Honestly, this is something that belongs in a general deck building class, but not very many people understand it properly, whic makes with testing process and tweking process harder, longer, and more frustrating. So I'll be breaking down the basic maths you need to know in order to calculate deck probabilities, honestly, it's not that bad
It goes like this, let;s start off with the very beginning. In any duel you find yourself in you'll have a 40 card deck. What does this mean? everything! It means you can calculate the exact chances of drawing any particular hand any particular duel. It goes like this, say we are looking for Insect knight in our first hand and we only have two in the deck. That means every 2 in 40 cards are Insect knight, which reduces to 1 in 20, which means when we first draw that card, we have a 5% chance of drawing Insect knight. The calculation looks like this:
(2/40)/2=1/20 1 divided by 20 =.05 multiply by 100 to get the percentage .05*100=5 so a 5% chance
But, let's say we didn't draw him the first time, so now the odds are 2/39 since there's one card missing. Well let's say we didn't get it again, so now we have 2/38. If you string these together for each of the five cards you draw you end up with something like this:
Where X=the number of copies of a card you have in a deck
And Y= the exact chances of drawing that card in that particular hand
This is assuming you didn't draw it until the fifth card. However, since that is the worst case scenario, we are safe making that assumption. Now, I assume you all have your scientific calc- just kidding xD I'll save you the calculation. This particular calculation ends up being this:
Seeing as this is a repeating decimal, we round up to .06, times 100, means we have a 6% chance of getting Insect Knight on your first hand. I don't know about you, but I want insect knight so I'll add another one into the deck and increase the odds, now let's rerun the calculation using our formula and that third copy:
After rounding we get .08, times 100 gives us an 8% chance of drawing insect knight.
So simply by adding one copy we have buffed up the odds by 2%. Now I can hear you, 2% isn't that much, and you're right, but think about it, math like this only grows the longer the duel goes on, the odds getting closer and closer to 100% certainty all the while, so lets say the duel is taking a while and you still have one Insect knight, and you need it bad(or whatever card you need) in your deck, which is now whittled down to 10 cards. Now, with just one copy in there, you have a 10% chance, but if you had added a third one, suddenly with that extra copy your odds are boosted to 20%! a whole 10% more!
This last step in deck building may be a bit boring, but every duelist needs to understand probability in order to properly construct a deck and tweak it to get that perfect mix, and it will DEFINITELY save you some time and effort in the long run.