There are many card games that allow you to build your own deck and then play it against opponents that did the same. Magic the Gathering might be the most familiar one for many people, but I'd also like to mention Eternal as a digital variant of it (if only because I'm playing it myself).
The rules for these games often put some restrictions on how you are allowed to build a legal deck. In Eternal, for example, decks must consist of at least 75 cards and at least 1/3 of it must be power cards. The rest then will be units, spells and weapons, basically the meat of the matter.
Now, in theory your deck could contain more cards than that. Choose 60 non-power cards, add 30 power cards for a total of 90 cards, and your deck is still legal according to the rules. However, ask people what size a deck should have, and they will tell you that it definitely needs to be exactly 75, and that every card on top of that will make your deck worse because doing so reduces your win probability. Some will consider you insane for even thinking about adding just a single card more than absolutely necessary. When asked for an explanation for this, it will often go something like this:
(a) Assume that all the cards in your deck have some value. Some will be more important to the strategy you are trying to play, while others are less important.
(b) Sort all cards according to this assumed value in descending order. There will be a "least important card" at the end of that list.
(c) Assume that you are playing your (oversized by one card) deck, and that at some point in the game, you draw the card you determined to be the least important one.
(d) Consider what would happen instead if that card had been removed from your deck before playing. You would have drawn a card that you determined to be more valuable instead. This means that it is better to play without that card in the first place.
Now, the general idea is definitely sound - but I still wonder if it isn't a bit too simplistic when it comes to actual gameplay instead of just theory:
First, consider that most games are over before maybe a third of the deck has been drawn. The "least important card" has a good chance of not entering play at all. This isn't a counterargument to the idea itself, but already lessens its impact to a fraction.
Second, consider the fact that the value of a card might depend not only on your own strategy, but also on that of the opponent. Perhaps card A will be valuable to you in one half of all games, and card B in the other half. In combination with a card that says
Choose which card you want to draw next turn.
it might be useful to play a copy of both A and B, and not choose between them. Of course, a counterargument to that could be that, perhaps, neither A nor B is the "least important card" in that case - but I feel this already muddies the waters a bit.
Most importantly, though: the whole idea of card games like these is that its individual cards don't exist in a vacuum, but have synergies with each other. For example, if there's one card that says
Use an enemy unit as your own this turn.
And another card that says
Kill one of your own units to gain a bit of power.
then both of these cards might be mediocre on their own, and not worth playing compared to other cards. However, in combination it means that you can steal an opponent unit, attack with that unit to do some damage - and then, if it survives because the opponent thinks he'll get the unit back after the turn, you can remove it from play to gain some additional benefit.
Depending on what synergies there are in the game, it might be worth playing some more cards to have access to more of these effects.
What I'm looking for - and this is why I also added the "mathematics" topic to this post - is a way to put all of this in proper stochastic terminology without shortcuts like "assume this, assume that", to eventually find out if having some more cards is really that bad. Is anyone interested in discussing this?