I removed the Ace and 2 thru 10 of hearts from a deck of cards. Also: I removed the Ace and 2 thru 10 of spades from a deck of cards.
The Ace acts as a 1 and the 10 acts as a 0. Both suits are considered 1-10.
I shuffled all 20 cards and flipped them up one at a time. I did this 4 times in a row and the 6 of spades ended last each time. Yes, I was careful to shuffle the cards generously in order to ensure a good mix.
What are the odds or probability of this happening?
I would guess that you are really asking the question..."what is the probability of getting any one of the 20 cards to appear last 4 times in a row", meaning that in your case the 6 of spades happened to come up, but you would have been equally amazed if the 3 of hearts had come up or any other card.
Given that assumption, the first round of 20 simply sets the "bar" for what card needs to appear last again the other 3 times. Since there are 20 cards, an even shuffle would give a 1 in 20 chance (5%) of the same card repeating the 2nd time, and a 5% * 5% (or 0.25%, one in 400) chance of the same card the first time appearing the next two times, or a 1 in 8000 chance of the same card repeating the 2nd, 3rd, and 4th times.
