3 Card Probablities with joker

[Tater10]

I can figure out "regular" 3 card poker without wild cards, but i want to add a joker (can be used to make pairs, 3 of a kind, as well as str8s and flushes)

Here are the numbers I come up with, am i close?
53,3 = 23,426 hands

3 of a kind: 52 natural + 78 with joker = 130/23426 (.005549)
Straight Flush: 48 natural + 136 with joker = 184/23426 (.007855)
Straight: 720 natural + 408 with joker = 1128/23426 (.04815)
Flush: 1096 natural + 212 with joker = 1308/23426 (.055835)

i have no idea how to do a pair.

Am i right? What is the probablility of getting a pair with a joker as a wild card? And how do you do it?

I want to compare probabilites for guts poker with and without a joker. I thought with a joker, straight flushes and 3 of a kind might show up more frequently, making for bigger pots. From what my numbers tell me, 3 of a kind would beat a straight flush with a joker.

Thanks!