Jelly, (削除) 5 (削除ここまで) 4 bytes

s4ZẎ

Try it online!

Turns out the way (削除) everyone else (削除ここまで) everyone else except The random guy is doing it saves a byte :(

The way I went...

ṙÐe20

Try it online!

How?

Fix every other card and intersperse it with a rotation of the deck left by 20 places (18 and 22 places also work; furthermore so does either direction of rotation as well as fixing either odd or even cards)

ṙÐe20 - Link: list of the card strings (lists of characters)
 20 - place a literal twenty on the right
 Ðe - apply to even indices:
ṙ - rotate left (by 20)

That is (using T for 10 and rj & bj for the Js):

input: AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj
 ṙ20: 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D
ṙÐe20: AS 9D 3S JD 5S KD 7S 2H 9S 4H JS 6H KS 8H 2D TH 4D QH 6D AC 8D 3C TD 5C QD 7C AH 9C 3H JC 5H KC 7H bj 9H 2S JH 4S KH 6S 2C 8S 4C TS 6C QS 8C AD TC 3D QC 5D rj 7D

Jelly, (削除) 5 (削除ここまで) 4 bytes

s4ZẎ

Try it online!

Turns out the way (削除) everyone else (削除ここまで) everyone else except The random guy is doing it saves a byte :(
Credit to G B for their method .

The way I went...

ṙÐe20

Try it online!

How?

Fix every other card and intersperse it with a rotation of the deck left by 20 places (18 and 22 places also work; furthermore so does either direction of rotation as well as fixing either odd or even cards)

ṙÐe20 - Link: list of the card strings (lists of characters)
 20 - place a literal twenty on the right
 Ðe - apply to even indices:
ṙ - rotate left (by 20)

That is (using T for 10 and rj & bj for the Js):

input: AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj
 ṙ20: 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D
ṙÐe20: AS 9D 3S JD 5S KD 7S 2H 9S 4H JS 6H KS 8H 2D TH 4D QH 6D AC 8D 3C TD 5C QD 7C AH 9C 3H JC 5H KC 7H bj 9H 2S JH 4S KH 6S 2C 8S 4C TS 6C QS 8C AD TC 3D QC 5D rj 7D

Jelly, 5 bytes

ṙÐe20

Try it online!

How?

Fix every other card and intersperse it with a rotation of the deck left by 20 places (18 and 22 places also work; furthermore so does either direction of rotation as well as fixing either odd or even cards)

ṙÐe20 - Link: list of the card strings (lists of characters)
 20 - place a literal twenty on the right
 Ðe - apply to even indices:
ṙ - rotate left (by 20)

That is (using T for 10 and rj & bj for the Js):

input: AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj
 ṙ20: 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D
ṙÐe20: AS 9D 3S JD 5S KD 7S 2H 9S 4H JS 6H KS 8H 2D TH 4D QH 6D AC 8D 3C TD 5C QD 7C AH 9C 3H JC 5H KC 7H bj 9H 2S JH 4S KH 6S 2C 8S 4C TS 6C QS 8C AD TC 3D QC 5D rj 7D

Jelly, (削除) 5 (削除ここまで) 4 bytes

s4ZẎ

Try it online!

Turns out the way (削除) everyone else (削除ここまで)everyone else except The random guy is doing it saves a byte :(

The way I went...

ṙÐe20

Try it online!

How?

Fix every other card and intersperse it with a rotation of the deck left by 20 places (18 and 22 places also work; furthermore so does either direction of rotation as well as fixing either odd or even cards)

ṙÐe20 - Link: list of the card strings (lists of characters)
 20 - place a literal twenty on the right
 Ðe - apply to even indices:
ṙ - rotate left (by 20)

That is (using T for 10 and rj & bj for the Js):

input: AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj
 ṙ20: 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D
ṙÐe20: AS 9D 3S JD 5S KD 7S 2H 9S 4H JS 6H KS 8H 2D TH 4D QH 6D AC 8D 3C TD 5C QD 7C AH 9C 3H JC 5H KC 7H bj 9H 2S JH 4S KH 6S 2C 8S 4C TS 6C QS 8C AD TC 3D QC 5D rj 7D

Jelly, 5 bytes

ṙÐe20

Try it online!

How?

Fix every other card and intersperse it with a rotation of the deck left by 20 places (18 and 22 places also work; furthermore so does either direction of rotation as well as fixing either odd or even cards)

Jelly, 5 bytes

ṙÐe20

Try it online!

How?

Fix every other card and intersperse it with a rotation of the deck left by 20 places (18 and 22 places also work; furthermore so does either direction of rotation as well as fixing either odd or even cards)

ṙÐe20 - Link: list of the card strings (lists of characters)
 20 - place a literal twenty on the right
 Ðe - apply to even indices:
ṙ - rotate left (by 20)

That is (using T for 10 and rj & bj for the Js):

input: AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj
 ṙ20: 8D 9D TD JD QD KD AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC rj bj AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS AD 2D 3D 4D 5D 6D 7D
ṙÐe20: AS 9D 3S JD 5S KD 7S 2H 9S 4H JS 6H KS 8H 2D TH 4D QH 6D AC 8D 3C TD 5C QD 7C AH 9C 3H JC 5H KC 7H bj 9H 2S JH 4S KH 6S 2C 8S 4C TS 6C QS 8C AD TC 3D QC 5D rj 7D