The text doesn't say. I presume we should resort to the fictional events and take it as "facts on the ground" or something, but I figured I'd check.
Easier than that. There aren't ties in S/Lay w/Me, because in order to win the match, you (and here I mean the text's "you") must beat the other person's roll, as the text says. If you end up with the same value as his or hers, then you didn't beat it and you don't win the match.
Best, Ron