BTW, I get 1 in 4,053.75. 4 ways to make those 8's. 47x46x5/3/2/4. Did I miss something?
16,215 ways to arrange the remaining 47 cards and 4 ways to make three 8's. 16215/4 = 4,053.75.
You didn't miss anything. I forgot that in spin poker, unlike regular three-hand poker, only one deck is used after the deal, not three, to fill in the hands. (4 choose 3)/ (47 choose 3) gives 4053.75 just as you wrote.
Apologies, TP.