normal Summon Oviraptor.
 Activate Oviraptor as CL1 and Lost World as CL2. Lost World gives opponent Juraegg Token. Oviraptor searches Miscellaneousaurus.
 Discard Miscellaneousaurus. Activate Oviraptor → Target Juraegg Token on opponent’s field to try to Special Summon Miscellaneousaurus in GY. Activate Lost World as CL2 to protect the Token by destroying a Babycerasaurus in your Deck.
 Babyceraus in GY activates its effect → Special Summon any Level 4 Dinosaur monster in Deck (Misc or Archasaur).
 Banish Misc from GY → Special Summon Archosaur from Deck.
 Activate Archosaur’s effect>destroy Babyscerasaurus in hand>search Double Evolution from Deck. Babycerasaurus effect triggers>Special Summon Misc from Deck.
 Overlay Misc+Oviraptor>Evolzar Dollka.
 Link Summon Linkuriboh using Archosaur. Link Summon Secure Gardna using Linkuriboh.
 Activate Double Evolution Pill banishing Linkuriboh and any Dino in GY → UCT.

Enter the combos above.
Combo 1: We select 2 Babycerasaurus and 1 Petiteranodon (it does the same thing as Babycerasaurus) for “Card Group 1” and 3 Miscellaneousaurus for “Card Group 2”. We want to draw at least 1 from Card Group 1 and 1 from Card Group 2, so we set the Min to 1. However, we don’t want to draw more than 2 Miscellaneousaurus because we need 1 Misc in the deck so it can be Special Summoned. Hence, for Card Group 2, set the max to 2 instead of 3.Furthermore, we need an Archosaur in the deck so it can be Special Summoned, so we can’t draw more than 1. Therefore, add Card Group 3 with min 0 and max 1. Next, we also want to have a Souleating Oviraptor in the deck, so we can only allow to draw up to 2 max copies. So add Card Group 4 with min 0 and max 2.
Additionally, we don’t want to draw PsyFrame Driver in our hand since that would make the Psyframe Gammas useless. Therefore, add a card group 5 and then pick min and max to 0 which will set a condition of not drawing this card.
Last, are the searchers. We have 3 Fossil Dig that can search for Babycerasaurus or Miscellaneousaurus. So we add 3 Fossil Dig under “Searchers” and put Card Group 1 and 2 for Targets.
Combo 2: Click “Add Combo”. We select 3 Lost World for Card Group 1, 3 Souleating Oviraptor for Card Group 2, and 2 Babycerasaurus+1 Petiteradonon for Card Group 3. We want the Max for Card Group 2 to equal 2 because we want at least 1 Souleating Oviraptor in the deck so it can be Special Summoned via Babycerasaurus. Similarly, Card Group 3 has a Max of 2 because we need 1 Babycerasaurus in the deck so it can be destroyed by Lost World.
Card Group 4 will be the Miscellaneousaurus which we don’t want to draw more than 2, so the Max is 2 since we need a Misc in the deck to Special Summon. Card Group 5 is Archosaur which we need at least 1 copy of in the deck as well, so the Max is 1. Set Card Group 6 to PsyFrame Driver just like in Combo 1.
As for the searchers, we have 3 Fossil Dig that can search for Card Group 2 or 3. We also have 1 Terraforming as Search Group 2 that can search for Lost World. Note that in this case, since Terraforming can only search for a single Card Group, it makes no difference if you were to just add Terraforming in Card Group 1. The probability will be the same.
The final answer we got for this Dino deck was only 50.95% even though we put several different combos. You can see it here.
The total probability of drawing any of the 2 combos is NOT the sum of the individual probabilities. Rather, we have to apply the Law of Total Probability so that there is no double counting or overlapping of possibilities. This is as follows:
2 Combos Total = [C1+C2] [C1*C2]
3 Combos Total = [C1+C2+C3]  [C1*C2 + C1*C3 + C2*C3] + [C1*C2*C3]
4 Combos Total = [C1+C2+C3+C4]  [C1*C2 + C1*C3 + C1*C4 + C2*C3 + C2*C4 + C3*C4] + [C1*C2*C3 + C2*C3*C4 + C1*C3*C4 + C1*C2*C4]  C1*C2*C3*C4
5 Combos Total = [C1+C2+C3+C4+C5]  [C1*C2 + C1*C3 + C1*C4 + C1*C5 + C2*C3 + C2*C4 + C2*C5 + C3*C4 + C3*C5 + C4*C5] + [C1*C2*C3 + C1*C2*C4 + C1*C3*C4 + C1*C2*C5 + C1*C3*C5 + C1*C4*C5 + C2*C3*C4 + C2*C3*C5 + C2*C4+C5 + C3*C4*C5]  [C1*C2*C3*C4 + C1*C2*C3*C5 + C1*C2*C4*C5 + C1*C3*C4*C5 + C2*C3*C4*C5] + C1*C2*C3*C4*C5
Note that there is one thing that we did not consider and that are the 3 Pot of Extragavance. That is, the probability of draw cards. This will be added later to the calculator. Pot of Extragavance can only be activated once per turn and so the probability may not increase by that much.
The other cards in the deck like Impermanence, Ash Blossom, Nibiru, and Gamma are all hand traps. These cards are nice to have to disrupt your opponent during the second turn, but is not considered in terms of consistency of the deck and first turn probability. Rather, one should try to make a deck that can recover if these hand traps were to disrupt a first turn combo. One should assume that the opponent will have at least 69 hand traps which means the likelihood of success decreases if we multiply the probability of a player opening the combos by the probability of the opponent opening with hand traps.
In general, a good deck should have a total probability of >60% in opening any of the possible combos they want in the first turn. To increase probability, add more copies of combo cards, add more searchers or thinners (draw cards). Remember that adding more cards to a deck, increases the population size, which also reduces probability so one must also remove cards after adding. Everything is a tradeoff. There is no perfect formula. It can be proven that a 60card deck is more consistent than a 40card deck if the right combos are possible. Similarly, even decks that are greater than 40 cards can be more consistent and this calculator is a great way to determine that.
Click here to see it yourself: YuGiOh Probability Calculator (Two more unique combos were added at the bottom to increase consistency. Note that these combos don’t overlap with each other to avoid double counting. This is why in Combo 1, Souleating Oviraptor’s min and max were set to 0 to avoid overlap with Combo 4.
It’s always important to define your end goal board you are aiming for before you define the combos. A deck may even have a 1card combo but could be weaker than a 2card combo. Imagine if that one card were to be negated by your opponent’s hand trap. Ultimately, the player should define their best combos that lead to the optimal first turn board.