The Whispering Jokers Card Trick

Sometimes called Prior Committment, but as Whispering Jokers, it fooled Penn and Teller (once), but can be done by anyone!

A deck of 52 cards, plus 2 jokers

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|6789012
....................................................  A B

Jokers A and B at positions P and Q, say 10 and 29

This splits the deck into "upper", "middle", and "lower" portions, labelled "u", "m", and "l".

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
uuuuuuuuuAmmmmmmmmmmmmmmmmmmBlllllllllllllllllllllllll
  (9)   P=10      (18)     Q=29        (25)

2 cuts, at C and D, say 13 and +24, revealing cards X and Y

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
uuuuuuuuuAmmX             A@P=10, X@C=13
mmmmmmmmmmmmmmmBlllllllY  B@Q-C=16, Y@D=24
lllllllllllllllll         (54-D-C)=17 remain

dupe 1's pile on top of bottom

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
uuuuuuuuuAmmXlllllllllllllllll A@P=10, X@C=13, 
mmmmmmmmmmmmmmmBlllllllY       B@Q-C=16, Y@D=24

dupe 2's pile on top of the lot

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
mmmmmmmmmmmmmmmBlllllllYuuuuuuuuuAmmXlllllllllllllllll
A@D+P=34, X@D+C=37, B@Q-C=16, Y@D=24

Split on, and remove jokers

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
mmmmmmmmmmmmmmm      length=Q-C-1 
lllllllYuuuuuuuuu    Y@D+C-Q=8, length=D+P-Q+C-1=17
mmXlllllllllllllllll X@D+C-D-P=C-P=3, length=54-D-P=20

Bottom on top of middle

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
mmmmmmmmmmmmmmm      length Q-C-1 
mmXllllllllllllllllllllllllYuuuuuuuuu  X@C-P=3, Y@54-D-P+D+C-Q=54-P+C-Q=28

Top on top

         1         2         3         4         5
1234|678901234|678901234|678901234|678901234|678901234
mmmmmmmmmmmmmmmmmXllllllllllllllllllllllllYuuuuuuuuu
X@C-P+Q-C-1=Q-P-1=18, Y@54-P+C-Q+Q-C-1=54-P-1=43

Conclusion

Position of X and Y are independent of C and D, only on Q and P. So write the numbers (P-Q-1) and (54-P-1) on the two jokers. In our example, that's 18 and 43. Note that 43=25+18, and see the first diagram describing the placement of the jokers.

Better explanation in video form

Singingbanana nails it here. The simpler colour-only explanation doesn't tell you what numbers to put on the cards, but makes the mechanics of the trick much easier to understand.