.
The chance is not pretty big. It's pretty small.
The chance of guessing the first card correctly is (1/52) = 0.0192
The chance of guessing the 2nd card correctly is (1/51) = 0.0196
The chance of guessing the 3rd card correctly is (1/50) = 0.02
The chance of guessing the 4th card correctly is (1/49) = 0.0204
The chance of guessing the 5th card correctly is (1/48) = 0.0208
The chance of guessing the 6th card correctly is (1/47) = 0.0217
The chance of guessing the 7th card correctly is (1/46) = 0.0217
The chance of guessing the 8th card correctly is (1/45) = 0.0222
The chance of guessing the 9th card correctly is (1/44) = 0.0227
The chance of guessing the 10th card correctly is (1/43) = 0.0233
.
.
.
and you keep going like that. Then the chance of guessing ALL of them
correctly is the product of all of the individual chances.
After the first ten, listed above, you're already down to
0.00000 00000 00000 00000 00000 00000 00000 00000 00000 00000 0712 .
You're not even 1 tenth of the way through the deck yet, and it just keeps
getting smaller as you keep going.
The chance of guessing the first 10 correctly is ( 42 ! ) / ( 52 ! ) .
That's the number I just wrote up there, with 51 zeroes after the decimal point.
The chance of guessing the whole deck correctly is 1 / ( 52 !) .
That number starts out with roughly 51 more zeroes.
You might say that it's roughly 1 percent of 1 "googoleth".
My estimation is: It's almost identical to zero.
