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The setting

A game with two players that take turns drawing a card from a deck with an even number of cards. The probability to draw a certain single card is according to the discrete uniform distribution.

For player one, cards can be classified as either desired or undesired. Players can see which card the other player has drawn.

There are two variants of the rules.

Variant "in order". Rules as stated above.

Variant "early". Rules are modified as follows. 1. Player two begins their turn and draws a card as usual and shows it to player one. 2. Then player two draws another card early for use in the next round, but does not show it to player one. Player two also does not use the card in the game so there is no way for player one to tell which card player two got. This happens before player one takes their turn. 3. When player one takes their turn, the deck contains one card less under variant "early" than variant "in order".

The question

Is the probability for player one to receive a desired card at step 3., as observed by player one themselves, different between variant "in order" and "early" ?

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  • $\begingroup$ What are your thoughts on it ? Pl show what you have tried. $\endgroup$
    – true blue anil
    Commented Apr 3, 2021 at 9:11

1 Answer 1

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Since I shall not be computing anything, I am answering.

For any even numbered deck of 2n cards, player 1 has the opportunity to draw n cards. (The "early" variant doesn't change this)

Now the card desired by player 1 is equally likely to be at any of the 2n places, so the probability remains the same.

All other details given are simply attempts to obfuscate the issue.

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