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If I had a 50 card deck, and I hypothetically had 5 aces, then drawing the top card off the deck has a 10% chance of being an ace. HOWEVER! If we are taking the phrase, every X cards in the most literal way possible, since I am supposed to see an ace every 10 cards, do my chances of getting an ace increase if I wait to take the 10th, 20th, 30th, etc card from the deck, instead of just the first one. Does it increase the odds? Decrease? Or do nothing?

Wiseman560
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    What exactly do you mean by "wait to take the 10th, 20th, 30th, etc card from the deck"? Please describe the process that you're envisaging in more detail. – joriki Mar 15 '20 at 10:14
  • You’ll be likely to get one ace every 10 cards, but that doesn’t mean that the ace will be exactly at the $10^{th}, 20^{th}$ ... position. – Vishu Mar 15 '20 at 10:23
  • "every X cards" is only meant "in average". In the given case, the probabilities however change with every drawn card, so the expected number of cards to be drawn is not $10$ in every position. But the probability for any card to be an ace is $1/10$ independent of the position of the card (if we assume that they were perfectly shuffled) – Peter Mar 15 '20 at 10:52

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As long as the order of the cards is random, as it should be in this kind of scenario, each card has the same probability of being an ace. The only way the probability would change is if you knew something about which cards had already been drawn - that would take us to the realm of conditional probabilities.

And your statement that "I am supposed to see an ace every 10 cards" seems a little suspicious. On average, you would expect a randomly-drawn subset of 10 cards to contain an ace, but randomness doesn't imply even spacing. That's probably not what you mean; it's probably just an issue with how I read it, but it's always good to be careful with language.

I. Riley
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