AitchTheLetter
• Posts: 194
Joined: May 28, 2022
May 10th, 2024 at 5:43:13 PM permalink
So I have had a little free time and been playing with decks of cards in that time and a thought occurred to me. I wanted to know how many shuffles (assuming perfect half deck cut, perfect riffle, no strip or cut) would it take to put the card that started on the bottom of the deck on the top and vice versa (does not have to be the same time). I have tried manually but A. I suck at shuffling consistently, I can do 1 perfect shuffle if I try really hard and B. I think the total will be very high and C. I suck at math (not really, I do good in classes but practical applications give me a headache)

Anyone with some free time want to teach me how to figure this one out for myself or know the answer already?
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ThatDonGuy
• Posts: 6414
Joined: Jun 22, 2011
May 10th, 2024 at 5:47:40 PM permalink
Quote: AitchTheLetter

So I have had a little free time and been playing with decks of cards in that time and a thought occurred to me. I wanted to know how many shuffles (assuming perfect half deck cut, perfect riffle, no strip or cut) would it take to put the card that started on the bottom of the deck on the top and vice versa (does not have to be the same time). I have tried manually but A. I suck at shuffling consistently, I can do 1 perfect shuffle if I try really hard and B. I think the total will be very high and C. I suck at math (not really, I do good in classes but practical applications give me a headache)

Anyone with some free time want to teach me how to figure this one out for myself or know the answer already?

Technically, in a "perfect shuffle," the top card remains on the top, and the bottom card on the bottom. I assume you mean a shuffle where, if the cards were originally in order 1-52, then it would be 27, 1, 28, 2, ..., 51, 25, 52, 26.

Assuming this is correct, I get the bottom card reaching the top and the top card reaching the bottom both in 26 shuffles.
AitchTheLetter
• Posts: 194
Joined: May 28, 2022
May 10th, 2024 at 7:41:02 PM permalink
Sorry i should have specified that. Realized after I hit post and was dealing with something.
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Mental
• Posts: 1381
Joined: Dec 10, 2018
May 11th, 2024 at 4:53:03 AM permalink
Quote: AitchTheLetter

So I have had a little free time and been playing with decks of cards in that time and a thought occurred to me. I wanted to know how many shuffles (assuming perfect half deck cut, perfect riffle, no strip or cut) would it take to put the card that started on the bottom of the deck on the top and vice versa (does not have to be the same time). I have tried manually but A. I suck at shuffling consistently, I can do 1 perfect shuffle if I try really hard and B. I think the total will be very high and C. I suck at math (not really, I do good in classes but practical applications give me a headache)

Anyone with some free time want to teach me how to figure this one out for myself or know the answer already?

You can do this in any spreadsheet in a few minutes in a few steps.

First, populate a column A with numbers 1-52 in order to represent the card index (use fill or a formula).

Next, create formulas in column B to transfer the card indices according to your desired shuffle. If you want a different shuffle procedure than the one I chose, you can use it by changing the formulas.

Finally, copy the second column to multiple columns to the right. It will just repeat the same shuffle procedure ad infinitum.

It took me more time to write this post than it took to 'do the math'.
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