These tables are helpful for looking at probabilities for seeing your starter cards or your side deck substitutions. You can always play test and see how things feel, but you can arrive at incorrect conclusions because your number of attempts is too low. These tables are the actual chances of you seeing the cards you want, in a given circumstance. To be clear, these tables show you the chance of drawing at least 1 of the intended cards.
All the calculations were done with this Hypergeometric Probability Calculator. I will being updating this post with a link to a future tutorial of how to use this tool.
Opening Hand Probabilities
This table is for the very first turn in Yu-Gi-Oh!, when a player only has 5 cards in hand. This table shows that if you side decked a certain number of cards within the given size of your deck, what chance you will have to see at least one of those cards. Your opening hand is 5 cards.
This table tells you the chance you have a
- starter card in your opening hand
- hand trap in your opening hand
- floodgate in your opening hand
- counter hand trap (such as Crossout Designator) in your opening hand
| Side Deck Cards Swapped In | 40 Card Deck | 60 Card Deck |
|---|---|---|
| 3 | 33.8% | 23.3% |
| 4 | 42.7% | 30.1% |
| 6 | 57.7% | 42.1% |
| 8 | 69.4% | 52.4% |
| 9 | 74.2% | 57.0% |
Going Second Probabilities
This table assumes your hand has 6 cards (5 initially and the 1 draw on your turn). This calculation is helpful for seeing if you can draw board breakers like Forbidden Droplet or Evenly Matched.. If you want to draw a hand trap to interrupt your opponent, look at the Opening Hand Probabilities table.
| Side Deck Cards Swapped In | 40 Card Deck | 60 Card Deck |
|---|---|---|
| 3 | 39.4% | 27.5% |
| 4 | 49.3% | 35.1% |
| 6 | 65.0% | 48.4% |
| 8 | 76.4% | 59.3% |
| 9 | 80.8% | 64.0% |
Fast, Easy, Learn 
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