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The Deck of Many Things (DMG, pp. 162-164) says:

Before you draw a card, you must declare how many cards you intend to draw and then draw them randomly [...] Any cards drawn in excess of this number have no effect. Otherwise, as soon as you draw a card from the deck, its magic takes effect. You must draw each card no more than 1 hour after the previous draw. If you fail to draw the chosen number, the remaining number of cards fly from the deck on their own and take effect all at once.

But it doesn't seem to specify an upper limit to how many cards can be picked. Is there one? Because of how dangerous the Deck of Many Things can be, I've only ever seen people pick up to 3, but could you declare 10? 30? 100?

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There is no practical limit

The first line of the description of the deck specifies:

Usually found in a box or pouch, this deck contains a number of cards made of ivory or vellum. Most (75 percent) of these decks have only thirteen cards, but the rest have twenty-two.

[...]

If you fail to draw the chosen number, the remaining number of cards fly from the deck on their own and take effect all at once.

In particular, the last sentence of this section suggests that the limit is either 13 or 22, as that is the total size of the Deck.

However the description specifies further:

Once a card is drawn, it fades from existence. Unless the card is the Fool or the Jester, the card reappears in the deck, making it possible to draw the same card twice.

So, once the Fool or the Jester card is drawn, it is no longer part of the Deck (and the Deck is permanently reduced in size). Otherwise, after each draw the card fades and reappears in the Deck.

As a result there is no practical limit on the number of cards you can draw, as the Deck replenishes itself.

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  • \$\begingroup\$ That's a good point about how the number of cards in the deck isn't even a limit because (apart from the jokers) the cards reappear in the deck. \$\endgroup\$ – NathanS Jul 4 at 10:50
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    \$\begingroup\$ When you draw Donjon or The Void, "you draw no more cards." Every deck has at least The Void in it. So, for a 13-card deck, 99% of the time, you will draw at most 57 cards not including The Void. For a 22-card deck, the number becomes 48 cards not including The Void or Donjon. Actually, the real numbers are lower because The Fool and Jester fade from existence once drawn, but that's harder to compute. \$\endgroup\$ – Kevin Jul 4 at 23:05
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    \$\begingroup\$ @Kevin Does "you draw no more cards" mean that "you fail to draw the chosen number" ? Strike that - already been covered. \$\endgroup\$ – A C Jul 5 at 0:26
  • \$\begingroup\$ @Kevin I think you can declare to draw, let's say, 500 cards, and not actually reaching for them. You'll trigger the 'cards fly off at once', thus blocking The Void or Donjon "Draw no more cards" condition of triggering. \$\endgroup\$ – T. Sar - Reinstate Monica Jul 5 at 15:41
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    \$\begingroup\$ I know, but I think it is fun to see the wacky things that can happen if you take the rules literally. For example, the rules explicitly says "and take effect all at once.", so one could argue that the cards fly out of the deck - several copies of them - circle the "target", and them trigger the effect. What could multiple donjons do to a single creature? Split its sould among several places! And so on, and so on. Those things can be really fun if done properly. \$\endgroup\$ – T. Sar - Reinstate Monica Jul 5 at 17:55
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There is no written limit to the number of cards that can be drawn, so yes, you should be able to declare however many cards you like. Yet the results are likely to be disastrous.

There is a relevant twitter exchange from 2017 where Christopher Perkins responds lightly to an inquiry by an interested twitter user, G. Collet:

‑ is it possible to fan the deck of many things ? if yes what would happen ?

‑ All the characters' heads explode.

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Theoretically, there is no upper limit at all because all but two of the cards reappear in the deck:

Once a card is drawn, it fades from existence. Unless the card is the Fool or the Jester, the card reappears in the deck, making it possible to draw the same card twice.

So, although exceedingly unlikely someone could draw an infinite amount of cards (or at least a very big number!) even though there's only (up to) 22 cards, you could declare that you wish to draw 100 cards.

This is unlikely to be a good result for the character however!

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  • \$\begingroup\$ That's a good point about how the number of cards in the deck isn't even a limit because (apart from the jokers) the cards reappear in the deck. \$\endgroup\$ – NathanS Jul 4 at 10:49

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