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Bit of missing information here so this will be a bit long...

What's missing is the number of cards you are dealt each hand.

Example 1) if all the cards are used, you will have 13 of the 52 cards each hand.

In each hand you would have 13/52 or 1 in 4 (25%) chance of having the card.

in two hands it would be 1/4 X1/4 = 1/16 (6.25%) chance of having the card both times.

in six hands 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 = 1 / 4096 chance of having the card all six times. That's 0.024 %

Example 2) if you are dealt only 5 cards, you will have 5 of the 52 cards each hand.

In each hand you would have 5/52 (10.4%) chance of having the card.

in two hands it would be 5/52 X 5/52 = 25/2704 (0.924%) chance of having the card both times.

in six hands 5/52 X 5/52 X 5/52 X 5/52 X 5/52 X 5/52 = 15625 / 19770609664 (about 1 in 1,265,319) chance of having the card all six times. That's 0.00008 %

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Q: What are the odds of being dealt the same card in a four player card game six times in a row?
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