In traditional American Euchre (send a clarification request if you
are playing British Euchre or another variation), a 24-card deck
composing only 9-A of each suit is used. Each of four players is
dealt five cards, with the remaining four used in the "kitty".
There are 42,504 possible 5-card Euchre hands. There is a
combinatorics formula for this, but Google makes it easy. To reach
this number, enter the following into the Google search box:
24 choose 5
That produces the result of 42,504 possible hands.
We're not looking for any particular hand but merely want to replicate
a second time the hand that's drawn the first time. Given whatever
hand is produced the first time (we don't care what it is), the odds
of that particular hand coming up a second time are 1 in 42,504.
The odds for receiving it three times or more are exponentially more
difficult. Indeed, receiving the same hand three times is roughly 1
in 1.8 BILLION. That is found by multiplying the odds in the second
hand (1/42,504) by by the identical odds in the third hand (1/42,504).
Please let me know if you have any further questions.